diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html
index a3ec780..4545ab8 100644
--- a/src/axiom-website/CATS/index.html
+++ b/src/axiom-website/CATS/index.html
@@ -469,6 +469,25 @@ See <a href="http://www.apmaths.uwo.ca/~arich/IntegrationProblems/AxiomSyntaxFil
   x^m (d+e x)^n (a+b x+c x^2)^p (part 5)
   <a href="rich11e.input.pamphlet">source</a>
   <a href="rich11e.input.pdf">pdf</a><br/>
+<br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 1)
+  <a href="rich12a.input.pamphlet">source</a>
+  <a href="rich12a.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 2)
+  <a href="rich12b.input.pamphlet">source</a>
+  <a href="rich12b.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 3)
+  <a href="rich12c.input.pamphlet">source</a>
+  <a href="rich12c.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 4)
+  <a href="rich12d.input.pamphlet">source</a>
+  <a href="rich12d.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 5)
+  <a href="rich12e.input.pamphlet">source</a>
+  <a href="rich12e.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 6)
+  <a href="rich12f.input.pamphlet">source</a>
+  <a href="rich12f.input.pdf">pdf</a><br/>
 
 <br/><hr/><br/>
 <h3>Rich Derivatives</h3><br/><br/>
@@ -587,6 +606,25 @@ Mathematica. This test suite shows Axiom's results.
   <a href="richder6e.input.pamphlet">source</a>
   <a href="richder6e.input.pdf">pdf</a><br/>
 <br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 1)
+  <a href="richder12a.input.pamphlet">source</a>
+  <a href="richder12a.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 2)
+  <a href="richder12b.input.pamphlet">source</a>
+  <a href="richder12b.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 3)
+  <a href="richder12c.input.pamphlet">source</a>
+  <a href="richder12c.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 4)
+  <a href="richder12d.input.pamphlet">source</a>
+  <a href="richder12d.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 5)
+  <a href="richder12e.input.pamphlet">source</a>
+  <a href="richder12e.input.pdf">pdf</a><br/>
+  (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 6)
+  <a href="richder12f.input.pamphlet">source</a>
+  <a href="richder12f.input.pdf">pdf</a><br/>
+<br/>
 
 <br/><hr/><br/>
 <h3>Rich</h3><br/><br/>
diff --git a/src/axiom-website/CATS/rich12a.input.pamphlet b/src/axiom-website/CATS/rich12a.input.pamphlet
new file mode 100644
index 0000000..2f89471
--- /dev/null
+++ b/src/axiom-website/CATS/rich12a.input.pamphlet
@@ -0,0 +1,50704 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich12a.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(d+e x)^m (f+g x)^n (a+b x+c x^2)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 255 supplied "optimal results".
+\item 307 matching answers.
+\item 0 cases where Axiom answer differs from Rubi
+\item 91 cases where Axiom supplied 2 results.
+\item 12 cases that Axiom failed to integrate.
+\item 31 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich12a.output
+)spool rich12a.output
+)set message test on
+)set message auto off
+)clear all
+
+
+--S 1 of 1457
+t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)
+--R 
+--R
+--R              3               2                  m
+--R   (1)  (B c x  + (A c + B b)x  + A b x)(e x + d)
+--R                                                    Type: Expression(Integer)
+--E 1
+
+--S 2 of 1457
+r0:=-d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*B*c*d-b*B*e-A*c*e)*_
+     (d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m))
+--R 
+--R
+--R   (2)
+--R             3         2                           m + 4
+--R       (B c m  + 6B c m  + 11B c m + 6B c)(e x + d)
+--R     + 
+--R                                   3                              2
+--R           ((A c + B b)e - 3B c d)m  + ((7A c + 7B b)e - 21B c d)m
+--R         + 
+--R           ((14A c + 14B b)e - 42B c d)m + (8A c + 8B b)e - 24B c d
+--R      *
+--R                  m + 3
+--R         (e x + d)
+--R     + 
+--R                 2                              2  3
+--R           (A b e  + (- 2A c - 2B b)d e + 3B c d )m
+--R         + 
+--R                  2                                 2  2
+--R           (8A b e  + (- 16A c - 16B b)d e + 24B c d )m
+--R         + 
+--R                   2                                 2            2
+--R           (19A b e  + (- 38A c - 38B b)d e + 57B c d )m + 12A b e
+--R         + 
+--R                                         2
+--R           (- 24A c - 24B b)d e + 36B c d
+--R      *
+--R                  m + 2
+--R         (e x + d)
+--R     + 
+--R                     2               2         3  3
+--R           (- A b d e  + (A c + B b)d e - B c d )m
+--R         + 
+--R                      2                 2          3  2
+--R           (- 9A b d e  + (9A c + 9B b)d e - 9B c d )m
+--R         + 
+--R                       2                   2           3              2
+--R           (- 26A b d e  + (26A c + 26B b)d e - 26B c d )m - 24A b d e
+--R         + 
+--R                           2           3
+--R           (24A c + 24B b)d e - 24B c d
+--R      *
+--R                  m + 1
+--R         (e x + d)
+--R  /
+--R      4 4      4 3      4 2      4       4
+--R     e m  + 10e m  + 35e m  + 50e m + 24e
+--R                                                    Type: Expression(Integer)
+--E 2
+
+--S 3 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R               4 3         4 2          4          4  4
+--R         (B c e m  + 6B c e m  + 11B c e m + 6B c e )x
+--R       + 
+--R                          4          3  3                  4           3  2
+--R             ((A c + B b)e  + B c d e )m  + ((7A c + 7B b)e  + 3B c d e )m
+--R           + 
+--R                              4           3                   4
+--R             ((14A c + 14B b)e  + 2B c d e )m + (8A c + 8B b)e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                   4                 3  3
+--R             (A b e  + (A c + B b)d e )m
+--R           + 
+--R                    4                   3         2 2  2
+--R             (8A b e  + (5A c + 5B b)d e  - 3B c d e )m
+--R           + 
+--R                     4                   3         2 2            4
+--R             (19A b e  + (4A c + 4B b)d e  - 3B c d e )m + 12A b e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                    3 3            3                   2 2  2
+--R             A b d e m  + (7A b d e  + (- 2A c - 2B b)d e )m
+--R           + 
+--R                       3                   2 2         3
+--R             (12A b d e  + (- 8A c - 8B b)d e  + 6B c d e)m
+--R        *
+--R           x
+--R       + 
+--R                2 2 2            2 2                 3             2 2
+--R         - A b d e m  + (- 7A b d e  + (2A c + 2B b)d e)m - 12A b d e
+--R       + 
+--R                       3          4
+--R         (8A c + 8B b)d e - 6B c d
+--R    *
+--R         m log(e x + d)
+--R       %e
+--R  /
+--R      4 4      4 3      4 2      4       4
+--R     e m  + 10e m  + 35e m  + 50e m + 24e
+--R                                         Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)
+--R                 4 3         4 2          4          4  4
+--R           (B c e m  + 6B c e m  + 11B c e m + 6B c e )x
+--R         + 
+--R                            4          3  3                  4           3  2
+--R               ((A c + B b)e  + B c d e )m  + ((7A c + 7B b)e  + 3B c d e )m
+--R             + 
+--R                                4           3                   4
+--R               ((14A c + 14B b)e  + 2B c d e )m + (8A c + 8B b)e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                     4                 3  3
+--R               (A b e  + (A c + B b)d e )m
+--R             + 
+--R                      4                   3         2 2  2
+--R               (8A b e  + (5A c + 5B b)d e  - 3B c d e )m
+--R             + 
+--R                       4                   3         2 2            4
+--R               (19A b e  + (4A c + 4B b)d e  - 3B c d e )m + 12A b e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      3 3            3                   2 2  2
+--R               A b d e m  + (7A b d e  + (- 2A c - 2B b)d e )m
+--R             + 
+--R                         3                   2 2         3
+--R               (12A b d e  + (- 8A c - 8B b)d e  + 6B c d e)m
+--R          *
+--R             x
+--R         + 
+--R                  2 2 2            2 2                 3             2 2
+--R           - A b d e m  + (- 7A b d e  + (2A c + 2B b)d e)m - 12A b d e
+--R         + 
+--R                         3          4
+--R           (8A c + 8B b)d e - 6B c d
+--R      *
+--R           m log(e x + d)
+--R         %e
+--R     + 
+--R               3         2                           m + 4
+--R       (- B c m  - 6B c m  - 11B c m - 6B c)(e x + d)
+--R     + 
+--R                                     3                                2
+--R           ((- A c - B b)e + 3B c d)m  + ((- 7A c - 7B b)e + 21B c d)m
+--R         + 
+--R           ((- 14A c - 14B b)e + 42B c d)m + (- 8A c - 8B b)e + 24B c d
+--R      *
+--R                  m + 3
+--R         (e x + d)
+--R     + 
+--R                   2                            2  3
+--R           (- A b e  + (2A c + 2B b)d e - 3B c d )m
+--R         + 
+--R                    2                               2  2
+--R           (- 8A b e  + (16A c + 16B b)d e - 24B c d )m
+--R         + 
+--R                     2                               2            2
+--R           (- 19A b e  + (38A c + 38B b)d e - 57B c d )m - 12A b e
+--R         + 
+--R                                       2
+--R           (24A c + 24B b)d e - 36B c d
+--R      *
+--R                  m + 2
+--R         (e x + d)
+--R     + 
+--R                   2                 2         3  3
+--R           (A b d e  + (- A c - B b)d e + B c d )m
+--R         + 
+--R                    2                   2          3  2
+--R           (9A b d e  + (- 9A c - 9B b)d e + 9B c d )m
+--R         + 
+--R                     2                     2           3              2
+--R           (26A b d e  + (- 26A c - 26B b)d e + 26B c d )m + 24A b d e
+--R         + 
+--R                             2           3
+--R           (- 24A c - 24B b)d e + 24B c d
+--R      *
+--R                  m + 1
+--R         (e x + d)
+--R  /
+--R      4 4      4 3      4 2      4       4
+--R     e m  + 10e m  + 35e m  + 50e m + 24e
+--R                                                    Type: Expression(Integer)
+--E 4
+
+--S 5 of 1457
+d0:=normalize(D(m0,x))
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1457
+t0:=(A+B*x)*(d+e*x)^5*(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R          5 8                5           4  7
+--R     B c e x  + ((A c + B b)e  + 5B c d e )x
+--R   + 
+--R           5                   4          2 3  6
+--R     (A b e  + (5A c + 5B b)d e  + 10B c d e )x
+--R   + 
+--R              4                   2 3          3 2  5
+--R     (5A b d e  + (10A c + 10B b)d e  + 10B c d e )x
+--R   + 
+--R             2 3                   3 2         4   4
+--R     (10A b d e  + (10A c + 10B b)d e  + 5B c d e)x
+--R   + 
+--R             3 2                 4         5  3          4                5  2
+--R     (10A b d e  + (5A c + 5B b)d e + B c d )x  + (5A b d e + (A c + B b)d )x
+--R   + 
+--R          5
+--R     A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 6
+
+--S 7 of 1457
+r0:=-1/6*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^6/e^4+1/7*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*(d+e*x)^7/e^4-1/8*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^8/e^4+_
+     1/9*B*c*(d+e*x)^9/e^4
+--R 
+--R
+--R   (2)
+--R       1      9 9     1       1      9   5        8  8
+--R       - B c e x  + ((- A c + - B b)e  + - B c d e )x
+--R       9              8       8          8
+--R     + 
+--R        1      9    5       5        8   10      2 7  7
+--R       (- A b e  + (- A c + - B b)d e  + -- B c d e )x
+--R        7           7       7             7
+--R     + 
+--R        5        8    5       5      2 7   5      3 6  6
+--R       (- A b d e  + (- A c + - B b)d e  + - B c d e )x
+--R        6             3       3            3
+--R     + 
+--R              2 7                 3 6        4 5  5
+--R       (2A b d e  + (2A c + 2B b)d e  + B c d e )x
+--R     + 
+--R        5      3 6    5       5      4 5   1      5 4  4
+--R       (- A b d e  + (- A c + - B b)d e  + - B c d e )x
+--R        2             4       4            4
+--R     + 
+--R        5      4 5    1       1      5 4  3   1      5 4 2    1      7 2
+--R       (- A b d e  + (- A c + - B b)d e )x  + - A b d e x  - -- A b d e
+--R        3             3       3               2              42
+--R     + 
+--R         1         1       8     1       9
+--R       (--- A c + --- B b)d e - --- B c d
+--R        168       168           504
+--R  /
+--R      4
+--R     e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 7
+
+--S 8 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1      5 9     1       1      5   5        4  8
+--R     - B c e x  + ((- A c + - B b)e  + - B c d e )x
+--R     9              8       8          8
+--R   + 
+--R      1      5    5       5        4   10      2 3  7
+--R     (- A b e  + (- A c + - B b)d e  + -- B c d e )x
+--R      7           7       7             7
+--R   + 
+--R      5        4    5       5      2 3   5      3 2  6
+--R     (- A b d e  + (- A c + - B b)d e  + - B c d e )x
+--R      6             3       3            3
+--R   + 
+--R            2 3                 3 2        4   5
+--R     (2A b d e  + (2A c + 2B b)d e  + B c d e)x
+--R   + 
+--R      5      3 2    5       5      4    1      5  4
+--R     (- A b d e  + (- A c + - B b)d e + - B c d )x
+--R      2             4       4           4
+--R   + 
+--R      5      4     1       1      5  3   1      5 2
+--R     (- A b d e + (- A c + - B b)d )x  + - A b d x
+--R      3            3       3             2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 8
+
+--S 9 of 1457
+m0:=a0-r0
+--R 
+--R
+--R         1      7 2       1         1       8     1       9
+--R        -- A b d e  + (- --- A c - --- B b)d e + --- B c d
+--R        42               168       168           504
+--R   (4)  ---------------------------------------------------
+--R                                  4
+--R                                 e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 9
+
+--S 10 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 10
+
+)clear all
+
+--S 11 of 1457
+t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R          4 7                4           3  6
+--R     B c e x  + ((A c + B b)e  + 4B c d e )x
+--R   + 
+--R           4                   3         2 2  5
+--R     (A b e  + (4A c + 4B b)d e  + 6B c d e )x
+--R   + 
+--R              3                 2 2         3   4
+--R     (4A b d e  + (6A c + 6B b)d e  + 4B c d e)x
+--R   + 
+--R            2 2                 3         4  3          3                4  2
+--R     (6A b d e  + (4A c + 4B b)d e + B c d )x  + (4A b d e + (A c + B b)d )x
+--R   + 
+--R          4
+--R     A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 11
+
+--S 12 of 1457
+r0:=-1/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^5/e^4+1/6*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^7/e^4+_
+     1/8*B*c*(d+e*x)^8/e^4
+--R 
+--R
+--R   (2)
+--R       1      8 8     1       1      8   4        7  7
+--R       - B c e x  + ((- A c + - B b)e  + - B c d e )x
+--R       8              7       7          7
+--R     + 
+--R        1      8    2       2        7        2 6  6
+--R       (- A b e  + (- A c + - B b)d e  + B c d e )x
+--R        6           3       3
+--R     + 
+--R        4        7    6       6      2 6   4      3 5  5
+--R       (- A b d e  + (- A c + - B b)d e  + - B c d e )x
+--R        5             5       5            5
+--R     + 
+--R        3      2 6               3 5   1      4 4  4
+--R       (- A b d e  + (A c + B b)d e  + - B c d e )x
+--R        2                              4
+--R     + 
+--R        4      3 5    1       1      4 4  3   1      4 4 2    1      6 2
+--R       (- A b d e  + (- A c + - B b)d e )x  + - A b d e x  - -- A b d e
+--R        3             3       3               2              30
+--R     + 
+--R         1         1       7     1       8
+--R       (--- A c + --- B b)d e - --- B c d
+--R        105       105           280
+--R  /
+--R      4
+--R     e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 12
+
+--S 13 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1      4 8     1       1      4   4        3  7
+--R     - B c e x  + ((- A c + - B b)e  + - B c d e )x
+--R     8              7       7          7
+--R   + 
+--R      1      4    2       2        3        2 2  6
+--R     (- A b e  + (- A c + - B b)d e  + B c d e )x
+--R      6           3       3
+--R   + 
+--R      4        3    6       6      2 2   4      3   5
+--R     (- A b d e  + (- A c + - B b)d e  + - B c d e)x
+--R      5             5       5            5
+--R   + 
+--R      3      2 2               3    1      4  4
+--R     (- A b d e  + (A c + B b)d e + - B c d )x
+--R      2                             4
+--R   + 
+--R      4      3     1       1      4  3   1      4 2
+--R     (- A b d e + (- A c + - B b)d )x  + - A b d x
+--R      3            3       3             2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 13
+
+--S 14 of 1457
+m0:=a0-r0
+--R 
+--R
+--R         1      6 2       1         1       7     1       8
+--R        -- A b d e  + (- --- A c - --- B b)d e + --- B c d
+--R        30               105       105           280
+--R   (4)  ---------------------------------------------------
+--R                                  4
+--R                                 e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 14
+
+--S 15 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 15
+
+)clear all
+
+--S 16 of 1457
+t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R          3 6                3           2  5
+--R     B c e x  + ((A c + B b)e  + 3B c d e )x
+--R   + 
+--R           3                   2         2   4
+--R     (A b e  + (3A c + 3B b)d e  + 3B c d e)x
+--R   + 
+--R              2                 2         3  3          2                3  2
+--R     (3A b d e  + (3A c + 3B b)d e + B c d )x  + (3A b d e + (A c + B b)d )x
+--R   + 
+--R          3
+--R     A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 1457
+r0:=-1/4*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^4/e^4+1/5*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^6/e^4+_
+     1/7*B*c*(d+e*x)^7/e^4
+--R 
+--R
+--R   (2)
+--R       1      7 7     1       1      7   1        6  6
+--R       - B c e x  + ((- A c + - B b)e  + - B c d e )x
+--R       7              6       6          2
+--R     + 
+--R        1      7    3       3        6   3      2 5  5
+--R       (- A b e  + (- A c + - B b)d e  + - B c d e )x
+--R        5           5       5            5
+--R     + 
+--R        3        6    3       3      2 5   1      3 4  4
+--R       (- A b d e  + (- A c + - B b)d e  + - B c d e )x
+--R        4             4       4            4
+--R     + 
+--R             2 5    1       1      3 4  3   1      3 4 2    1      5 2
+--R       (A b d e  + (- A c + - B b)d e )x  + - A b d e x  - -- A b d e
+--R                    3       3               2              20
+--R     + 
+--R         1        1      6     1       7
+--R       (-- A c + -- B b)d e - --- B c d
+--R        60       60           140
+--R  /
+--R      4
+--R     e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 17
+
+--S 18 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1      3 7     1       1      3   1        2  6
+--R     - B c e x  + ((- A c + - B b)e  + - B c d e )x
+--R     7              6       6          2
+--R   + 
+--R      1      3    3       3        2   3      2   5
+--R     (- A b e  + (- A c + - B b)d e  + - B c d e)x
+--R      5           5       5            5
+--R   + 
+--R      3        2    3       3      2    1      3  4
+--R     (- A b d e  + (- A c + - B b)d e + - B c d )x
+--R      4             4       4           4
+--R   + 
+--R           2     1       1      3  3   1      3 2
+--R     (A b d e + (- A c + - B b)d )x  + - A b d x
+--R                 3       3             2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 1457
+m0:=a0-r0
+--R 
+--R
+--R         1      5 2       1        1      6     1       7
+--R        -- A b d e  + (- -- A c - -- B b)d e + --- B c d
+--R        20               60       60           140
+--R   (4)  -------------------------------------------------
+--R                                 4
+--R                                e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 19
+
+--S 20 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 20
+
+)clear all
+
+--S 21 of 1457
+t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R          2 5                2             4
+--R     B c e x  + ((A c + B b)e  + 2B c d e)x
+--R   + 
+--R           2                           2  3                           2  2
+--R     (A b e  + (2A c + 2B b)d e + B c d )x  + (2A b d e + (A c + B b)d )x
+--R   + 
+--R          2
+--R     A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 21
+
+--S 22 of 1457
+r0:=1/2*A*b*d^2*x^2+1/3*d*(b*B*d+A*c*d+2*A*b*e)*x^3+1/4*(A*e*(2*c*d+b*e)+_
+     B*d*(c*d+2*b*e))*x^4+1/5*e*(2*B*c*d+b*B*e+A*c*e)*x^5+1/6*B*c*e^2*x^6
+--R 
+--R
+--R   (2)
+--R     1      2 6     1       1      2   2          5
+--R     - B c e x  + ((- A c + - B b)e  + - B c d e)x
+--R     6              5       5          5
+--R   + 
+--R      1      2    1       1           1      2  4
+--R     (- A b e  + (- A c + - B b)d e + - B c d )x
+--R      4           2       2           4
+--R   + 
+--R      2            1       1      2  3   1      2 2
+--R     (- A b d e + (- A c + - B b)d )x  + - A b d x
+--R      3            3       3             2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 22
+
+--S 23 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1      2 6     1       1      2   2          5
+--R     - B c e x  + ((- A c + - B b)e  + - B c d e)x
+--R     6              5       5          5
+--R   + 
+--R      1      2    1       1           1      2  4
+--R     (- A b e  + (- A c + - B b)d e + - B c d )x
+--R      4           2       2           4
+--R   + 
+--R      2            1       1      2  3   1      2 2
+--R     (- A b d e + (- A c + - B b)d )x  + - A b d x
+--R      3            3       3             2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 23
+
+--S 24 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 24
+
+--S 25 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 25
+
+)clear all
+
+--S 26 of 1457
+t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R          4                          3                          2
+--R   B c e x  + ((A c + B b)e + B c d)x  + (A b e + (A c + B b)d)x  + A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 26
+
+--S 27 of 1457
+r0:=1/2*A*b*d*x^2+1/3*(b*B*d+A*c*d+A*b*e)*x^3+1/4*(B*c*d+b*B*e+A*c*e)*x^4+_
+     1/5*B*c*e*x^5
+--R 
+--R
+--R   (2)
+--R     1        5     1       1         1        4
+--R     - B c e x  + ((- A c + - B b)e + - B c d)x
+--R     5              4       4         4
+--R   + 
+--R      1          1       1        3   1        2
+--R     (- A b e + (- A c + - B b)d)x  + - A b d x
+--R      3          3       3            2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 27
+
+--S 28 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1        5     1       1         1        4
+--R     - B c e x  + ((- A c + - B b)e + - B c d)x
+--R     5              4       4         4
+--R   + 
+--R      1          1       1        3   1        2
+--R     (- A b e + (- A c + - B b)d)x  + - A b d x
+--R      3          3       3            2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 28
+
+--S 29 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 29
+
+--S 30 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 30
+
+)clear all
+
+--S 31 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)
+--R 
+--R
+--R             3               2
+--R   (1)  B c x  + (A c + B b)x  + A b x
+--R                                                    Type: Polynomial(Integer)
+--E 31
+
+--S 32 of 1457
+r0:=1/2*A*b*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4
+--R 
+--R
+--R        1      4    1       1      3   1      2
+--R   (2)  - B c x  + (- A c + - B b)x  + - A b x
+--R        4           3       3          2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 32
+
+--S 33 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R        1      4    1       1      3   1      2
+--R   (3)  - B c x  + (- A c + - B b)x  + - A b x
+--R        4           3       3          2
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 33
+
+--S 34 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 34
+
+--S 35 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 35
+
+)clear all
+
+--S 36 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)
+--R 
+--R
+--R             3               2
+--R        B c x  + (A c + B b)x  + A b x
+--R   (1)  ------------------------------
+--R                    e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 1457
+r0:=(B*d-A*e)*(c*d-b*e)*x/e^3-1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+_
+     1/3*B*c*x^3/e-d*(B*d-A*e)*(c*d-b*e)*log(d+e*x)/e^4
+--R 
+--R
+--R   (2)
+--R                  2                 2          3                      3 3
+--R       (- 6A b d e  + (6A c + 6B b)d e - 6B c d )log(e x + d) + 2B c e x
+--R     + 
+--R                      3           2  2
+--R       ((3A c + 3B b)e  - 3B c d e )x
+--R     + 
+--R              3                     2         2
+--R       (6A b e  + (- 6A c - 6B b)d e  + 6B c d e)x
+--R  /
+--R       4
+--R     6e
+--R                                                    Type: Expression(Integer)
+--E 37
+
+--S 38 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  2                 2          3                      3 3
+--R       (- 6A b d e  + (6A c + 6B b)d e - 6B c d )log(e x + d) + 2B c e x
+--R     + 
+--R                      3           2  2
+--R       ((3A c + 3B b)e  - 3B c d e )x
+--R     + 
+--R              3                     2         2
+--R       (6A b e  + (- 6A c - 6B b)d e  + 6B c d e)x
+--R  /
+--R       4
+--R     6e
+--R                                         Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 39
+
+--S 40 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^2
+--R 
+--R
+--R             3               2
+--R        B c x  + (A c + B b)x  + A b x
+--R   (1)  ------------------------------
+--R               2 2             2
+--R              e x  + 2d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 1457
+r0:=-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+d*(B*d-A*e)*_
+     (c*d-b*e)/(e^4*(d+e*x))+(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*log(d+e*x)/e^4
+--R 
+--R
+--R   (2)
+--R                  3                     2         2              2
+--R           (2A b e  + (- 4A c - 4B b)d e  + 6B c d e)x + 2A b d e
+--R         + 
+--R                           2          3
+--R           (- 4A c - 4B b)d e + 6B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R            3 3                  3           2  2
+--R       B c e x  + ((2A c + 2B b)e  - 3B c d e )x
+--R     + 
+--R                      2         2              2                   2          3
+--R     ((2A c + 2B b)d e  - 4B c d e)x + 2A b d e  + (- 2A c - 2B b)d e + 2B c d
+--R  /
+--R       5        4
+--R     2e x + 2d e
+--R                                                    Type: Expression(Integer)
+--E 42
+
+--S 43 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  3                     2         2              2
+--R           (2A b e  + (- 4A c - 4B b)d e  + 6B c d e)x + 2A b d e
+--R         + 
+--R                           2          3
+--R           (- 4A c - 4B b)d e + 6B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R            3 3                  3           2  2
+--R       B c e x  + ((2A c + 2B b)e  - 3B c d e )x
+--R     + 
+--R                      2         2              2                   2          3
+--R     ((2A c + 2B b)d e  - 4B c d e)x + 2A b d e  + (- 2A c - 2B b)d e + 2B c d
+--R  /
+--R       5        4
+--R     2e x + 2d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 44
+
+--S 45 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^3
+--R 
+--R
+--R             3               2
+--R        B c x  + (A c + B b)x  + A b x
+--R   (1)  ------------------------------
+--R          3 3       2 2     2       3
+--R         e x  + 3d e x  + 3d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 1457
+r0:=B*c*x/e^3+1/2*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^2)+(-B*d*(3*c*d-_
+     2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x))-(3*B*c*d-b*B*e-A*c*e)*log(d+_
+     e*x)/e^4
+--R 
+--R
+--R   (2)
+--R                          3           2  2                    2          2
+--R           ((2A c + 2B b)e  - 6B c d e )x  + ((4A c + 4B b)d e  - 12B c d e)x
+--R         + 
+--R                         2          3
+--R           (2A c + 2B b)d e - 6B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R             3 3           2 2            3                   2         2
+--R       2B c e x  + 4B c d e x  + (- 2A b e  + (4A c + 4B b)d e  - 4B c d e)x
+--R     + 
+--R                2                 2          3
+--R       - A b d e  + (3A c + 3B b)d e - 5B c d
+--R  /
+--R       6 2       5      2 4
+--R     2e x  + 4d e x + 2d e
+--R                                                    Type: Expression(Integer)
+--E 47
+
+--S 48 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                          3           2  2                    2          2
+--R           ((2A c + 2B b)e  - 6B c d e )x  + ((4A c + 4B b)d e  - 12B c d e)x
+--R         + 
+--R                         2          3
+--R           (2A c + 2B b)d e - 6B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R             3 3           2 2            3                   2         2
+--R       2B c e x  + 4B c d e x  + (- 2A b e  + (4A c + 4B b)d e  - 4B c d e)x
+--R     + 
+--R                2                 2          3
+--R       - A b d e  + (3A c + 3B b)d e - 5B c d
+--R  /
+--R       6 2       5      2 4
+--R     2e x  + 4d e x + 2d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 49
+
+--S 50 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^4
+--R 
+--R
+--R                 3               2
+--R            B c x  + (A c + B b)x  + A b x
+--R   (1)  --------------------------------------
+--R         4 4       3 3     2 2 2     3       4
+--R        e x  + 4d e x  + 6d e x  + 4d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 1457
+r0:=1/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^3)+1/2*(-B*d*(3*c*d-2*b*e)+_
+     A*e*(2*c*d-b*e))/(e^4*(d+e*x)^2)+(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+_
+     B*c*log(d+e*x)/e^4
+--R 
+--R
+--R   (2)
+--R              3 3            2 2          2            3
+--R       (6B c e x  + 18B c d e x  + 18B c d e x + 6B c d )log(e x + d)
+--R     + 
+--R                        3            2  2
+--R       ((- 6A c - 6B b)e  + 18B c d e )x
+--R     + 
+--R                3                     2          2             2
+--R       (- 3A b e  + (- 6A c - 6B b)d e  + 27B c d e)x - A b d e
+--R     + 
+--R                       2           3
+--R       (- 2A c - 2B b)d e + 11B c d
+--R  /
+--R       7 3        6 2      2 5      3 4
+--R     6e x  + 18d e x  + 18d e x + 6d e
+--R                                                    Type: Expression(Integer)
+--E 52
+
+--S 53 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R              3 3            2 2          2            3
+--R       (6B c e x  + 18B c d e x  + 18B c d e x + 6B c d )log(e x + d)
+--R     + 
+--R                        3            2  2
+--R       ((- 6A c - 6B b)e  + 18B c d e )x
+--R     + 
+--R                3                     2          2             2
+--R       (- 3A b e  + (- 6A c - 6B b)d e  + 27B c d e)x - A b d e
+--R     + 
+--R                       2           3
+--R       (- 2A c - 2B b)d e + 11B c d
+--R  /
+--R       7 3        6 2      2 5      3 4
+--R     6e x  + 18d e x  + 18d e x + 6d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 54
+
+--S 55 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^5
+--R 
+--R
+--R                       3               2
+--R                  B c x  + (A c + B b)x  + A b x
+--R   (1)  --------------------------------------------------
+--R         5 5       4 4      2 3 3      3 2 2     4       5
+--R        e x  + 5d e x  + 10d e x  + 10d e x  + 5d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 56
+
+--S 57 of 1457
+r0:=1/4*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^4)+1/3*(-B*d*(3*c*d-2*b*e)+_
+     A*e*(2*c*d-b*e))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/(e^4*_
+     (d+e*x)^2)-B*c/(e^4*(d+e*x))
+--R 
+--R
+--R   (2)
+--R              3 3       1       1      3   3        2  2
+--R       - B c e x  + ((- - A c - - B b)e  - - B c d e )x
+--R                        2       2          2
+--R     + 
+--R          1      3      1       1        2        2       1        2
+--R       (- - A b e  + (- - A c - - B b)d e  - B c d e)x - -- A b d e
+--R          3             3       3                        12
+--R     + 
+--R           1        1      2    1      3
+--R       (- -- A c - -- B b)d e - - B c d
+--R          12       12           4
+--R  /
+--R      8 4       7 3     2 6 2     3 5     4 4
+--R     e x  + 4d e x  + 6d e x  + 4d e x + d e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 57
+
+--S 58 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                3 3                    3            2  2
+--R       - 12B c e x  + ((- 6A c - 6B b)e  - 18B c d e )x
+--R     + 
+--R                3                     2          2             2
+--R       (- 4A b e  + (- 4A c - 4B b)d e  - 12B c d e)x - A b d e
+--R     + 
+--R                     2          3
+--R       (- A c - B b)d e - 3B c d
+--R  /
+--R        8 4        7 3      2 6 2      3 5       4 4
+--R     12e x  + 48d e x  + 72d e x  + 48d e x + 12d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 59
+
+--S 60 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^6
+--R 
+--R
+--R                             3               2
+--R                        B c x  + (A c + B b)x  + A b x
+--R   (1)  -------------------------------------------------------------
+--R         6 6       5 5      2 4 4      3 3 3      4 2 2     5       6
+--R        e x  + 6d e x  + 15d e x  + 20d e x  + 15d e x  + 6d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 1457
+r0:=1/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^5)+1/4*(-B*d*(3*c*d-2*b*e)+_
+     A*e*(2*c*d-b*e))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/(e^4*_
+     (d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2)
+--R 
+--R
+--R   (2)
+--R         1      3 3       1       1      3   1        2  2
+--R       - - B c e x  + ((- - A c - - B b)e  - - B c d e )x
+--R         2                3       3          2
+--R     + 
+--R          1      3      1       1        2   1      2       1        2
+--R       (- - A b e  + (- - A c - - B b)d e  - - B c d e)x - -- A b d e
+--R          4             6       6            4             20
+--R     + 
+--R           1        1      2     1      3
+--R       (- -- A c - -- B b)d e - -- B c d
+--R          30       30           20
+--R  /
+--R      9 5       8 4      2 7 3      3 6 2     4 5     5 4
+--R     e x  + 5d e x  + 10d e x  + 10d e x  + 5d e x + d e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 62
+
+--S 63 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                3 3                      3            2  2
+--R       - 30B c e x  + ((- 20A c - 20B b)e  - 30B c d e )x
+--R     + 
+--R                 3                       2          2              2
+--R       (- 15A b e  + (- 10A c - 10B b)d e  - 15B c d e)x - 3A b d e
+--R     + 
+--R                       2          3
+--R       (- 2A c - 2B b)d e - 3B c d
+--R  /
+--R        9 5         8 4       2 7 3       3 6 2       4 5       5 4
+--R     60e x  + 300d e x  + 600d e x  + 600d e x  + 300d e x + 60d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 64
+
+--S 65 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^7
+--R 
+--R
+--R   (1)
+--R                             3               2
+--R                        B c x  + (A c + B b)x  + A b x
+--R   ------------------------------------------------------------------------
+--R    7 7       6 6      2 5 5      3 4 4      4 3 3      5 2 2     6       7
+--R   e x  + 7d e x  + 21d e x  + 35d e x  + 35d e x  + 21d e x  + 7d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 66
+
+--S 67 of 1457
+r0:=1/6*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^6)+1/5*(-B*d*(3*c*d-2*b*e)+_
+     A*e*(2*c*d-b*e))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/(e^4*_
+     (d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3)
+--R 
+--R
+--R   (2)
+--R         1      3 3       1       1      3   1        2  2
+--R       - - B c e x  + ((- - A c - - B b)e  - - B c d e )x
+--R         3                4       4          4
+--R     + 
+--R          1      3       1        1        2    1      2       1        2
+--R       (- - A b e  + (- -- A c - -- B b)d e  - -- B c d e)x - -- A b d e
+--R          5             10       10            10             30
+--R     + 
+--R           1        1      2     1      3
+--R       (- -- A c - -- B b)d e - -- B c d
+--R          60       60           60
+--R  /
+--R      10 6       9 5      2 8 4      3 7 3      4 6 2     5 5     6 4
+--R     e  x  + 6d e x  + 15d e x  + 20d e x  + 15d e x  + 6d e x + d e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 67
+
+--S 68 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                3 3                      3            2  2
+--R       - 20B c e x  + ((- 15A c - 15B b)e  - 15B c d e )x
+--R     + 
+--R                 3                     2         2              2
+--R       (- 12A b e  + (- 6A c - 6B b)d e  - 6B c d e)x - 2A b d e
+--R     + 
+--R                     2         3
+--R       (- A c - B b)d e - B c d
+--R  /
+--R          10 6         9 5       2 8 4        3 7 3       4 6 2       5 5
+--R       60e  x  + 360d e x  + 900d e x  + 1200d e x  + 900d e x  + 360d e x
+--R     + 
+--R          6 4
+--R       60d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 69
+
+--S 70 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 1457
+t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^2
+--R 
+--R
+--R            2 5       2           4                2  3      2 2          m
+--R   (1)  (B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x )(e x + d)
+--R                                                    Type: Expression(Integer)
+--E 71
+
+--S 72 of 1457
+r0:=-d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(1+m)/(e^6*(1+m))+d*(c*d-b*e)*_
+     (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^6*(2+m))+_
+     (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_
+     3*b^2*e^2))*(d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-_
+     B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(4+m)/(e^6*(4+m))-_
+     c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*_
+     (d+e*x)^(6+m)/(e^6*(6+m))
+--R 
+--R
+--R   (2)
+--R             2 5        2 4        2 3         2 2         2          2
+--R         (B c m  + 15B c m  + 85B c m  + 225B c m  + 274B c m + 120B c )
+--R      *
+--R                  m + 6
+--R         (e x + d)
+--R     + 
+--R                2                  2   5          2                    2   4
+--R           ((A c  + 2B b c)e - 5B c d)m  + ((16A c  + 32B b c)e - 80B c d)m
+--R         + 
+--R                  2                      2   3
+--R           ((95A c  + 190B b c)e - 475B c d)m
+--R         + 
+--R                   2                       2   2
+--R           ((260A c  + 520B b c)e - 1300B c d)m
+--R         + 
+--R                 2                       2             2                      2
+--R         ((324A c  + 648B b c)e - 1620B c d)m + (144A c  + 288B b c)e - 720B c d
+--R      *
+--R                  m + 5
+--R         (e x + d)
+--R     + 
+--R                         2  2          2                     2 2  5
+--R           ((2A b c + B b )e  + (- 4A c  - 8B b c)d e + 10B c d )m
+--R         + 
+--R                            2  2           2                        2 2  4
+--R           ((34A b c + 17B b )e  + (- 68A c  - 136B b c)d e + 170B c d )m
+--R         + 
+--R                              2  2            2                         2 2  3
+--R           ((214A b c + 107B b )e  + (- 428A c  - 856B b c)d e + 1070B c d )m
+--R         + 
+--R                              2  2             2                          2 2  2
+--R           ((614A b c + 307B b )e  + (- 1228A c  - 2456B b c)d e + 3070B c d )m
+--R         + 
+--R                              2  2             2                          2 2
+--R           ((792A b c + 396B b )e  + (- 1584A c  - 3168B b c)d e + 3960B c d )m
+--R         + 
+--R                             2  2            2                          2 2
+--R           (360A b c + 180B b )e  + (- 720A c  - 1440B b c)d e + 1800B c d
+--R      *
+--R                  m + 4
+--R         (e x + d)
+--R     + 
+--R               2 3                   2    2        2            2         2 3  5
+--R           (A b e  + (- 6A b c - 3B b )d e  + (6A c  + 12B b c)d e - 10B c d )m
+--R         + 
+--R                    2 3                      2    2          2             2
+--R               18A b e  + (- 108A b c - 54B b )d e  + (108A c  + 216B b c)d e
+--R             + 
+--R                       2 3
+--R               - 180B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                     2 3                       2    2          2              2
+--R               121A b e  + (- 726A b c - 363B b )d e  + (726A c  + 1452B b c)d e
+--R             + 
+--R                        2 3
+--R               - 1210B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                     2 3                         2    2
+--R               372A b e  + (- 2232A b c - 1116B b )d e
+--R             + 
+--R                       2              2           2 3
+--R               (2232A c  + 4464B b c)d e - 3720B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                     2 3                         2    2
+--R               508A b e  + (- 3048A b c - 1524B b )d e
+--R             + 
+--R                       2              2           2 3
+--R               (3048A c  + 6096B b c)d e - 5080B c d
+--R          *
+--R             m
+--R         + 
+--R                 2 3                        2    2           2              2
+--R           240A b e  + (- 1440A b c - 720B b )d e  + (1440A c  + 2880B b c)d e
+--R         + 
+--R                    2 3
+--R           - 2400B c d
+--R      *
+--R                  m + 3
+--R         (e x + d)
+--R     + 
+--R                     2   3                 2  2 2          2           3
+--R               - 2A b d e  + (6A b c + 3B b )d e  + (- 4A c  - 8B b c)d e
+--R             + 
+--R                   2 4
+--R               5B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                      2   3                    2  2 2           2             3
+--R               - 38A b d e  + (114A b c + 57B b )d e  + (- 76A c  - 152B b c)d e
+--R             + 
+--R                    2 4
+--R               95B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                       2   3                     2  2 2
+--R               - 274A b d e  + (822A b c + 411B b )d e
+--R             + 
+--R                        2              3          2 4
+--R               (- 548A c  - 1096B b c)d e + 685B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                       2   3                       2  2 2
+--R               - 922A b d e  + (2766A b c + 1383B b )d e
+--R             + 
+--R                         2              3           2 4
+--R               (- 1844A c  - 3688B b c)d e + 2305B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                        2   3                       2  2 2
+--R               - 1404A b d e  + (4212A b c + 2106B b )d e
+--R             + 
+--R                         2              3           2 4
+--R               (- 2808A c  - 5616B b c)d e + 3510B c d
+--R          *
+--R             m
+--R         + 
+--R                   2   3                       2  2 2
+--R           - 720A b d e  + (2160A b c + 1080B b )d e
+--R         + 
+--R                     2              3           2 4
+--R           (- 1440A c  - 2880B b c)d e + 1800B c d
+--R      *
+--R                  m + 2
+--R         (e x + d)
+--R     + 
+--R               2 2 3                  2  3 2       2           4       2 5  5
+--R           (A b d e  + (- 2A b c - B b )d e  + (A c  + 2B b c)d e - B c d )m
+--R         + 
+--R                    2 2 3                     2  3 2         2            4
+--R               20A b d e  + (- 40A b c - 20B b )d e  + (20A c  + 40B b c)d e
+--R             + 
+--R                      2 5
+--R               - 20B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                     2 2 3                       2  3 2
+--R               155A b d e  + (- 310A b c - 155B b )d e
+--R             + 
+--R                      2             4          2 5
+--R               (155A c  + 310B b c)d e - 155B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                     2 2 3                        2  3 2
+--R               580A b d e  + (- 1160A b c - 580B b )d e
+--R             + 
+--R                      2              4          2 5
+--R               (580A c  + 1160B b c)d e - 580B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                      2 2 3                         2  3 2
+--R               1044A b d e  + (- 2088A b c - 1044B b )d e
+--R             + 
+--R                       2              4           2 5
+--R               (1044A c  + 2088B b c)d e - 1044B c d
+--R          *
+--R             m
+--R         + 
+--R                 2 2 3                        2  3 2          2              4
+--R           720A b d e  + (- 1440A b c - 720B b )d e  + (720A c  + 1440B b c)d e
+--R         + 
+--R                   2 5
+--R           - 720B c d
+--R      *
+--R                  m + 1
+--R         (e x + d)
+--R  /
+--R      6 6      6 5       6 4       6 3        6 2        6        6
+--R     e m  + 21e m  + 175e m  + 735e m  + 1624e m  + 1764e m + 720e
+--R                                                    Type: Expression(Integer)
+--E 72
+
+--S 73 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                2 6 5        2 6 4        2 6 3         2 6 2         2 6
+--R             B c e m  + 15B c e m  + 85B c e m  + 225B c e m  + 274B c e m
+--R           + 
+--R                   2 6
+--R             120B c e
+--R        *
+--R            6
+--R           x
+--R       + 
+--R                  2           6      2   5  5
+--R             ((A c  + 2B b c)e  + B c d e )m
+--R           + 
+--R                    2            6        2   5  4
+--R             ((16A c  + 32B b c)e  + 10B c d e )m
+--R           + 
+--R                    2             6        2   5  3
+--R             ((95A c  + 190B b c)e  + 35B c d e )m
+--R           + 
+--R                     2             6        2   5  2
+--R             ((260A c  + 520B b c)e  + 50B c d e )m
+--R           + 
+--R                     2             6        2   5            2             6
+--R             ((324A c  + 648B b c)e  + 24B c d e )m + (144A c  + 288B b c)e
+--R        *
+--R            5
+--R           x
+--R       + 
+--R                           2  6       2             5  5
+--R             ((2A b c + B b )e  + (A c  + 2B b c)d e )m
+--R           + 
+--R                              2  6         2              5       2 2 4  4
+--R             ((34A b c + 17B b )e  + (12A c  + 24B b c)d e  - 5B c d e )m
+--R           + 
+--R                                2  6         2              5        2 2 4  3
+--R             ((214A b c + 107B b )e  + (47A c  + 94B b c)d e  - 30B c d e )m
+--R           + 
+--R                                2  6         2               5        2 2 4  2
+--R             ((614A b c + 307B b )e  + (72A c  + 144B b c)d e  - 55B c d e )m
+--R           + 
+--R                                2  6         2              5        2 2 4
+--R             ((792A b c + 396B b )e  + (36A c  + 72B b c)d e  - 30B c d e )m
+--R           + 
+--R                               2  6
+--R             (360A b c + 180B b )e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                 2 6                2    5  5
+--R             (A b e  + (2A b c + B b )d e )m
+--R           + 
+--R                   2 6                   2    5          2           2 4  4
+--R             (18A b e  + (28A b c + 14B b )d e  + (- 4A c  - 8B b c)d e )m
+--R           + 
+--R                       2 6                    2    5           2            2 4
+--R                 121A b e  + (130A b c + 65B b )d e  + (- 36A c  - 72B b c)d e
+--R               + 
+--R                      2 3 3
+--R                 20B c d e
+--R            *
+--R                3
+--R               m
+--R           + 
+--R                       2 6                     2    5
+--R                 372A b e  + (224A b c + 112B b )d e
+--R               + 
+--R                         2             2 4        2 3 3
+--R                 (- 80A c  - 160B b c)d e  + 60B c d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                       2 6                    2    5           2            2 4
+--R                 508A b e  + (120A b c + 60B b )d e  + (- 48A c  - 96B b c)d e
+--R               + 
+--R                      2 3 3
+--R                 40B c d e
+--R            *
+--R               m
+--R           + 
+--R                   2 6
+--R             240A b e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                2   5 5         2   5                   2  2 4  4
+--R             A b d e m  + (16A b d e  + (- 6A b c - 3B b )d e )m
+--R           + 
+--R                   2   5                     2  2 4         2            3 3  3
+--R             (89A b d e  + (- 72A b c - 36B b )d e  + (12A c  + 24B b c)d e )m
+--R           + 
+--R                       2   5                       2  2 4
+--R                 194A b d e  + (- 246A b c - 123B b )d e
+--R               + 
+--R                       2             3 3        2 4 2
+--R                 (84A c  + 168B b c)d e  - 60B c d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                       2   5                      2  2 4
+--R                 120A b d e  + (- 180A b c - 90B b )d e
+--R               + 
+--R                       2             3 3        2 4 2
+--R                 (72A c  + 144B b c)d e  - 60B c d e
+--R            *
+--R               m
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                   2 2 4 4           2 2 4                  2  3 3  3
+--R             - 2A b d e m  + (- 30A b d e  + (12A b c + 6B b )d e )m
+--R           + 
+--R                         2 2 4                    2  3 3
+--R                 - 148A b d e  + (132A b c + 66B b )d e
+--R               + 
+--R                         2            4 2
+--R                 (- 24A c  - 48B b c)d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                         2 2 4                     2  3 3
+--R                 - 240A b d e  + (360A b c + 180B b )d e
+--R               + 
+--R                          2             4 2         2 5
+--R                 (- 144A c  - 288B b c)d e  + 120B c d e
+--R            *
+--R               m
+--R        *
+--R           x
+--R       + 
+--R             2 3 3 3         2 3 3                    2  4 2  2
+--R         2A b d e m  + (30A b d e  + (- 12A b c - 6B b )d e )m
+--R       + 
+--R                2 3 3                      2  4 2         2            5
+--R         (148A b d e  + (- 132A b c - 66B b )d e  + (24A c  + 48B b c)d e)m
+--R       + 
+--R               2 3 3                       2  4 2          2             5
+--R         240A b d e  + (- 360A b c - 180B b )d e  + (144A c  + 288B b c)d e
+--R       + 
+--R                 2 6
+--R         - 120B c d
+--R    *
+--R         m log(e x + d)
+--R       %e
+--R  /
+--R      6 6      6 5       6 4       6 3        6 2        6        6
+--R     e m  + 21e m  + 175e m  + 735e m  + 1624e m  + 1764e m + 720e
+--R                                         Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)
+--R                  2 6 5        2 6 4        2 6 3         2 6 2         2 6
+--R               B c e m  + 15B c e m  + 85B c e m  + 225B c e m  + 274B c e m
+--R             + 
+--R                     2 6
+--R               120B c e
+--R          *
+--R              6
+--R             x
+--R         + 
+--R                    2           6      2   5  5
+--R               ((A c  + 2B b c)e  + B c d e )m
+--R             + 
+--R                      2            6        2   5  4
+--R               ((16A c  + 32B b c)e  + 10B c d e )m
+--R             + 
+--R                      2             6        2   5  3
+--R               ((95A c  + 190B b c)e  + 35B c d e )m
+--R             + 
+--R                       2             6        2   5  2
+--R               ((260A c  + 520B b c)e  + 50B c d e )m
+--R             + 
+--R                       2             6        2   5            2             6
+--R               ((324A c  + 648B b c)e  + 24B c d e )m + (144A c  + 288B b c)e
+--R          *
+--R              5
+--R             x
+--R         + 
+--R                             2  6       2             5  5
+--R               ((2A b c + B b )e  + (A c  + 2B b c)d e )m
+--R             + 
+--R                                2  6         2              5       2 2 4  4
+--R               ((34A b c + 17B b )e  + (12A c  + 24B b c)d e  - 5B c d e )m
+--R             + 
+--R                                  2  6         2              5        2 2 4  3
+--R               ((214A b c + 107B b )e  + (47A c  + 94B b c)d e  - 30B c d e )m
+--R             + 
+--R                                  2  6         2               5        2 2 4  2
+--R               ((614A b c + 307B b )e  + (72A c  + 144B b c)d e  - 55B c d e )m
+--R             + 
+--R                                  2  6         2              5        2 2 4
+--R               ((792A b c + 396B b )e  + (36A c  + 72B b c)d e  - 30B c d e )m
+--R             + 
+--R                                 2  6
+--R               (360A b c + 180B b )e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                   2 6                2    5  5
+--R               (A b e  + (2A b c + B b )d e )m
+--R             + 
+--R                     2 6                   2    5          2           2 4  4
+--R               (18A b e  + (28A b c + 14B b )d e  + (- 4A c  - 8B b c)d e )m
+--R             + 
+--R                         2 6                    2    5
+--R                   121A b e  + (130A b c + 65B b )d e
+--R                 + 
+--R                           2            2 4        2 3 3
+--R                   (- 36A c  - 72B b c)d e  + 20B c d e
+--R              *
+--R                  3
+--R                 m
+--R             + 
+--R                         2 6                     2    5
+--R                   372A b e  + (224A b c + 112B b )d e
+--R                 + 
+--R                           2             2 4        2 3 3
+--R                   (- 80A c  - 160B b c)d e  + 60B c d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                         2 6                    2    5
+--R                   508A b e  + (120A b c + 60B b )d e
+--R                 + 
+--R                           2            2 4        2 3 3
+--R                   (- 48A c  - 96B b c)d e  + 40B c d e
+--R              *
+--R                 m
+--R             + 
+--R                     2 6
+--R               240A b e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                  2   5 5         2   5                   2  2 4  4
+--R               A b d e m  + (16A b d e  + (- 6A b c - 3B b )d e )m
+--R             + 
+--R                          2   5                     2  2 4
+--R                     89A b d e  + (- 72A b c - 36B b )d e
+--R                   + 
+--R                           2            3 3
+--R                     (12A c  + 24B b c)d e
+--R              *
+--R                  3
+--R                 m
+--R             + 
+--R                         2   5                       2  2 4
+--R                   194A b d e  + (- 246A b c - 123B b )d e
+--R                 + 
+--R                         2             3 3        2 4 2
+--R                   (84A c  + 168B b c)d e  - 60B c d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                         2   5                      2  2 4
+--R                   120A b d e  + (- 180A b c - 90B b )d e
+--R                 + 
+--R                         2             3 3        2 4 2
+--R                   (72A c  + 144B b c)d e  - 60B c d e
+--R              *
+--R                 m
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                     2 2 4 4           2 2 4                  2  3 3  3
+--R               - 2A b d e m  + (- 30A b d e  + (12A b c + 6B b )d e )m
+--R             + 
+--R                           2 2 4                    2  3 3
+--R                   - 148A b d e  + (132A b c + 66B b )d e
+--R                 + 
+--R                           2            4 2
+--R                   (- 24A c  - 48B b c)d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                           2 2 4                     2  3 3
+--R                   - 240A b d e  + (360A b c + 180B b )d e
+--R                 + 
+--R                            2             4 2         2 5
+--R                   (- 144A c  - 288B b c)d e  + 120B c d e
+--R              *
+--R                 m
+--R          *
+--R             x
+--R         + 
+--R               2 3 3 3         2 3 3                    2  4 2  2
+--R           2A b d e m  + (30A b d e  + (- 12A b c - 6B b )d e )m
+--R         + 
+--R                  2 3 3                      2  4 2         2            5
+--R           (148A b d e  + (- 132A b c - 66B b )d e  + (24A c  + 48B b c)d e)m
+--R         + 
+--R                 2 3 3                       2  4 2          2             5
+--R           240A b d e  + (- 360A b c - 180B b )d e  + (144A c  + 288B b c)d e
+--R         + 
+--R                   2 6
+--R           - 120B c d
+--R      *
+--R           m log(e x + d)
+--R         %e
+--R     + 
+--R               2 5        2 4        2 3         2 2         2          2
+--R         (- B c m  - 15B c m  - 85B c m  - 225B c m  - 274B c m - 120B c )
+--R      *
+--R                  m + 6
+--R         (e x + d)
+--R     + 
+--R                  2                  2   5            2                    2   4
+--R           ((- A c  - 2B b c)e + 5B c d)m  + ((- 16A c  - 32B b c)e + 80B c d)m
+--R         + 
+--R                    2                      2   3
+--R           ((- 95A c  - 190B b c)e + 475B c d)m
+--R         + 
+--R                     2                       2   2
+--R           ((- 260A c  - 520B b c)e + 1300B c d)m
+--R         + 
+--R                     2                       2               2
+--R           ((- 324A c  - 648B b c)e + 1620B c d)m + (- 144A c  - 288B b c)e
+--R         + 
+--R                 2
+--R           720B c d
+--R      *
+--R                  m + 5
+--R         (e x + d)
+--R     + 
+--R                           2  2        2                     2 2  5
+--R           ((- 2A b c - B b )e  + (4A c  + 8B b c)d e - 10B c d )m
+--R         + 
+--R                              2  2         2                        2 2  4
+--R           ((- 34A b c - 17B b )e  + (68A c  + 136B b c)d e - 170B c d )m
+--R         + 
+--R                                2  2          2                         2 2  3
+--R           ((- 214A b c - 107B b )e  + (428A c  + 856B b c)d e - 1070B c d )m
+--R         + 
+--R                                2  2           2                          2 2  2
+--R           ((- 614A b c - 307B b )e  + (1228A c  + 2456B b c)d e - 3070B c d )m
+--R         + 
+--R                                2  2           2                          2 2
+--R           ((- 792A b c - 396B b )e  + (1584A c  + 3168B b c)d e - 3960B c d )m
+--R         + 
+--R                               2  2          2                          2 2
+--R           (- 360A b c - 180B b )e  + (720A c  + 1440B b c)d e - 1800B c d
+--R      *
+--R                  m + 4
+--R         (e x + d)
+--R     + 
+--R                      2 3                 2    2          2            2
+--R                 - A b e  + (6A b c + 3B b )d e  + (- 6A c  - 12B b c)d e
+--R               + 
+--R                      2 3
+--R                 10B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                      2 3                    2    2            2             2
+--R               - 18A b e  + (108A b c + 54B b )d e  + (- 108A c  - 216B b c)d e
+--R             + 
+--R                     2 3
+--R               180B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                       2 3                     2    2
+--R               - 121A b e  + (726A b c + 363B b )d e
+--R             + 
+--R                        2              2           2 3
+--R               (- 726A c  - 1452B b c)d e + 1210B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                       2 3                       2    2
+--R               - 372A b e  + (2232A b c + 1116B b )d e
+--R             + 
+--R                         2              2           2 3
+--R               (- 2232A c  - 4464B b c)d e + 3720B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                       2 3                       2    2
+--R               - 508A b e  + (3048A b c + 1524B b )d e
+--R             + 
+--R                         2              2           2 3
+--R               (- 3048A c  - 6096B b c)d e + 5080B c d
+--R          *
+--R             m
+--R         + 
+--R                   2 3                      2    2             2              2
+--R           - 240A b e  + (1440A b c + 720B b )d e  + (- 1440A c  - 2880B b c)d e
+--R         + 
+--R                  2 3
+--R           2400B c d
+--R      *
+--R                  m + 3
+--R         (e x + d)
+--R     + 
+--R                     2   3                   2  2 2        2           3
+--R                 2A b d e  + (- 6A b c - 3B b )d e  + (4A c  + 8B b c)d e
+--R               + 
+--R                       2 4
+--R                 - 5B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                    2   3                      2  2 2         2             3
+--R               38A b d e  + (- 114A b c - 57B b )d e  + (76A c  + 152B b c)d e
+--R             + 
+--R                      2 4
+--R               - 95B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                     2   3                       2  2 2
+--R               274A b d e  + (- 822A b c - 411B b )d e
+--R             + 
+--R                      2              3          2 4
+--R               (548A c  + 1096B b c)d e - 685B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                     2   3                         2  2 2
+--R               922A b d e  + (- 2766A b c - 1383B b )d e
+--R             + 
+--R                       2              3           2 4
+--R               (1844A c  + 3688B b c)d e - 2305B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                      2   3                         2  2 2
+--R               1404A b d e  + (- 4212A b c - 2106B b )d e
+--R             + 
+--R                       2              3           2 4
+--R               (2808A c  + 5616B b c)d e - 3510B c d
+--R          *
+--R             m
+--R         + 
+--R                 2   3                         2  2 2
+--R           720A b d e  + (- 2160A b c - 1080B b )d e
+--R         + 
+--R                   2              3           2 4
+--R           (1440A c  + 2880B b c)d e - 1800B c d
+--R      *
+--R                  m + 2
+--R         (e x + d)
+--R     + 
+--R                 2 2 3                2  3 2         2           4       2 5  5
+--R           (- A b d e  + (2A b c + B b )d e  + (- A c  - 2B b c)d e + B c d )m
+--R         + 
+--R                      2 2 3                   2  3 2           2            4
+--R               - 20A b d e  + (40A b c + 20B b )d e  + (- 20A c  - 40B b c)d e
+--R             + 
+--R                    2 5
+--R               20B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                       2 2 3                     2  3 2
+--R               - 155A b d e  + (310A b c + 155B b )d e
+--R             + 
+--R                        2             4          2 5
+--R               (- 155A c  - 310B b c)d e + 155B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                       2 2 3                      2  3 2
+--R               - 580A b d e  + (1160A b c + 580B b )d e
+--R             + 
+--R                        2              4          2 5
+--R               (- 580A c  - 1160B b c)d e + 580B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                        2 2 3                       2  3 2
+--R               - 1044A b d e  + (2088A b c + 1044B b )d e
+--R             + 
+--R                         2              4           2 5
+--R               (- 1044A c  - 2088B b c)d e + 1044B c d
+--R          *
+--R             m
+--R         + 
+--R                   2 2 3                      2  3 2
+--R           - 720A b d e  + (1440A b c + 720B b )d e
+--R         + 
+--R                    2              4          2 5
+--R           (- 720A c  - 1440B b c)d e + 720B c d
+--R      *
+--R                  m + 1
+--R         (e x + d)
+--R  /
+--R      6 6      6 5       6 4       6 3        6 2        6        6
+--R     e m  + 21e m  + 175e m  + 735e m  + 1624e m  + 1764e m + 720e
+--R                                                    Type: Expression(Integer)
+--E 74
+
+--S 75 of 1457
+d0:=normalize(D(m0,x))
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 1457
+t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R        2 4 9        2           4       2   3  8
+--R     B c e x  + ((A c  + 2B b c)e  + 4B c d e )x
+--R   + 
+--R                   2  4        2             3       2 2 2  7
+--R     ((2A b c + B b )e  + (4A c  + 8B b c)d e  + 6B c d e )x
+--R   + 
+--R         2 4                 2    3        2            2 2       2 3   6
+--R     (A b e  + (8A b c + 4B b )d e  + (6A c  + 12B b c)d e  + 4B c d e)x
+--R   + 
+--R          2   3                  2  2 2        2           3       2 4  5
+--R     (4A b d e  + (12A b c + 6B b )d e  + (4A c  + 8B b c)d e + B c d )x
+--R   + 
+--R          2 2 2                 2  3        2           4  4
+--R     (6A b d e  + (8A b c + 4B b )d e + (A c  + 2B b c)d )x
+--R   + 
+--R          2 3                 2  4  3      2 4 2
+--R     (4A b d e + (2A b c + B b )d )x  + A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 76
+
+--S 77 of 1457
+r0:=-1/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^5/e^6+1/6*d*(c*d-b*e)*(B*d*_
+     (5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^6/e^6+1/7*(A*e*(6*c^2*d^2-_
+     6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_
+     (d+e*x)^7/e^6-1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_
+     b^2*e^2))*(d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_
+     (d+e*x)^9/e^6+1/10*B*c^2*(d+e*x)^10/e^6
+--R 
+--R
+--R   (2)
+--R        1    2 10 10     1    2   2        10   4    2   9  9
+--R       -- B c e  x   + ((- A c  + - B b c)e   + - B c d e )x
+--R       10                9        9             9
+--R     + 
+--R         1         1    2  10    1    2            9   3    2 2 8  8
+--R       ((- A b c + - B b )e   + (- A c  + B b c)d e  + - B c d e )x
+--R         4         8             2                     4
+--R     + 
+--R           1    2 10    8         4    2    9    6    2   12        2 8
+--R           - A b e   + (- A b c + - B b )d e  + (- A c  + -- B b c)d e
+--R           7            7         7              7         7
+--R         + 
+--R           4    2 3 7
+--R           - B c d e
+--R           7
+--R      *
+--R          7
+--R         x
+--R     + 
+--R             2    2   9                2  2 8    2    2   4        3 7
+--R             - A b d e  + (2A b c + B b )d e  + (- A c  + - B b c)d e
+--R             3                                   3        3
+--R           + 
+--R             1    2 4 6
+--R             - B c d e
+--R             6
+--R      *
+--R          6
+--R         x
+--R     + 
+--R        6    2 2 8    8         4    2  3 7    1    2   2        4 6  5
+--R       (- A b d e  + (- A b c + - B b )d e  + (- A c  + - B b c)d e )x
+--R        5             5         5              5        5
+--R     + 
+--R           2 3 7    1         1    2  4 6  4   1    2 4 6 3    1     2 7 3
+--R       (A b d e  + (- A b c + - B b )d e )x  + - A b d e x  + --- A b d e
+--R                    2         4                3              105
+--R     + 
+--R           1           1     2  8 2     1     2    1         9      1     2 10
+--R       (- --- A b c - --- B b )d e  + (--- A c  + --- B b c)d e - ---- B c d
+--R          140         280              630        315             1260
+--R  /
+--R      6
+--R     e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 77
+
+--S 78 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R      1    2 4 10     1    2   2        4   4    2   3  9
+--R     -- B c e x   + ((- A c  + - B b c)e  + - B c d e )x
+--R     10               9        9            9
+--R   + 
+--R       1         1    2  4    1    2            3   3    2 2 2  8
+--R     ((- A b c + - B b )e  + (- A c  + B b c)d e  + - B c d e )x
+--R       4         8            2                     4
+--R   + 
+--R      1    2 4    8         4    2    3    6    2   12        2 2   4    2 3   7
+--R     (- A b e  + (- A b c + - B b )d e  + (- A c  + -- B b c)d e  + - B c d e)x
+--R      7           7         7              7         7              7
+--R   + 
+--R      2    2   3                2  2 2    2    2   4        3    1    2 4  6
+--R     (- A b d e  + (2A b c + B b )d e  + (- A c  + - B b c)d e + - B c d )x
+--R      3                                   3        3             6
+--R   + 
+--R      6    2 2 2    8         4    2  3     1    2   2        4  5
+--R     (- A b d e  + (- A b c + - B b )d e + (- A c  + - B b c)d )x
+--R      5             5         5             5        5
+--R   + 
+--R         2 3     1         1    2  4  4   1    2 4 3
+--R     (A b d e + (- A b c + - B b )d )x  + - A b d x
+--R                 2         4              3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 78
+
+--S 79 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)
+--R          1     2 7 3     1           1     2  8 2       1     2    1         9
+--R       - --- A b d e  + (--- A b c + --- B b )d e  + (- --- A c  - --- B b c)d e
+--R         105             140         280                630        315
+--R     + 
+--R         1     2 10
+--R       ---- B c d
+--R       1260
+--R  /
+--R      6
+--R     e
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 79
+
+--S 80 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                Type: Fraction(Polynomial(Fraction(Integer)))
+--E 80
+
+)clear all
+
+--S 81 of 1457
+t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R        2 3 8        2           3       2   2  7
+--R     B c e x  + ((A c  + 2B b c)e  + 3B c d e )x
+--R   + 
+--R                   2  3        2             2       2 2   6
+--R     ((2A b c + B b )e  + (3A c  + 6B b c)d e  + 3B c d e)x
+--R   + 
+--R         2 3                 2    2        2           2       2 3  5
+--R     (A b e  + (6A b c + 3B b )d e  + (3A c  + 6B b c)d e + B c d )x
+--R   + 
+--R          2   2                 2  2        2           3  4
+--R     (3A b d e  + (6A b c + 3B b )d e + (A c  + 2B b c)d )x
+--R   + 
+--R          2 2                 2  3  3      2 3 2
+--R     (3A b d e + (2A b c + B b )d )x  + A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 81
+
+--S 82 of 1457
+r0:=1/3*A*b^2*d^3*x^3+1/4*b*d^2*(b*B*d+2*A*c*d+3*A*b*e)*x^4+1/5*d*(A*c^2*_
+     d^2+3*b^2*e*(B*d+A*e)+2*b*c*d*(B*d+3*A*e))*x^5+1/6*(A*e*(3*c^2*d^2+_
+     6*b*c*d*e+b^2*e^2)+B*d*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^6+1/7*e*_
+     (A*c*e*(3*c*d+2*b*e)+B*(3*c^2*d^2+6*b*c*d*e+b^2*e^2))*x^7+_
+     1/8*c*e^2*(3*B*c*d+2*b*B*e+A*c*e)*x^8+1/9*B*c^2*e^3*x^9
+--R 
+--R
+--R   (2)
+--R     1    2 3 9     1    2   1        3   3    2   2  8
+--R     - B c e x  + ((- A c  + - B b c)e  + - B c d e )x
+--R     9              8        4            8
+--R   + 
+--R       2         1    2  3    3    2   6          2   3    2 2   7
+--R     ((- A b c + - B b )e  + (- A c  + - B b c)d e  + - B c d e)x
+--R       7         7            7        7              7
+--R   + 
+--R      1    2 3            1    2    2    1    2          2    1    2 3  6
+--R     (- A b e  + (A b c + - B b )d e  + (- A c  + B b c)d e + - B c d )x
+--R      6                   2              2                    6
+--R   + 
+--R      3    2   2    6         3    2  2     1    2   2        3  5
+--R     (- A b d e  + (- A b c + - B b )d e + (- A c  + - B b c)d )x
+--R      5             5         5             5        5
+--R   + 
+--R      3    2 2     1         1    2  3  4   1    2 3 3
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      4            2         4              3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 82
+
+--S 83 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1    2 3 9     1    2   1        3   3    2   2  8
+--R     - B c e x  + ((- A c  + - B b c)e  + - B c d e )x
+--R     9              8        4            8
+--R   + 
+--R       2         1    2  3    3    2   6          2   3    2 2   7
+--R     ((- A b c + - B b )e  + (- A c  + - B b c)d e  + - B c d e)x
+--R       7         7            7        7              7
+--R   + 
+--R      1    2 3            1    2    2    1    2          2    1    2 3  6
+--R     (- A b e  + (A b c + - B b )d e  + (- A c  + B b c)d e + - B c d )x
+--R      6                   2              2                    6
+--R   + 
+--R      3    2   2    6         3    2  2     1    2   2        3  5
+--R     (- A b d e  + (- A b c + - B b )d e + (- A c  + - B b c)d )x
+--R      5             5         5             5        5
+--R   + 
+--R      3    2 2     1         1    2  3  4   1    2 3 3
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      4            2         4              3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 83
+
+--S 84 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 84
+
+--S 85 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 85
+
+)clear all
+
+--S 86 of 1457
+t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R        2 2 7        2           2       2     6
+--R     B c e x  + ((A c  + 2B b c)e  + 2B c d e)x
+--R   + 
+--R                   2  2        2                   2 2  5
+--R     ((2A b c + B b )e  + (2A c  + 4B b c)d e + B c d )x
+--R   + 
+--R         2 2                 2           2           2  4
+--R     (A b e  + (4A b c + 2B b )d e + (A c  + 2B b c)d )x
+--R   + 
+--R          2                   2  2  3      2 2 2
+--R     (2A b d e + (2A b c + B b )d )x  + A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 86
+
+--S 87 of 1457
+r0:=1/3*A*b^2*d^2*x^3+1/4*b*d*(b*B*d+2*A*c*d+2*A*b*e)*x^4+1/5*(A*c^2*d^2+_
+     b^2*e*(2*B*d+A*e)+2*b*c*d*(B*d+2*A*e))*x^5+1/6*(2*A*c*e*(c*d+b*e)+_
+     B*(c^2*d^2+4*b*c*d*e+b^2*e^2))*x^6+1/7*c*e*(A*c*e+2*B*(c*d+b*e))*_
+     x^7+1/8*B*c^2*e^2*x^8
+--R 
+--R
+--R   (2)
+--R     1    2 2 8     1    2   2        2   2    2     7
+--R     - B c e x  + ((- A c  + - B b c)e  + - B c d e)x
+--R     8              7        7            7
+--R   + 
+--R       1         1    2  2    1    2   2             1    2 2  6
+--R     ((- A b c + - B b )e  + (- A c  + - B b c)d e + - B c d )x
+--R       3         6            3        3             6
+--R   + 
+--R      1    2 2    4         2    2        1    2   2        2  5
+--R     (- A b e  + (- A b c + - B b )d e + (- A c  + - B b c)d )x
+--R      5           5         5             5        5
+--R   + 
+--R      1    2       1         1    2  2  4   1    2 2 3
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      2            2         4              3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 87
+
+--S 88 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1    2 2 8     1    2   2        2   2    2     7
+--R     - B c e x  + ((- A c  + - B b c)e  + - B c d e)x
+--R     8              7        7            7
+--R   + 
+--R       1         1    2  2    1    2   2             1    2 2  6
+--R     ((- A b c + - B b )e  + (- A c  + - B b c)d e + - B c d )x
+--R       3         6            3        3             6
+--R   + 
+--R      1    2 2    4         2    2        1    2   2        2  5
+--R     (- A b e  + (- A b c + - B b )d e + (- A c  + - B b c)d )x
+--R      5           5         5             5        5
+--R   + 
+--R      1    2       1         1    2  2  4   1    2 2 3
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      2            2         4              3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 88
+
+--S 89 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 89
+
+--S 90 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 90
+
+)clear all
+
+--S 91 of 1457
+t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R        2   6        2                 2   5
+--R     B c e x  + ((A c  + 2B b c)e + B c d)x
+--R   + 
+--R                   2         2             4       2                 2    3
+--R     ((2A b c + B b )e + (A c  + 2B b c)d)x  + (A b e + (2A b c + B b )d)x
+--R   + 
+--R        2   2
+--R     A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 91
+
+--S 92 of 1457
+r0:=1/3*A*b^2*d*x^3+1/4*b*(b*B*d+2*A*c*d+A*b*e)*x^4+1/5*(A*c^2*d+b^2*B*e+_
+     2*b*c*(B*d+A*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7
+--R 
+--R
+--R   (2)
+--R     1    2   7     1    2   1           1    2   6
+--R     - B c e x  + ((- A c  + - B b c)e + - B c d)x
+--R     7              6        3           6
+--R   + 
+--R       2         1    2      1    2   2          5
+--R     ((- A b c + - B b )e + (- A c  + - B b c)d)x
+--R       5         5           5        5
+--R   + 
+--R      1    2     1         1    2    4   1    2   3
+--R     (- A b e + (- A b c + - B b )d)x  + - A b d x
+--R      4          2         4             3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 92
+
+--S 93 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1    2   7     1    2   1           1    2   6
+--R     - B c e x  + ((- A c  + - B b c)e + - B c d)x
+--R     7              6        3           6
+--R   + 
+--R       2         1    2      1    2   2          5
+--R     ((- A b c + - B b )e + (- A c  + - B b c)d)x
+--R       5         5           5        5
+--R   + 
+--R      1    2     1         1    2    4   1    2   3
+--R     (- A b e + (- A b c + - B b )d)x  + - A b d x
+--R      4          2         4             3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 93
+
+--S 94 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 94
+
+--S 95 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 95
+
+)clear all
+
+--S 96 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R   (1)  B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R                                                    Type: Polynomial(Integer)
+--E 96
+
+--S 97 of 1457
+r0:=1/3*A*b^2*x^3+1/4*b*(b*B+2*A*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6
+--R 
+--R
+--R        1    2 6    1    2   2        5    1         1    2  4   1    2 3
+--R   (2)  - B c x  + (- A c  + - B b c)x  + (- A b c + - B b )x  + - A b x
+--R        6           5        5             2         4           3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 97
+
+--S 98 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R        1    2 6    1    2   2        5    1         1    2  4   1    2 3
+--R   (3)  - B c x  + (- A c  + - B b c)x  + (- A b c + - B b )x  + - A b x
+--R        6           5        5             2         4           3
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 98
+
+--S 99 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 99
+
+--S 100 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 100
+
+)clear all
+
+--S 101 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R        B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R   (1)  -------------------------------------------------------
+--R                                e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 1457
+r0:=d*(B*d-A*e)*(c*d-b*e)^2*x/e^5-1/2*(B*d-A*e)*(c*d-b*e)^2*x^2/e^4-_
+     1/3*(A*c*e*(c*d-2*b*e)-B*(c*d-b*e)^2)*x^3/e^3-1/4*c*(B*c*d-2*b*B*e-_
+     A*c*e)*x^4/e^2+1/5*B*c^2*x^5/e-d^2*(B*d-A*e)*(c*d-b*e)^2*log(d+e*x)/e^6
+--R 
+--R
+--R   (2)
+--R                2 2 3                      2  3 2         2             4
+--R           60A b d e  + (- 120A b c - 60B b )d e  + (60A c  + 120B b c)d e
+--R         + 
+--R                  2 5
+--R           - 60B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R            2 5 5          2            5        2   4  4
+--R       12B c e x  + ((15A c  + 30B b c)e  - 15B c d e )x
+--R     + 
+--R                        2  5           2              4        2 2 3  3
+--R       ((40A b c + 20B b )e  + (- 20A c  - 40B b c)d e  + 20B c d e )x
+--R     + 
+--R                2 5                     2    4         2            2 3
+--R           30A b e  + (- 60A b c - 30B b )d e  + (30A c  + 60B b c)d e
+--R         + 
+--R                  2 3 2
+--R           - 30B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                  2   4                    2  2 3           2             3 2
+--R           - 60A b d e  + (120A b c + 60B b )d e  + (- 60A c  - 120B b c)d e
+--R         + 
+--R                2 4
+--R           60B c d e
+--R      *
+--R         x
+--R  /
+--R        6
+--R     60e
+--R                                                    Type: Expression(Integer)
+--E 102
+
+--S 103 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                2 2 3                      2  3 2         2             4
+--R           60A b d e  + (- 120A b c - 60B b )d e  + (60A c  + 120B b c)d e
+--R         + 
+--R                  2 5
+--R           - 60B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R            2 5 5          2            5        2   4  4
+--R       12B c e x  + ((15A c  + 30B b c)e  - 15B c d e )x
+--R     + 
+--R                        2  5           2              4        2 2 3  3
+--R       ((40A b c + 20B b )e  + (- 20A c  - 40B b c)d e  + 20B c d e )x
+--R     + 
+--R                2 5                     2    4         2            2 3
+--R           30A b e  + (- 60A b c - 30B b )d e  + (30A c  + 60B b c)d e
+--R         + 
+--R                  2 3 2
+--R           - 30B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                  2   4                    2  2 3           2             3 2
+--R           - 60A b d e  + (120A b c + 60B b )d e  + (- 60A c  - 120B b c)d e
+--R         + 
+--R                2 4
+--R           60B c d e
+--R      *
+--R         x
+--R  /
+--R        6
+--R     60e
+--R                                         Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 104
+
+--S 105 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^2
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R        B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R   (1)  -------------------------------------------------------
+--R                            2 2             2
+--R                           e x  + 2d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 1457
+r0:=-(c*d-b*e)*(2*B*d*(2*c*d-b*e)-A*e*(3*c*d-b*e))*x/e^5+1/2*(c*d-b*e)*_
+     (3*B*c*d-b*B*e-2*A*c*e)*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+_
+     1/4*B*c^2*x^4/e^2+d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x))+d*_
+     (c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*log(d+e*x)/e^6
+--R 
+--R
+--R   (2)
+--R                      2   4                   2  2 3           2            3 2
+--R               - 24A b d e  + (72A b c + 36B b )d e  + (- 48A c  - 96B b c)d e
+--R             + 
+--R                    2 4
+--R               60B c d e
+--R          *
+--R             x
+--R         + 
+--R                  2 2 3                   2  3 2           2            4
+--R           - 24A b d e  + (72A b c + 36B b )d e  + (- 48A c  - 96B b c)d e
+--R         + 
+--R                2 5
+--R           60B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           2 5 5         2           5       2   4  4
+--R       3B c e x  + ((4A c  + 8B b c)e  - 5B c d e )x
+--R     + 
+--R                       2  5          2              4        2 2 3  3
+--R       ((12A b c + 6B b )e  + (- 8A c  - 16B b c)d e  + 10B c d e )x
+--R     + 
+--R                2 5                     2    4         2            2 3
+--R           12A b e  + (- 36A b c - 18B b )d e  + (24A c  + 48B b c)d e
+--R         + 
+--R                  2 3 2
+--R           - 30B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                2   4                     2  2 3         2            3 2
+--R           12A b d e  + (- 48A b c - 24B b )d e  + (36A c  + 72B b c)d e
+--R         + 
+--R                  2 4
+--R           - 48B c d e
+--R      *
+--R         x
+--R     + 
+--R            2 2 3                   2  3 2           2            4         2 5
+--R     - 12A b d e  + (24A b c + 12B b )d e  + (- 12A c  - 24B b c)d e + 12B c d
+--R  /
+--R        7         6
+--R     12e x + 12d e
+--R                                                    Type: Expression(Integer)
+--E 107
+
+--S 108 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                      2   4                   2  2 3           2            3 2
+--R               - 24A b d e  + (72A b c + 36B b )d e  + (- 48A c  - 96B b c)d e
+--R             + 
+--R                    2 4
+--R               60B c d e
+--R          *
+--R             x
+--R         + 
+--R                  2 2 3                   2  3 2           2            4
+--R           - 24A b d e  + (72A b c + 36B b )d e  + (- 48A c  - 96B b c)d e
+--R         + 
+--R                2 5
+--R           60B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           2 5 5         2           5       2   4  4
+--R       3B c e x  + ((4A c  + 8B b c)e  - 5B c d e )x
+--R     + 
+--R                       2  5          2              4        2 2 3  3
+--R       ((12A b c + 6B b )e  + (- 8A c  - 16B b c)d e  + 10B c d e )x
+--R     + 
+--R                2 5                     2    4         2            2 3
+--R           12A b e  + (- 36A b c - 18B b )d e  + (24A c  + 48B b c)d e
+--R         + 
+--R                  2 3 2
+--R           - 30B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                2   4                     2  2 3         2            3 2
+--R           12A b d e  + (- 48A b c - 24B b )d e  + (36A c  + 72B b c)d e
+--R         + 
+--R                  2 4
+--R           - 48B c d e
+--R      *
+--R         x
+--R     + 
+--R            2 2 3                   2  3 2           2            4         2 5
+--R     - 12A b d e  + (24A b c + 12B b )d e  + (- 12A c  - 24B b c)d e + 12B c d
+--R  /
+--R        7         6
+--R     12e x + 12d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 109
+
+--S 110 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^3
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R        B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R   (1)  -------------------------------------------------------
+--R                       3 3       2 2     2       3
+--R                      e x  + 3d e x  + 3d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 1457
+r0:=-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2-6*b*c*d*e+b^2*e^2))*x/e^5-1/2*c*_
+     (3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*d^2*(B*d-A*e)*_
+     (c*d-b*e)^2/(e^6*(d+e*x)^2)-d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*_
+     (2*c*d-b*e))/(e^6*(d+e*x))+(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-_
+     B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*log(d+e*x)/e^6
+--R 
+--R
+--R   (2)
+--R                   2 5                     2    4         2            2 3
+--R               6A b e  + (- 36A b c - 18B b )d e  + (36A c  + 72B b c)d e
+--R             + 
+--R                      2 3 2
+--R               - 60B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    2   4                     2  2 3         2             3 2
+--R               12A b d e  + (- 72A b c - 36B b )d e  + (72A c  + 144B b c)d e
+--R             + 
+--R                       2 4
+--R               - 120B c d e
+--R          *
+--R             x
+--R         + 
+--R             2 2 3                     2  3 2         2            4         2 5
+--R         6A b d e  + (- 36A b c - 18B b )d e  + (36A c  + 72B b c)d e - 60B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           2 5 5         2           5       2   4  4
+--R       2B c e x  + ((3A c  + 6B b c)e  - 5B c d e )x
+--R     + 
+--R                       2  5           2              4        2 2 3  3
+--R       ((12A b c + 6B b )e  + (- 12A c  - 24B b c)d e  + 20B c d e )x
+--R     + 
+--R                        2    4           2            2 3        2 3 2  2
+--R       ((24A b c + 12B b )d e  + (- 33A c  - 66B b c)d e  + 63B c d e )x
+--R     + 
+--R                2   4                     2  2 3        2            3 2
+--R           12A b d e  + (- 24A b c - 12B b )d e  + (6A c  + 12B b c)d e
+--R         + 
+--R               2 4
+--R           6B c d e
+--R      *
+--R         x
+--R     + 
+--R           2 2 3                     2  3 2         2            4         2 5
+--R       9A b d e  + (- 30A b c - 15B b )d e  + (21A c  + 42B b c)d e - 27B c d
+--R  /
+--R       8 2        7      2 6
+--R     6e x  + 12d e x + 6d e
+--R                                                    Type: Expression(Integer)
+--E 112
+
+--S 113 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                   2 5                     2    4         2            2 3
+--R               6A b e  + (- 36A b c - 18B b )d e  + (36A c  + 72B b c)d e
+--R             + 
+--R                      2 3 2
+--R               - 60B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    2   4                     2  2 3         2             3 2
+--R               12A b d e  + (- 72A b c - 36B b )d e  + (72A c  + 144B b c)d e
+--R             + 
+--R                       2 4
+--R               - 120B c d e
+--R          *
+--R             x
+--R         + 
+--R             2 2 3                     2  3 2         2            4         2 5
+--R         6A b d e  + (- 36A b c - 18B b )d e  + (36A c  + 72B b c)d e - 60B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           2 5 5         2           5       2   4  4
+--R       2B c e x  + ((3A c  + 6B b c)e  - 5B c d e )x
+--R     + 
+--R                       2  5           2              4        2 2 3  3
+--R       ((12A b c + 6B b )e  + (- 12A c  - 24B b c)d e  + 20B c d e )x
+--R     + 
+--R                        2    4           2            2 3        2 3 2  2
+--R       ((24A b c + 12B b )d e  + (- 33A c  - 66B b c)d e  + 63B c d e )x
+--R     + 
+--R                2   4                     2  2 3        2            3 2
+--R           12A b d e  + (- 24A b c - 12B b )d e  + (6A c  + 12B b c)d e
+--R         + 
+--R               2 4
+--R           6B c d e
+--R      *
+--R         x
+--R     + 
+--R           2 2 3                     2  3 2         2            4         2 5
+--R       9A b d e  + (- 30A b c - 15B b )d e  + (21A c  + 42B b c)d e - 27B c d
+--R  /
+--R       8 2        7      2 6
+--R     6e x  + 12d e x + 6d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 114
+
+--S 115 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^4
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R        B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R   (1)  -------------------------------------------------------
+--R                  4 4       3 3     2 2 2     3       4
+--R                 e x  + 4d e x  + 6d e x  + 4d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 1457
+r0:=-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*d^2*(B*d-A*e)*_
+     (c*d-b*e)^2/(e^6*(d+e*x)^3)-1/2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_
+     2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^2)+(-A*e*(6*c^2*d^2-6*b*c*d*e+_
+     b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x))-_
+     (2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*log(d+e*x)/e^6
+--R 
+--R
+--R   (2)
+--R                           2  5           2              4        2 2 3  3
+--R           ((12A b c + 6B b )e  + (- 24A c  - 48B b c)d e  + 60B c d e )x
+--R         + 
+--R                            2    4           2             2 3         2 3 2  2
+--R           ((36A b c + 18B b )d e  + (- 72A c  - 144B b c)d e  + 180B c d e )x
+--R         + 
+--R                            2  2 3           2             3 2         2 4
+--R           ((36A b c + 18B b )d e  + (- 72A c  - 144B b c)d e  + 180B c d e)x
+--R         + 
+--R                          2  3 2           2            4         2 5
+--R           (12A b c + 6B b )d e  + (- 24A c  - 48B b c)d e + 60B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           2 5 5         2            5        2   4  4
+--R       3B c e x  + ((6A c  + 12B b c)e  - 15B c d e )x
+--R     + 
+--R              2              4        2 2 3  3
+--R       ((18A c  + 36B b c)d e  - 63B c d e )x
+--R     + 
+--R                 2 5                   2    4           2            2 3
+--R           - 6A b e  + (36A b c + 18B b )d e  + (- 18A c  - 36B b c)d e
+--R         + 
+--R                 2 3 2
+--R           - 9B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                 2   4                   2  2 3           2             3 2
+--R           - 6A b d e  + (54A b c + 27B b )d e  + (- 54A c  - 108B b c)d e
+--R         + 
+--R                2 4
+--R           81B c d e
+--R      *
+--R         x
+--R     + 
+--R           2 2 3                   2  3 2           2            4         2 5
+--R     - 2A b d e  + (22A b c + 11B b )d e  + (- 26A c  - 52B b c)d e + 47B c d
+--R  /
+--R       9 3        8 2      2 7      3 6
+--R     6e x  + 18d e x  + 18d e x + 6d e
+--R                                                    Type: Expression(Integer)
+--E 117
+
+--S 118 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                           2  5           2              4        2 2 3  3
+--R           ((12A b c + 6B b )e  + (- 24A c  - 48B b c)d e  + 60B c d e )x
+--R         + 
+--R                            2    4           2             2 3         2 3 2  2
+--R           ((36A b c + 18B b )d e  + (- 72A c  - 144B b c)d e  + 180B c d e )x
+--R         + 
+--R                            2  2 3           2             3 2         2 4
+--R           ((36A b c + 18B b )d e  + (- 72A c  - 144B b c)d e  + 180B c d e)x
+--R         + 
+--R                          2  3 2           2            4         2 5
+--R           (12A b c + 6B b )d e  + (- 24A c  - 48B b c)d e + 60B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           2 5 5         2            5        2   4  4
+--R       3B c e x  + ((6A c  + 12B b c)e  - 15B c d e )x
+--R     + 
+--R              2              4        2 2 3  3
+--R       ((18A c  + 36B b c)d e  - 63B c d e )x
+--R     + 
+--R                 2 5                   2    4           2            2 3
+--R           - 6A b e  + (36A b c + 18B b )d e  + (- 18A c  - 36B b c)d e
+--R         + 
+--R                 2 3 2
+--R           - 9B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                 2   4                   2  2 3           2             3 2
+--R           - 6A b d e  + (54A b c + 27B b )d e  + (- 54A c  - 108B b c)d e
+--R         + 
+--R                2 4
+--R           81B c d e
+--R      *
+--R         x
+--R     + 
+--R           2 2 3                   2  3 2           2            4         2 5
+--R     - 2A b d e  + (22A b c + 11B b )d e  + (- 26A c  - 52B b c)d e + 47B c d
+--R  /
+--R       9 3        8 2      2 7      3 6
+--R     6e x  + 18d e x  + 18d e x + 6d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 119
+
+--S 120 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 1457
+t0:=(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R          3 7       3         2  6          2       2   5        2       3  4
+--R       B c x  + (A c  + 3B b c )x  + (3A b c  + 3B b c)x  + (3A b c + B b )x
+--R     + 
+--R          3 3
+--R       A b x
+--R  *
+--R              m
+--R     (e x + d)
+--R                                                    Type: Expression(Integer)
+--E 121
+
+--S 122 of 1457
+r0:=-d^3*(B*d-A*e)*(c*d-b*e)^3*(d+e*x)^(1+m)/(e^8*(1+m))+d^2*(c*d-b*e)^2*_
+     (B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^8*(2+m))+_
+     3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_
+     8*b*c*d*e+2*b^2*e^2))*(d+e*x)^(3+m)/(e^8*(3+m))+(B*d*(35*c^3*d^3-_
+     60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-A*e*(20*c^3*d^3-30*b*c^2*_
+     d^2*e+12*b^2*c*d*e^2-b^3*e^3))*(d+e*x)^(4+m)/(e^8*(4+m))+(3*A*c*e*_
+     (5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*(35*c^3*d^3-45*b*c^2*d^2*e+15*b^2*_
+     c*d*e^2-b^3*e^3))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-_
+     B*(7*c^2*d^2-6*b*c*d*e+b^2*e^2))*(d+e*x)^(6+m)/(e^8*(6+m))-c^2*_
+     (7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*_
+     (d+e*x)^(8+m)/(e^8*(8+m))
+--R 
+--R
+--R   (2)
+--R              3 7        3 6         3 5          3 4          3 3           3 2
+--R           B c m  + 28B c m  + 322B c m  + 1960B c m  + 6769B c m  + 13132B c m
+--R         + 
+--R                   3           3
+--R           13068B c m + 5040B c
+--R      *
+--R                  m + 8
+--R         (e x + d)
+--R     + 
+--R                3         2         3   7          3          2           3   6
+--R           ((A c  + 3B b c )e - 7B c d)m  + ((29A c  + 87B b c )e - 203B c d)m
+--R         + 
+--R                   3            2            3   5
+--R           ((343A c  + 1029B b c )e - 2401B c d)m
+--R         + 
+--R                    3            2             3   4
+--R           ((2135A c  + 6405B b c )e - 14945B c d)m
+--R         + 
+--R                    3             2             3   3
+--R           ((7504A c  + 22512B b c )e - 52528B c d)m
+--R         + 
+--R                     3             2              3   2
+--R           ((14756A c  + 44268B b c )e - 103292B c d)m
+--R         + 
+--R                     3             2              3
+--R           ((14832A c  + 44496B b c )e - 103824B c d)m
+--R         + 
+--R                   3             2             3
+--R           (5760A c  + 17280B b c )e - 40320B c d
+--R      *
+--R                  m + 7
+--R         (e x + d)
+--R     + 
+--R                   2       2   2          3          2            3 2  7
+--R           ((3A b c  + 3B b c)e  + (- 6A c  - 18B b c )d e + 21B c d )m
+--R         + 
+--R                    2        2   2            3           2             3 2  6
+--R           ((90A b c  + 90B b c)e  + (- 180A c  - 540B b c )d e + 630B c d )m
+--R         + 
+--R                         2          2   2             3            2
+--R               (1098A b c  + 1098B b c)e  + (- 2196A c  - 6588B b c )d e
+--R             + 
+--R                      3 2
+--R               7686B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                         2          2   2              3             2
+--R               (7020A b c  + 7020B b c)e  + (- 14040A c  - 42120B b c )d e
+--R             + 
+--R                       3 2
+--R               49140B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                          2           2   2              3              2
+--R               (25227A b c  + 25227B b c)e  + (- 50454A c  - 151362B b c )d e
+--R             + 
+--R                        3 2
+--R               176589B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                          2           2   2               3              2
+--R               (50490A b c  + 50490B b c)e  + (- 100980A c  - 302940B b c )d e
+--R             + 
+--R                        3 2
+--R               353430B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                          2           2   2               3              2
+--R               (51432A b c  + 51432B b c)e  + (- 102864A c  - 308592B b c )d e
+--R             + 
+--R                        3 2
+--R               360024B c d
+--R          *
+--R             m
+--R         + 
+--R                      2           2   2              3              2
+--R           (20160A b c  + 20160B b c)e  + (- 40320A c  - 120960B b c )d e
+--R         + 
+--R                    3 2
+--R           141120B c d
+--R      *
+--R                  m + 6
+--R         (e x + d)
+--R     + 
+--R                    2       3  3             2        2     2
+--R               (3A b c + B b )e  + (- 15A b c  - 15B b c)d e
+--R             + 
+--R                     3          2  2         3 3
+--R               (15A c  + 45B b c )d e - 35B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                     2         3  3              2         2     2
+--R               (93A b c + 31B b )e  + (- 465A b c  - 465B b c)d e
+--R             + 
+--R                      3            2  2           3 3
+--R               (465A c  + 1395B b c )d e - 1085B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                       2          3  3               2          2     2
+--R               (1173A b c + 391B b )e  + (- 5865A b c  - 5865B b c)d e
+--R             + 
+--R                       3             2  2            3 3
+--R               (5865A c  + 17595B b c )d e - 13685B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                       2           3  3                2           2     2
+--R               (7743A b c + 2581B b )e  + (- 38715A b c  - 38715B b c)d e
+--R             + 
+--R                        3              2  2            3 3
+--R               (38715A c  + 116145B b c )d e - 90335B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                        2           3  3                 2            2     2
+--R               (28632A b c + 9544B b )e  + (- 143160A b c  - 143160B b c)d e
+--R             + 
+--R                         3              2  2             3 3
+--R               (143160A c  + 429480B b c )d e - 334040B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                        2            3  3                 2            2     2
+--R               (58692A b c + 19564B b )e  + (- 293460A b c  - 293460B b c)d e
+--R             + 
+--R                         3              2  2             3 3
+--R               (293460A c  + 880380B b c )d e - 684740B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                        2            3  3                 2            2     2
+--R               (60912A b c + 20304B b )e  + (- 304560A b c  - 304560B b c)d e
+--R             + 
+--R                         3              2  2             3 3
+--R               (304560A c  + 913680B b c )d e - 710640B c d
+--R          *
+--R             m
+--R         + 
+--R                    2           3  3                 2            2     2
+--R           (24192A b c + 8064B b )e  + (- 120960A b c  - 120960B b c)d e
+--R         + 
+--R                     3              2  2             3 3
+--R           (120960A c  + 362880B b c )d e - 282240B c d
+--R      *
+--R                  m + 5
+--R         (e x + d)
+--R     + 
+--R                  3 4           2        3    3           2        2   2 2
+--R               A b e  + (- 12A b c - 4B b )d e  + (30A b c  + 30B b c)d e
+--R             + 
+--R                       3          2  3         3 4
+--R               (- 20A c  - 60B b c )d e + 35B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                    3 4            2          3    3
+--R               32A b e  + (- 384A b c - 128B b )d e
+--R             + 
+--R                        2         2   2 2            3            2  3
+--R               (960A b c  + 960B b c)d e  + (- 640A c  - 1920B b c )d e
+--R             + 
+--R                      3 4
+--R               1120B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                     3 4             2           3    3
+--R               418A b e  + (- 5016A b c - 1672B b )d e
+--R             + 
+--R                          2           2   2 2             3             2  3
+--R               (12540A b c  + 12540B b c)d e  + (- 8360A c  - 25080B b c )d e
+--R             + 
+--R                       3 4
+--R               14630B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                      3 4              2            3    3
+--R               2864A b e  + (- 34368A b c - 11456B b )d e
+--R             + 
+--R                          2           2   2 2              3              2  3
+--R               (85920A b c  + 85920B b c)d e  + (- 57280A c  - 171840B b c )d e
+--R             + 
+--R                        3 4
+--R               100240B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                       3 4               2            3    3
+--R               10993A b e  + (- 131916A b c - 43972B b )d e
+--R             + 
+--R                           2            2   2 2
+--R               (329790A b c  + 329790B b c)d e
+--R             + 
+--R                           3              2  3             3 4
+--R               (- 219860A c  - 659580B b c )d e + 384755B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                       3 4               2            3    3
+--R               23312A b e  + (- 279744A b c - 93248B b )d e
+--R             + 
+--R                           2            2   2 2
+--R               (699360A b c  + 699360B b c)d e
+--R             + 
+--R                           3               2  3             3 4
+--R               (- 466240A c  - 1398720B b c )d e + 815920B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                       3 4               2            3    3
+--R               24876A b e  + (- 298512A b c - 99504B b )d e
+--R             + 
+--R                           2            2   2 2
+--R               (746280A b c  + 746280B b c)d e
+--R             + 
+--R                           3               2  3             3 4
+--R               (- 497520A c  - 1492560B b c )d e + 870660B c d
+--R          *
+--R             m
+--R         + 
+--R                   3 4               2            3    3
+--R           10080A b e  + (- 120960A b c - 40320B b )d e
+--R         + 
+--R                       2            2   2 2               3              2  3
+--R           (302400A b c  + 302400B b c)d e  + (- 201600A c  - 604800B b c )d e
+--R         + 
+--R                    3 4
+--R           352800B c d
+--R      *
+--R                  m + 4
+--R         (e x + d)
+--R     + 
+--R                     3   4         2        3  2 3             2        2   3 2
+--R               - 3A b d e  + (18A b c + 6B b )d e  + (- 30A b c  - 30B b c)d e
+--R             + 
+--R                     3          2  4         3 5
+--R               (15A c  + 45B b c )d e - 21B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                      3   4          2          3  2 3
+--R               - 99A b d e  + (594A b c + 198B b )d e
+--R             + 
+--R                          2         2   3 2          3            2  4
+--R               (- 990A b c  - 990B b c)d e  + (495A c  + 1485B b c )d e
+--R             + 
+--R                       3 5
+--R               - 693B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                        3   4           2           3  2 3
+--R               - 1341A b d e  + (8046A b c + 2682B b )d e
+--R             + 
+--R                            2           2   3 2           3             2  4
+--R               (- 13410A b c  - 13410B b c)d e  + (6705A c  + 20115B b c )d e
+--R             + 
+--R                        3 5
+--R               - 9387B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                        3   4            2            3  2 3
+--R               - 9585A b d e  + (57510A b c + 19170B b )d e
+--R             + 
+--R                            2           2   3 2            3              2  4
+--R               (- 95850A b c  - 95850B b c)d e  + (47925A c  + 143775B b c )d e
+--R             + 
+--R                         3 5
+--R               - 67095B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                         3   4             2            3  2 3
+--R               - 38592A b d e  + (231552A b c + 77184B b )d e
+--R             + 
+--R                             2            2   3 2
+--R               (- 385920A b c  - 385920B b c)d e
+--R             + 
+--R                         3              2  4             3 5
+--R               (192960A c  + 578880B b c )d e - 270144B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                         3   4             2             3  2 3
+--R               - 86076A b d e  + (516456A b c + 172152B b )d e
+--R             + 
+--R                             2            2   3 2
+--R               (- 860760A b c  - 860760B b c)d e
+--R             + 
+--R                         3               2  4             3 5
+--R               (430380A c  + 1291140B b c )d e - 602532B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                         3   4             2             3  2 3
+--R               - 96144A b d e  + (576864A b c + 192288B b )d e
+--R             + 
+--R                             2            2   3 2
+--R               (- 961440A b c  - 961440B b c)d e
+--R             + 
+--R                         3               2  4             3 5
+--R               (480720A c  + 1442160B b c )d e - 673008B c d
+--R          *
+--R             m
+--R         + 
+--R                     3   4             2            3  2 3
+--R           - 40320A b d e  + (241920A b c + 80640B b )d e
+--R         + 
+--R                         2            2   3 2             3              2  4
+--R           (- 403200A b c  - 403200B b c)d e  + (201600A c  + 604800B b c )d e
+--R         + 
+--R                      3 5
+--R           - 282240B c d
+--R      *
+--R                  m + 3
+--R         (e x + d)
+--R     + 
+--R                   3 2 4           2        3  3 3           2        2   4 2
+--R               3A b d e  + (- 12A b c - 4B b )d e  + (15A b c  + 15B b c)d e
+--R             + 
+--R                      3          2  5        3 6
+--R               (- 6A c  - 18B b c )d e + 7B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                     3 2 4            2          3  3 3
+--R               102A b d e  + (- 408A b c - 136B b )d e
+--R             + 
+--R                      2         2   4 2            3           2  5          3 6
+--R             (510A b c  + 510B b c)d e  + (- 204A c  - 612B b c )d e + 238B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                      3 2 4             2           3  3 3
+--R               1434A b d e  + (- 5736A b c - 1912B b )d e
+--R             + 
+--R                         2          2   4 2             3            2  5
+--R               (7170A b c  + 7170B b c)d e  + (- 2868A c  - 8604B b c )d e
+--R             + 
+--R                      3 6
+--R               3346B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                       3 2 4              2            3  3 3
+--R               10740A b d e  + (- 42960A b c - 14320B b )d e
+--R             + 
+--R                          2           2   4 2              3             2  5
+--R               (53700A b c  + 53700B b c)d e  + (- 21480A c  - 64440B b c )d e
+--R             + 
+--R                       3 6
+--R               25060B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                       3 2 4               2            3  3 3
+--R               45867A b d e  + (- 183468A b c - 61156B b )d e
+--R             + 
+--R                           2            2   4 2
+--R               (229335A b c  + 229335B b c)d e
+--R             + 
+--R                          3              2  5             3 6
+--R               (- 91734A c  - 275202B b c )d e + 107023B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                        3 2 4               2             3  3 3
+--R               110118A b d e  + (- 440472A b c - 146824B b )d e
+--R             + 
+--R                           2            2   4 2
+--R               (550590A b c  + 550590B b c)d e
+--R             + 
+--R                           3              2  5             3 6
+--R               (- 220236A c  - 660708B b c )d e + 256942B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                        3 2 4               2             3  3 3
+--R               134136A b d e  + (- 536544A b c - 178848B b )d e
+--R             + 
+--R                           2            2   4 2
+--R               (670680A b c  + 670680B b c)d e
+--R             + 
+--R                           3              2  5             3 6
+--R               (- 268272A c  - 804816B b c )d e + 312984B c d
+--R          *
+--R             m
+--R         + 
+--R                   3 2 4               2            3  3 3
+--R           60480A b d e  + (- 241920A b c - 80640B b )d e
+--R         + 
+--R                       2            2   4 2               3              2  5
+--R           (302400A b c  + 302400B b c)d e  + (- 120960A c  - 362880B b c )d e
+--R         + 
+--R                    3 6
+--R           141120B c d
+--R      *
+--R                  m + 2
+--R         (e x + d)
+--R     + 
+--R                    3 3 4        2       3  4 3            2       2   5 2
+--R               - A b d e  + (3A b c + B b )d e  + (- 3A b c  - 3B b c)d e
+--R             + 
+--R                   3         2  6       3 7
+--R               (A c  + 3B b c )d e - B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                      3 3 4          2         3  4 3
+--R               - 35A b d e  + (105A b c + 35B b )d e
+--R             + 
+--R                        2         2   5 2         3           2  6         3 7
+--R             (- 105A b c  - 105B b c)d e  + (35A c  + 105B b c )d e - 35B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                       3 3 4           2          3  4 3
+--R               - 511A b d e  + (1533A b c + 511B b )d e
+--R             + 
+--R                           2          2   5 2          3            2  6
+--R               (- 1533A b c  - 1533B b c)d e  + (511A c  + 1533B b c )d e
+--R             + 
+--R                       3 7
+--R               - 511B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                        3 3 4            2           3  4 3
+--R               - 4025A b d e  + (12075A b c + 4025B b )d e
+--R             + 
+--R                            2           2   5 2           3             2  6
+--R               (- 12075A b c  - 12075B b c)d e  + (4025A c  + 12075B b c )d e
+--R             + 
+--R                        3 7
+--R               - 4025B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                         3 3 4            2            3  4 3
+--R               - 18424A b d e  + (55272A b c + 18424B b )d e
+--R             + 
+--R                            2           2   5 2            3             2  6
+--R               (- 55272A b c  - 55272B b c)d e  + (18424A c  + 55272B b c )d e
+--R             + 
+--R                         3 7
+--R               - 18424B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                         3 3 4             2            3  4 3
+--R               - 48860A b d e  + (146580A b c + 48860B b )d e
+--R             + 
+--R                             2            2   5 2
+--R               (- 146580A b c  - 146580B b c)d e
+--R             + 
+--R                        3              2  6            3 7
+--R               (48860A c  + 146580B b c )d e - 48860B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                         3 3 4             2            3  4 3
+--R               - 69264A b d e  + (207792A b c + 69264B b )d e
+--R             + 
+--R                             2            2   5 2
+--R               (- 207792A b c  - 207792B b c)d e
+--R             + 
+--R                        3              2  6            3 7
+--R               (69264A c  + 207792B b c )d e - 69264B c d
+--R          *
+--R             m
+--R         + 
+--R                     3 3 4             2            3  4 3
+--R           - 40320A b d e  + (120960A b c + 40320B b )d e
+--R         + 
+--R                         2            2   5 2            3              2  6
+--R           (- 120960A b c  - 120960B b c)d e  + (40320A c  + 120960B b c )d e
+--R         + 
+--R                     3 7
+--R           - 40320B c d
+--R      *
+--R                  m + 1
+--R         (e x + d)
+--R  /
+--R        8 8      8 7       8 6        8 5         8 4         8 3          8 2
+--R       e m  + 36e m  + 546e m  + 4536e m  + 22449e m  + 67284e m  + 118124e m
+--R     + 
+--R              8          8
+--R       109584e m + 40320e
+--R                                                    Type: Expression(Integer)
+--E 122
+
+--S 123 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                3 8 7        3 8 6         3 8 5          3 8 4          3 8 3
+--R             B c e m  + 28B c e m  + 322B c e m  + 1960B c e m  + 6769B c e m
+--R           + 
+--R                     3 8 2           3 8           3 8
+--R             13132B c e m  + 13068B c e m + 5040B c e
+--R        *
+--R            8
+--R           x
+--R       + 
+--R                  3         2  8      3   7  7
+--R             ((A c  + 3B b c )e  + B c d e )m
+--R           + 
+--R                    3          2  8        3   7  6
+--R             ((29A c  + 87B b c )e  + 21B c d e )m
+--R           + 
+--R                     3            2  8         3   7  5
+--R             ((343A c  + 1029B b c )e  + 175B c d e )m
+--R           + 
+--R                      3            2  8         3   7  4
+--R             ((2135A c  + 6405B b c )e  + 735B c d e )m
+--R           + 
+--R                      3             2  8          3   7  3
+--R             ((7504A c  + 22512B b c )e  + 1624B c d e )m
+--R           + 
+--R                       3             2  8          3   7  2
+--R             ((14756A c  + 44268B b c )e  + 1764B c d e )m
+--R           + 
+--R                       3             2  8         3   7
+--R             ((14832A c  + 44496B b c )e  + 720B c d e )m
+--R           + 
+--R                     3             2  8
+--R             (5760A c  + 17280B b c )e
+--R        *
+--R            7
+--R           x
+--R       + 
+--R                     2       2   8       3         2    7  7
+--R             ((3A b c  + 3B b c)e  + (A c  + 3B b c )d e )m
+--R           + 
+--R                      2        2   8         3          2    7       3 2 6  6
+--R             ((90A b c  + 90B b c)e  + (23A c  + 69B b c )d e  - 7B c d e )m
+--R           + 
+--R                           2          2   8          3           2    7
+--R                 (1098A b c  + 1098B b c)e  + (205A c  + 615B b c )d e
+--R               + 
+--R                         3 2 6
+--R                 - 105B c d e
+--R            *
+--R                5
+--R               m
+--R           + 
+--R                           2          2   8          3            2    7
+--R                 (7020A b c  + 7020B b c)e  + (905A c  + 2715B b c )d e
+--R               + 
+--R                         3 2 6
+--R                 - 595B c d e
+--R            *
+--R                4
+--R               m
+--R           + 
+--R                            2           2   8           3            2    7
+--R                 (25227A b c  + 25227B b c)e  + (2074A c  + 6222B b c )d e
+--R               + 
+--R                          3 2 6
+--R                 - 1575B c d e
+--R            *
+--R                3
+--R               m
+--R           + 
+--R                            2           2   8           3            2    7
+--R                 (50490A b c  + 50490B b c)e  + (2312A c  + 6936B b c )d e
+--R               + 
+--R                          3 2 6
+--R                 - 1918B c d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                            2           2   8          3            2    7
+--R                 (51432A b c  + 51432B b c)e  + (960A c  + 2880B b c )d e
+--R               + 
+--R                         3 2 6
+--R                 - 840B c d e
+--R            *
+--R               m
+--R           + 
+--R                        2           2   8
+--R             (20160A b c  + 20160B b c)e
+--R        *
+--R            6
+--R           x
+--R       + 
+--R                   2       3  8          2       2     7  7
+--R             ((3A b c + B b )e  + (3A b c  + 3B b c)d e )m
+--R           + 
+--R                       2         3  8           2        2     7
+--R                 (93A b c + 31B b )e  + (75A b c  + 75B b c)d e
+--R               + 
+--R                        3          2  2 6
+--R                 (- 6A c  - 18B b c )d e
+--R            *
+--R                6
+--R               m
+--R           + 
+--R                         2          3  8            2         2     7
+--R                 (1173A b c + 391B b )e  + (723A b c  + 723B b c)d e
+--R               + 
+--R                          3           2  2 6        3 3 5
+--R                 (- 108A c  - 324B b c )d e  + 42B c d e
+--R            *
+--R                5
+--R               m
+--R           + 
+--R                         2           3  8             2          2     7
+--R                 (7743A b c + 2581B b )e  + (3405A b c  + 3405B b c)d e
+--R               + 
+--R                          3            2  2 6         3 3 5
+--R                 (- 690A c  - 2070B b c )d e  + 420B c d e
+--R            *
+--R                4
+--R               m
+--R           + 
+--R                          2           3  8             2          2     7
+--R                 (28632A b c + 9544B b )e  + (8202A b c  + 8202B b c)d e
+--R               + 
+--R                           3            2  2 6          3 3 5
+--R                 (- 1980A c  - 5940B b c )d e  + 1470B c d e
+--R            *
+--R                3
+--R               m
+--R           + 
+--R                          2            3  8             2          2     7
+--R                 (58692A b c + 19564B b )e  + (9480A b c  + 9480B b c)d e
+--R               + 
+--R                           3            2  2 6          3 3 5
+--R                 (- 2544A c  - 7632B b c )d e  + 2100B c d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                          2            3  8             2          2     7
+--R                 (60912A b c + 20304B b )e  + (4032A b c  + 4032B b c)d e
+--R               + 
+--R                           3            2  2 6          3 3 5
+--R                 (- 1152A c  - 3456B b c )d e  + 1008B c d e
+--R            *
+--R               m
+--R           + 
+--R                      2           3  8
+--R             (24192A b c + 8064B b )e
+--R        *
+--R            5
+--R           x
+--R       + 
+--R                 3 8        2       3    7  7
+--R             (A b e  + (3A b c + B b )d e )m
+--R           + 
+--R                   3 8         2         3    7             2        2   2 6  6
+--R             (32A b e  + (81A b c + 27B b )d e  + (- 15A b c  - 15B b c)d e )m
+--R           + 
+--R                       3 8          2          3    7
+--R                 418A b e  + (849A b c + 283B b )d e
+--R               + 
+--R                            2         2   2 6         3          2  3 5
+--R                 (- 315A b c  - 315B b c)d e  + (30A c  + 90B b c )d e
+--R            *
+--R                5
+--R               m
+--R           + 
+--R                        3 8           2           3    7
+--R                 2864A b e  + (4347A b c + 1449B b )d e
+--R               + 
+--R                             2          2   2 6          3            2  3 5
+--R                 (- 2355A b c  - 2355B b c)d e  + (420A c  + 1260B b c )d e
+--R               + 
+--R                         3 4 4
+--R                 - 210B c d e
+--R            *
+--R                4
+--R               m
+--R           + 
+--R                         3 8            2           3    7
+--R                 10993A b e  + (11244A b c + 3748B b )d e
+--R               + 
+--R                             2          2   2 6           3            2  3 5
+--R                 (- 7605A b c  - 7605B b c)d e  + (1770A c  + 5310B b c )d e
+--R               + 
+--R                          3 4 4
+--R                 - 1260B c d e
+--R            *
+--R                3
+--R               m
+--R           + 
+--R                         3 8            2           3    7
+--R                 23312A b e  + (13716A b c + 4572B b )d e
+--R               + 
+--R                              2           2   2 6           3            2  3 5
+--R                 (- 10590A b c  - 10590B b c)d e  + (2820A c  + 8460B b c )d e
+--R               + 
+--R                          3 4 4
+--R                 - 2310B c d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                         3 8           2           3    7
+--R                 24876A b e  + (6048A b c + 2016B b )d e
+--R               + 
+--R                             2          2   2 6           3            2  3 5
+--R                 (- 5040A b c  - 5040B b c)d e  + (1440A c  + 4320B b c )d e
+--R               + 
+--R                          3 4 4
+--R                 - 1260B c d e
+--R            *
+--R               m
+--R           + 
+--R                     3 8
+--R             10080A b e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                3   7 7         3   7           2        3  2 6  6
+--R             A b d e m  + (29A b d e  + (- 12A b c - 4B b )d e )m
+--R           + 
+--R                       3   7            2         3  2 6
+--R                 331A b d e  + (- 288A b c - 96B b )d e
+--R               + 
+--R                         2        2   3 5
+--R                 (60A b c  + 60B b c)d e
+--R            *
+--R                5
+--R               m
+--R           + 
+--R                        3   7             2          3  2 6
+--R                 1871A b d e  + (- 2532A b c - 844B b )d e
+--R               + 
+--R                           2          2   3 5            3           2  4 4
+--R                 (1080A b c  + 1080B b c)d e  + (- 120A c  - 360B b c )d e
+--R            *
+--R                4
+--R               m
+--R           + 
+--R                        3   7             2           3  2 6
+--R                 5380A b d e  + (- 9792A b c - 3264B b )d e
+--R               + 
+--R                           2          2   3 5             3            2  4 4
+--R                 (6180A b c  + 6180B b c)d e  + (- 1320A c  - 3960B b c )d e
+--R               + 
+--R                       3 5 3
+--R                 840B c d e
+--R            *
+--R                3
+--R               m
+--R           + 
+--R                        3   7              2           3  2 6
+--R                 7172A b d e  + (- 15600A b c - 5200B b )d e
+--R               + 
+--R                            2           2   3 5             3            2  4 4
+--R                 (11880A b c  + 11880B b c)d e  + (- 3120A c  - 9360B b c )d e
+--R               + 
+--R                        3 5 3
+--R                 2520B c d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                        3   7             2           3  2 6
+--R                 3360A b d e  + (- 8064A b c - 2688B b )d e
+--R               + 
+--R                           2          2   3 5             3            2  4 4
+--R                 (6720A b c  + 6720B b c)d e  + (- 1920A c  - 5760B b c )d e
+--R               + 
+--R                        3 5 3
+--R                 1680B c d e
+--R            *
+--R               m
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                   3 2 6 6           3 2 6         2         3  3 5  5
+--R             - 3A b d e m  + (- 81A b d e  + (36A b c + 12B b )d e )m
+--R           + 
+--R                         3 2 6          2          3  3 5
+--R                 - 831A b d e  + (792A b c + 264B b )d e
+--R               + 
+--R                            2         2   4 4
+--R                 (- 180A b c  - 180B b c)d e
+--R            *
+--R                4
+--R               m
+--R           + 
+--R                          3 2 6           2           3  3 5
+--R                 - 3951A b d e  + (6012A b c + 2004B b )d e
+--R               + 
+--R                             2          2   4 4          3            2  5 3
+--R                 (- 2880A b c  - 2880B b c)d e  + (360A c  + 1080B b c )d e
+--R            *
+--R                3
+--R               m
+--R           + 
+--R                          3 2 6            2           3  3 5
+--R                 - 8238A b d e  + (17352A b c + 5784B b )d e
+--R               + 
+--R                              2           2   4 4           3            2  5 3
+--R                 (- 12780A b c  - 12780B b c)d e  + (3240A c  + 9720B b c )d e
+--R               + 
+--R                          3 6 2
+--R                 - 2520B c d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                          3 2 6            2           3  3 5
+--R                 - 5040A b d e  + (12096A b c + 4032B b )d e
+--R               + 
+--R                              2           2   4 4           3            2  5 3
+--R                 (- 10080A b c  - 10080B b c)d e  + (2880A c  + 8640B b c )d e
+--R               + 
+--R                          3 6 2
+--R                 - 2520B c d e
+--R            *
+--R               m
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                 3 3 5 5          3 3 5           2         3  4 4  4
+--R             6A b d e m  + (156A b d e  + (- 72A b c - 24B b )d e )m
+--R           + 
+--R                        3 3 5             2          3  4 4
+--R                 1506A b d e  + (- 1512A b c - 504B b )d e
+--R               + 
+--R                          2         2   5 3
+--R                 (360A b c  + 360B b c)d e
+--R            *
+--R                3
+--R               m
+--R           + 
+--R                        3 3 5              2           3  4 4
+--R                 6396A b d e  + (- 10512A b c - 3504B b )d e
+--R               + 
+--R                           2          2   5 3            3            2  6 2
+--R                 (5400A b c  + 5400B b c)d e  + (- 720A c  - 2160B b c )d e
+--R            *
+--R                2
+--R               m
+--R           + 
+--R                         3 3 5              2           3  4 4
+--R                 10080A b d e  + (- 24192A b c - 8064B b )d e
+--R               + 
+--R                            2           2   5 3             3             2  6 2
+--R                 (20160A b c  + 20160B b c)d e  + (- 5760A c  - 17280B b c )d e
+--R               + 
+--R                        3 7
+--R                 5040B c d e
+--R            *
+--R               m
+--R        *
+--R           x
+--R       + 
+--R               3 4 4 4            3 4 4         2         3  5 3  3
+--R         - 6A b d e m  + (- 156A b d e  + (72A b c + 24B b )d e )m
+--R       + 
+--R                      3 4 4           2          3  5 3
+--R             - 1506A b d e  + (1512A b c + 504B b )d e
+--R           + 
+--R                        2         2   6 2
+--R             (- 360A b c  - 360B b c)d e
+--R        *
+--R            2
+--R           m
+--R       + 
+--R                      3 4 4            2           3  5 3
+--R             - 6396A b d e  + (10512A b c + 3504B b )d e
+--R           + 
+--R                         2          2   6 2          3            2  7
+--R             (- 5400A b c  - 5400B b c)d e  + (720A c  + 2160B b c )d e
+--R        *
+--R           m
+--R       + 
+--R                   3 4 4            2           3  5 3
+--R         - 10080A b d e  + (24192A b c + 8064B b )d e
+--R       + 
+--R                      2           2   6 2           3             2  7
+--R         (- 20160A b c  - 20160B b c)d e  + (5760A c  + 17280B b c )d e
+--R       + 
+--R                  3 8
+--R         - 5040B c d
+--R    *
+--R         m log(e x + d)
+--R       %e
+--R  /
+--R        8 8      8 7       8 6        8 5         8 4         8 3          8 2
+--R       e m  + 36e m  + 546e m  + 4536e m  + 22449e m  + 67284e m  + 118124e m
+--R     + 
+--R              8          8
+--R       109584e m + 40320e
+--R                                         Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)
+--R                  3 8 7        3 8 6         3 8 5          3 8 4          3 8 3
+--R               B c e m  + 28B c e m  + 322B c e m  + 1960B c e m  + 6769B c e m
+--R             + 
+--R                       3 8 2           3 8           3 8
+--R               13132B c e m  + 13068B c e m + 5040B c e
+--R          *
+--R              8
+--R             x
+--R         + 
+--R                    3         2  8      3   7  7
+--R               ((A c  + 3B b c )e  + B c d e )m
+--R             + 
+--R                      3          2  8        3   7  6
+--R               ((29A c  + 87B b c )e  + 21B c d e )m
+--R             + 
+--R                       3            2  8         3   7  5
+--R               ((343A c  + 1029B b c )e  + 175B c d e )m
+--R             + 
+--R                        3            2  8         3   7  4
+--R               ((2135A c  + 6405B b c )e  + 735B c d e )m
+--R             + 
+--R                        3             2  8          3   7  3
+--R               ((7504A c  + 22512B b c )e  + 1624B c d e )m
+--R             + 
+--R                         3             2  8          3   7  2
+--R               ((14756A c  + 44268B b c )e  + 1764B c d e )m
+--R             + 
+--R                         3             2  8         3   7
+--R               ((14832A c  + 44496B b c )e  + 720B c d e )m
+--R             + 
+--R                       3             2  8
+--R               (5760A c  + 17280B b c )e
+--R          *
+--R              7
+--R             x
+--R         + 
+--R                       2       2   8       3         2    7  7
+--R               ((3A b c  + 3B b c)e  + (A c  + 3B b c )d e )m
+--R             + 
+--R                        2        2   8         3          2    7       3 2 6  6
+--R               ((90A b c  + 90B b c)e  + (23A c  + 69B b c )d e  - 7B c d e )m
+--R             + 
+--R                             2          2   8          3           2    7
+--R                   (1098A b c  + 1098B b c)e  + (205A c  + 615B b c )d e
+--R                 + 
+--R                           3 2 6
+--R                   - 105B c d e
+--R              *
+--R                  5
+--R                 m
+--R             + 
+--R                             2          2   8          3            2    7
+--R                   (7020A b c  + 7020B b c)e  + (905A c  + 2715B b c )d e
+--R                 + 
+--R                           3 2 6
+--R                   - 595B c d e
+--R              *
+--R                  4
+--R                 m
+--R             + 
+--R                              2           2   8           3            2    7
+--R                   (25227A b c  + 25227B b c)e  + (2074A c  + 6222B b c )d e
+--R                 + 
+--R                            3 2 6
+--R                   - 1575B c d e
+--R              *
+--R                  3
+--R                 m
+--R             + 
+--R                              2           2   8           3            2    7
+--R                   (50490A b c  + 50490B b c)e  + (2312A c  + 6936B b c )d e
+--R                 + 
+--R                            3 2 6
+--R                   - 1918B c d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                              2           2   8          3            2    7
+--R                   (51432A b c  + 51432B b c)e  + (960A c  + 2880B b c )d e
+--R                 + 
+--R                           3 2 6
+--R                   - 840B c d e
+--R              *
+--R                 m
+--R             + 
+--R                          2           2   8
+--R               (20160A b c  + 20160B b c)e
+--R          *
+--R              6
+--R             x
+--R         + 
+--R                     2       3  8          2       2     7  7
+--R               ((3A b c + B b )e  + (3A b c  + 3B b c)d e )m
+--R             + 
+--R                         2         3  8           2        2     7
+--R                   (93A b c + 31B b )e  + (75A b c  + 75B b c)d e
+--R                 + 
+--R                          3          2  2 6
+--R                   (- 6A c  - 18B b c )d e
+--R              *
+--R                  6
+--R                 m
+--R             + 
+--R                           2          3  8            2         2     7
+--R                   (1173A b c + 391B b )e  + (723A b c  + 723B b c)d e
+--R                 + 
+--R                            3           2  2 6        3 3 5
+--R                   (- 108A c  - 324B b c )d e  + 42B c d e
+--R              *
+--R                  5
+--R                 m
+--R             + 
+--R                           2           3  8             2          2     7
+--R                   (7743A b c + 2581B b )e  + (3405A b c  + 3405B b c)d e
+--R                 + 
+--R                            3            2  2 6         3 3 5
+--R                   (- 690A c  - 2070B b c )d e  + 420B c d e
+--R              *
+--R                  4
+--R                 m
+--R             + 
+--R                            2           3  8             2          2     7
+--R                   (28632A b c + 9544B b )e  + (8202A b c  + 8202B b c)d e
+--R                 + 
+--R                             3            2  2 6          3 3 5
+--R                   (- 1980A c  - 5940B b c )d e  + 1470B c d e
+--R              *
+--R                  3
+--R                 m
+--R             + 
+--R                            2            3  8             2          2     7
+--R                   (58692A b c + 19564B b )e  + (9480A b c  + 9480B b c)d e
+--R                 + 
+--R                             3            2  2 6          3 3 5
+--R                   (- 2544A c  - 7632B b c )d e  + 2100B c d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                            2            3  8             2          2     7
+--R                   (60912A b c + 20304B b )e  + (4032A b c  + 4032B b c)d e
+--R                 + 
+--R                             3            2  2 6          3 3 5
+--R                   (- 1152A c  - 3456B b c )d e  + 1008B c d e
+--R              *
+--R                 m
+--R             + 
+--R                        2           3  8
+--R               (24192A b c + 8064B b )e
+--R          *
+--R              5
+--R             x
+--R         + 
+--R                   3 8        2       3    7  7
+--R               (A b e  + (3A b c + B b )d e )m
+--R             + 
+--R                          3 8         2         3    7
+--R                     32A b e  + (81A b c + 27B b )d e
+--R                   + 
+--R                               2        2   2 6
+--R                     (- 15A b c  - 15B b c)d e
+--R              *
+--R                  6
+--R                 m
+--R             + 
+--R                         3 8          2          3    7
+--R                   418A b e  + (849A b c + 283B b )d e
+--R                 + 
+--R                              2         2   2 6         3          2  3 5
+--R                   (- 315A b c  - 315B b c)d e  + (30A c  + 90B b c )d e
+--R              *
+--R                  5
+--R                 m
+--R             + 
+--R                          3 8           2           3    7
+--R                   2864A b e  + (4347A b c + 1449B b )d e
+--R                 + 
+--R                               2          2   2 6          3            2  3 5
+--R                   (- 2355A b c  - 2355B b c)d e  + (420A c  + 1260B b c )d e
+--R                 + 
+--R                           3 4 4
+--R                   - 210B c d e
+--R              *
+--R                  4
+--R                 m
+--R             + 
+--R                           3 8            2           3    7
+--R                   10993A b e  + (11244A b c + 3748B b )d e
+--R                 + 
+--R                               2          2   2 6           3            2  3 5
+--R                   (- 7605A b c  - 7605B b c)d e  + (1770A c  + 5310B b c )d e
+--R                 + 
+--R                            3 4 4
+--R                   - 1260B c d e
+--R              *
+--R                  3
+--R                 m
+--R             + 
+--R                           3 8            2           3    7
+--R                   23312A b e  + (13716A b c + 4572B b )d e
+--R                 + 
+--R                                2           2   2 6
+--R                   (- 10590A b c  - 10590B b c)d e
+--R                 + 
+--R                           3            2  3 5          3 4 4
+--R                   (2820A c  + 8460B b c )d e  - 2310B c d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                           3 8           2           3    7
+--R                   24876A b e  + (6048A b c + 2016B b )d e
+--R                 + 
+--R                               2          2   2 6           3            2  3 5
+--R                   (- 5040A b c  - 5040B b c)d e  + (1440A c  + 4320B b c )d e
+--R                 + 
+--R                            3 4 4
+--R                   - 1260B c d e
+--R              *
+--R                 m
+--R             + 
+--R                       3 8
+--R               10080A b e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                  3   7 7         3   7           2        3  2 6  6
+--R               A b d e m  + (29A b d e  + (- 12A b c - 4B b )d e )m
+--R             + 
+--R                         3   7            2         3  2 6
+--R                   331A b d e  + (- 288A b c - 96B b )d e
+--R                 + 
+--R                           2        2   3 5
+--R                   (60A b c  + 60B b c)d e
+--R              *
+--R                  5
+--R                 m
+--R             + 
+--R                          3   7             2          3  2 6
+--R                   1871A b d e  + (- 2532A b c - 844B b )d e
+--R                 + 
+--R                             2          2   3 5            3           2  4 4
+--R                   (1080A b c  + 1080B b c)d e  + (- 120A c  - 360B b c )d e
+--R              *
+--R                  4
+--R                 m
+--R             + 
+--R                          3   7             2           3  2 6
+--R                   5380A b d e  + (- 9792A b c - 3264B b )d e
+--R                 + 
+--R                             2          2   3 5             3            2  4 4
+--R                   (6180A b c  + 6180B b c)d e  + (- 1320A c  - 3960B b c )d e
+--R                 + 
+--R                         3 5 3
+--R                   840B c d e
+--R              *
+--R                  3
+--R                 m
+--R             + 
+--R                          3   7              2           3  2 6
+--R                   7172A b d e  + (- 15600A b c - 5200B b )d e
+--R                 + 
+--R                              2           2   3 5
+--R                   (11880A b c  + 11880B b c)d e
+--R                 + 
+--R                             3            2  4 4          3 5 3
+--R                   (- 3120A c  - 9360B b c )d e  + 2520B c d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                          3   7             2           3  2 6
+--R                   3360A b d e  + (- 8064A b c - 2688B b )d e
+--R                 + 
+--R                             2          2   3 5             3            2  4 4
+--R                   (6720A b c  + 6720B b c)d e  + (- 1920A c  - 5760B b c )d e
+--R                 + 
+--R                          3 5 3
+--R                   1680B c d e
+--R              *
+--R                 m
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                     3 2 6 6           3 2 6         2         3  3 5  5
+--R               - 3A b d e m  + (- 81A b d e  + (36A b c + 12B b )d e )m
+--R             + 
+--R                           3 2 6          2          3  3 5
+--R                   - 831A b d e  + (792A b c + 264B b )d e
+--R                 + 
+--R                              2         2   4 4
+--R                   (- 180A b c  - 180B b c)d e
+--R              *
+--R                  4
+--R                 m
+--R             + 
+--R                            3 2 6           2           3  3 5
+--R                   - 3951A b d e  + (6012A b c + 2004B b )d e
+--R                 + 
+--R                               2          2   4 4          3            2  5 3
+--R                   (- 2880A b c  - 2880B b c)d e  + (360A c  + 1080B b c )d e
+--R              *
+--R                  3
+--R                 m
+--R             + 
+--R                            3 2 6            2           3  3 5
+--R                   - 8238A b d e  + (17352A b c + 5784B b )d e
+--R                 + 
+--R                                2           2   4 4
+--R                   (- 12780A b c  - 12780B b c)d e
+--R                 + 
+--R                           3            2  5 3          3 6 2
+--R                   (3240A c  + 9720B b c )d e  - 2520B c d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                            3 2 6            2           3  3 5
+--R                   - 5040A b d e  + (12096A b c + 4032B b )d e
+--R                 + 
+--R                                2           2   4 4
+--R                   (- 10080A b c  - 10080B b c)d e
+--R                 + 
+--R                           3            2  5 3          3 6 2
+--R                   (2880A c  + 8640B b c )d e  - 2520B c d e
+--R              *
+--R                 m
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                   3 3 5 5          3 3 5           2         3  4 4  4
+--R               6A b d e m  + (156A b d e  + (- 72A b c - 24B b )d e )m
+--R             + 
+--R                          3 3 5             2          3  4 4
+--R                   1506A b d e  + (- 1512A b c - 504B b )d e
+--R                 + 
+--R                            2         2   5 3
+--R                   (360A b c  + 360B b c)d e
+--R              *
+--R                  3
+--R                 m
+--R             + 
+--R                          3 3 5              2           3  4 4
+--R                   6396A b d e  + (- 10512A b c - 3504B b )d e
+--R                 + 
+--R                             2          2   5 3            3            2  6 2
+--R                   (5400A b c  + 5400B b c)d e  + (- 720A c  - 2160B b c )d e
+--R              *
+--R                  2
+--R                 m
+--R             + 
+--R                           3 3 5              2           3  4 4
+--R                   10080A b d e  + (- 24192A b c - 8064B b )d e
+--R                 + 
+--R                              2           2   5 3
+--R                   (20160A b c  + 20160B b c)d e
+--R                 + 
+--R                             3             2  6 2          3 7
+--R                   (- 5760A c  - 17280B b c )d e  + 5040B c d e
+--R              *
+--R                 m
+--R          *
+--R             x
+--R         + 
+--R                 3 4 4 4            3 4 4         2         3  5 3  3
+--R           - 6A b d e m  + (- 156A b d e  + (72A b c + 24B b )d e )m
+--R         + 
+--R                        3 4 4           2          3  5 3
+--R               - 1506A b d e  + (1512A b c + 504B b )d e
+--R             + 
+--R                          2         2   6 2
+--R               (- 360A b c  - 360B b c)d e
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                        3 4 4            2           3  5 3
+--R               - 6396A b d e  + (10512A b c + 3504B b )d e
+--R             + 
+--R                           2          2   6 2          3            2  7
+--R               (- 5400A b c  - 5400B b c)d e  + (720A c  + 2160B b c )d e
+--R          *
+--R             m
+--R         + 
+--R                     3 4 4            2           3  5 3
+--R           - 10080A b d e  + (24192A b c + 8064B b )d e
+--R         + 
+--R                        2           2   6 2           3             2  7
+--R           (- 20160A b c  - 20160B b c)d e  + (5760A c  + 17280B b c )d e
+--R         + 
+--R                    3 8
+--R           - 5040B c d
+--R      *
+--R           m log(e x + d)
+--R         %e
+--R     + 
+--R                3 7        3 6         3 5          3 4          3 3
+--R           - B c m  - 28B c m  - 322B c m  - 1960B c m  - 6769B c m
+--R         + 
+--R                     3 2           3           3
+--R           - 13132B c m  - 13068B c m - 5040B c
+--R      *
+--R                  m + 8
+--R         (e x + d)
+--R     + 
+--R                  3         2         3   7
+--R           ((- A c  - 3B b c )e + 7B c d)m
+--R         + 
+--R                    3          2           3   6
+--R           ((- 29A c  - 87B b c )e + 203B c d)m
+--R         + 
+--R                     3            2            3   5
+--R           ((- 343A c  - 1029B b c )e + 2401B c d)m
+--R         + 
+--R                      3            2             3   4
+--R           ((- 2135A c  - 6405B b c )e + 14945B c d)m
+--R         + 
+--R                      3             2             3   3
+--R           ((- 7504A c  - 22512B b c )e + 52528B c d)m
+--R         + 
+--R                       3             2              3   2
+--R           ((- 14756A c  - 44268B b c )e + 103292B c d)m
+--R         + 
+--R                       3             2              3
+--R           ((- 14832A c  - 44496B b c )e + 103824B c d)m
+--R         + 
+--R                     3             2             3
+--R           (- 5760A c  - 17280B b c )e + 40320B c d
+--R      *
+--R                  m + 7
+--R         (e x + d)
+--R     + 
+--R                     2       2   2        3          2            3 2  7
+--R           ((- 3A b c  - 3B b c)e  + (6A c  + 18B b c )d e - 21B c d )m
+--R         + 
+--R                      2        2   2          3           2             3 2  6
+--R           ((- 90A b c  - 90B b c)e  + (180A c  + 540B b c )d e - 630B c d )m
+--R         + 
+--R                           2          2   2           3            2
+--R               (- 1098A b c  - 1098B b c)e  + (2196A c  + 6588B b c )d e
+--R             + 
+--R                        3 2
+--R               - 7686B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                           2          2   2            3             2
+--R               (- 7020A b c  - 7020B b c)e  + (14040A c  + 42120B b c )d e
+--R             + 
+--R                         3 2
+--R               - 49140B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                            2           2   2            3              2
+--R               (- 25227A b c  - 25227B b c)e  + (50454A c  + 151362B b c )d e
+--R             + 
+--R                          3 2
+--R               - 176589B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                            2           2   2             3              2
+--R               (- 50490A b c  - 50490B b c)e  + (100980A c  + 302940B b c )d e
+--R             + 
+--R                          3 2
+--R               - 353430B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                            2           2   2             3              2
+--R               (- 51432A b c  - 51432B b c)e  + (102864A c  + 308592B b c )d e
+--R             + 
+--R                          3 2
+--R               - 360024B c d
+--R          *
+--R             m
+--R         + 
+--R                        2           2   2            3              2
+--R           (- 20160A b c  - 20160B b c)e  + (40320A c  + 120960B b c )d e
+--R         + 
+--R                      3 2
+--R           - 141120B c d
+--R      *
+--R                  m + 6
+--R         (e x + d)
+--R     + 
+--R                      2       3  3           2        2     2
+--R               (- 3A b c - B b )e  + (15A b c  + 15B b c)d e
+--R             + 
+--R                       3          2  2         3 3
+--R               (- 15A c  - 45B b c )d e + 35B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                       2         3  3            2         2     2
+--R               (- 93A b c - 31B b )e  + (465A b c  + 465B b c)d e
+--R             + 
+--R                        3            2  2           3 3
+--R               (- 465A c  - 1395B b c )d e + 1085B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                         2          3  3             2          2     2
+--R               (- 1173A b c - 391B b )e  + (5865A b c  + 5865B b c)d e
+--R             + 
+--R                         3             2  2            3 3
+--R               (- 5865A c  - 17595B b c )d e + 13685B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                         2           3  3              2           2     2
+--R               (- 7743A b c - 2581B b )e  + (38715A b c  + 38715B b c)d e
+--R             + 
+--R                          3              2  2            3 3
+--R               (- 38715A c  - 116145B b c )d e + 90335B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                          2           3  3               2            2     2
+--R               (- 28632A b c - 9544B b )e  + (143160A b c  + 143160B b c)d e
+--R             + 
+--R                           3              2  2             3 3
+--R               (- 143160A c  - 429480B b c )d e + 334040B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                          2            3  3               2            2     2
+--R               (- 58692A b c - 19564B b )e  + (293460A b c  + 293460B b c)d e
+--R             + 
+--R                           3              2  2             3 3
+--R               (- 293460A c  - 880380B b c )d e + 684740B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                          2            3  3               2            2     2
+--R               (- 60912A b c - 20304B b )e  + (304560A b c  + 304560B b c)d e
+--R             + 
+--R                           3              2  2             3 3
+--R               (- 304560A c  - 913680B b c )d e + 710640B c d
+--R          *
+--R             m
+--R         + 
+--R                      2           3  3               2            2     2
+--R           (- 24192A b c - 8064B b )e  + (120960A b c  + 120960B b c)d e
+--R         + 
+--R                       3              2  2             3 3
+--R           (- 120960A c  - 362880B b c )d e + 282240B c d
+--R      *
+--R                  m + 5
+--R         (e x + d)
+--R     + 
+--R                    3 4         2        3    3             2        2   2 2
+--R               - A b e  + (12A b c + 4B b )d e  + (- 30A b c  - 30B b c)d e
+--R             + 
+--R                     3          2  3         3 4
+--R               (20A c  + 60B b c )d e - 35B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                      3 4          2          3    3
+--R               - 32A b e  + (384A b c + 128B b )d e
+--R             + 
+--R                          2         2   2 2          3            2  3
+--R               (- 960A b c  - 960B b c)d e  + (640A c  + 1920B b c )d e
+--R             + 
+--R                        3 4
+--R               - 1120B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                       3 4           2           3    3
+--R               - 418A b e  + (5016A b c + 1672B b )d e
+--R             + 
+--R                            2           2   2 2           3             2  3
+--R               (- 12540A b c  - 12540B b c)d e  + (8360A c  + 25080B b c )d e
+--R             + 
+--R                         3 4
+--R               - 14630B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                        3 4            2            3    3
+--R               - 2864A b e  + (34368A b c + 11456B b )d e
+--R             + 
+--R                            2           2   2 2            3              2  3
+--R               (- 85920A b c  - 85920B b c)d e  + (57280A c  + 171840B b c )d e
+--R             + 
+--R                          3 4
+--R               - 100240B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                         3 4             2            3    3
+--R               - 10993A b e  + (131916A b c + 43972B b )d e
+--R             + 
+--R                             2            2   2 2
+--R               (- 329790A b c  - 329790B b c)d e
+--R             + 
+--R                         3              2  3             3 4
+--R               (219860A c  + 659580B b c )d e - 384755B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                         3 4             2            3    3
+--R               - 23312A b e  + (279744A b c + 93248B b )d e
+--R             + 
+--R                             2            2   2 2
+--R               (- 699360A b c  - 699360B b c)d e
+--R             + 
+--R                         3               2  3             3 4
+--R               (466240A c  + 1398720B b c )d e - 815920B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                         3 4             2            3    3
+--R               - 24876A b e  + (298512A b c + 99504B b )d e
+--R             + 
+--R                             2            2   2 2
+--R               (- 746280A b c  - 746280B b c)d e
+--R             + 
+--R                         3               2  3             3 4
+--R               (497520A c  + 1492560B b c )d e - 870660B c d
+--R          *
+--R             m
+--R         + 
+--R                     3 4             2            3    3
+--R           - 10080A b e  + (120960A b c + 40320B b )d e
+--R         + 
+--R                         2            2   2 2             3              2  3
+--R           (- 302400A b c  - 302400B b c)d e  + (201600A c  + 604800B b c )d e
+--R         + 
+--R                      3 4
+--R           - 352800B c d
+--R      *
+--R                  m + 4
+--R         (e x + d)
+--R     + 
+--R                   3   4           2        3  2 3           2        2   3 2
+--R               3A b d e  + (- 18A b c - 6B b )d e  + (30A b c  + 30B b c)d e
+--R             + 
+--R                       3          2  4         3 5
+--R               (- 15A c  - 45B b c )d e + 21B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                    3   4            2          3  2 3
+--R               99A b d e  + (- 594A b c - 198B b )d e
+--R             + 
+--R                        2         2   3 2            3            2  4
+--R               (990A b c  + 990B b c)d e  + (- 495A c  - 1485B b c )d e
+--R             + 
+--R                     3 5
+--R               693B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                      3   4             2           3  2 3
+--R               1341A b d e  + (- 8046A b c - 2682B b )d e
+--R             + 
+--R                          2           2   3 2             3             2  4
+--R               (13410A b c  + 13410B b c)d e  + (- 6705A c  - 20115B b c )d e
+--R             + 
+--R                      3 5
+--R               9387B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                      3   4              2            3  2 3
+--R               9585A b d e  + (- 57510A b c - 19170B b )d e
+--R             + 
+--R                          2           2   3 2              3              2  4
+--R               (95850A b c  + 95850B b c)d e  + (- 47925A c  - 143775B b c )d e
+--R             + 
+--R                       3 5
+--R               67095B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                       3   4               2            3  2 3
+--R               38592A b d e  + (- 231552A b c - 77184B b )d e
+--R             + 
+--R                           2            2   3 2
+--R               (385920A b c  + 385920B b c)d e
+--R             + 
+--R                           3              2  4             3 5
+--R               (- 192960A c  - 578880B b c )d e + 270144B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                       3   4               2             3  2 3
+--R               86076A b d e  + (- 516456A b c - 172152B b )d e
+--R             + 
+--R                           2            2   3 2
+--R               (860760A b c  + 860760B b c)d e
+--R             + 
+--R                           3               2  4             3 5
+--R               (- 430380A c  - 1291140B b c )d e + 602532B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                       3   4               2             3  2 3
+--R               96144A b d e  + (- 576864A b c - 192288B b )d e
+--R             + 
+--R                           2            2   3 2
+--R               (961440A b c  + 961440B b c)d e
+--R             + 
+--R                           3               2  4             3 5
+--R               (- 480720A c  - 1442160B b c )d e + 673008B c d
+--R          *
+--R             m
+--R         + 
+--R                   3   4               2            3  2 3
+--R           40320A b d e  + (- 241920A b c - 80640B b )d e
+--R         + 
+--R                       2            2   3 2               3              2  4
+--R           (403200A b c  + 403200B b c)d e  + (- 201600A c  - 604800B b c )d e
+--R         + 
+--R                    3 5
+--R           282240B c d
+--R      *
+--R                  m + 3
+--R         (e x + d)
+--R     + 
+--R                     3 2 4         2        3  3 3             2        2   4 2
+--R               - 3A b d e  + (12A b c + 4B b )d e  + (- 15A b c  - 15B b c)d e
+--R             + 
+--R                    3          2  5        3 6
+--R               (6A c  + 18B b c )d e - 7B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                       3 2 4          2          3  3 3
+--R               - 102A b d e  + (408A b c + 136B b )d e
+--R             + 
+--R                        2         2   4 2          3           2  5          3 6
+--R             (- 510A b c  - 510B b c)d e  + (204A c  + 612B b c )d e - 238B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                        3 2 4           2           3  3 3
+--R               - 1434A b d e  + (5736A b c + 1912B b )d e
+--R             + 
+--R                           2          2   4 2           3            2  5
+--R               (- 7170A b c  - 7170B b c)d e  + (2868A c  + 8604B b c )d e
+--R             + 
+--R                        3 6
+--R               - 3346B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                         3 2 4            2            3  3 3
+--R               - 10740A b d e  + (42960A b c + 14320B b )d e
+--R             + 
+--R                            2           2   4 2            3             2  5
+--R               (- 53700A b c  - 53700B b c)d e  + (21480A c  + 64440B b c )d e
+--R             + 
+--R                         3 6
+--R               - 25060B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                         3 2 4             2            3  3 3
+--R               - 45867A b d e  + (183468A b c + 61156B b )d e
+--R             + 
+--R                             2            2   4 2
+--R               (- 229335A b c  - 229335B b c)d e
+--R             + 
+--R                        3              2  5             3 6
+--R               (91734A c  + 275202B b c )d e - 107023B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                          3 2 4             2             3  3 3
+--R               - 110118A b d e  + (440472A b c + 146824B b )d e
+--R             + 
+--R                             2            2   4 2
+--R               (- 550590A b c  - 550590B b c)d e
+--R             + 
+--R                         3              2  5             3 6
+--R               (220236A c  + 660708B b c )d e - 256942B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                          3 2 4             2             3  3 3
+--R               - 134136A b d e  + (536544A b c + 178848B b )d e
+--R             + 
+--R                             2            2   4 2
+--R               (- 670680A b c  - 670680B b c)d e
+--R             + 
+--R                         3              2  5             3 6
+--R               (268272A c  + 804816B b c )d e - 312984B c d
+--R          *
+--R             m
+--R         + 
+--R                     3 2 4             2            3  3 3
+--R           - 60480A b d e  + (241920A b c + 80640B b )d e
+--R         + 
+--R                         2            2   4 2             3              2  5
+--R           (- 302400A b c  - 302400B b c)d e  + (120960A c  + 362880B b c )d e
+--R         + 
+--R                      3 6
+--R           - 141120B c d
+--R      *
+--R                  m + 2
+--R         (e x + d)
+--R     + 
+--R                  3 3 4          2       3  4 3          2       2   5 2
+--R               A b d e  + (- 3A b c - B b )d e  + (3A b c  + 3B b c)d e
+--R             + 
+--R                     3         2  6       3 7
+--R               (- A c  - 3B b c )d e + B c d
+--R          *
+--R              7
+--R             m
+--R         + 
+--R                    3 3 4            2         3  4 3
+--R               35A b d e  + (- 105A b c - 35B b )d e
+--R             + 
+--R                      2         2   5 2           3           2  6         3 7
+--R             (105A b c  + 105B b c)d e  + (- 35A c  - 105B b c )d e + 35B c d
+--R          *
+--R              6
+--R             m
+--R         + 
+--R                     3 3 4             2          3  4 3
+--R               511A b d e  + (- 1533A b c - 511B b )d e
+--R             + 
+--R                         2          2   5 2            3            2  6
+--R               (1533A b c  + 1533B b c)d e  + (- 511A c  - 1533B b c )d e
+--R             + 
+--R                     3 7
+--R               511B c d
+--R          *
+--R              5
+--R             m
+--R         + 
+--R                      3 3 4              2           3  4 3
+--R               4025A b d e  + (- 12075A b c - 4025B b )d e
+--R             + 
+--R                          2           2   5 2             3             2  6
+--R               (12075A b c  + 12075B b c)d e  + (- 4025A c  - 12075B b c )d e
+--R             + 
+--R                      3 7
+--R               4025B c d
+--R          *
+--R              4
+--R             m
+--R         + 
+--R                       3 3 4              2            3  4 3
+--R               18424A b d e  + (- 55272A b c - 18424B b )d e
+--R             + 
+--R                          2           2   5 2              3             2  6
+--R               (55272A b c  + 55272B b c)d e  + (- 18424A c  - 55272B b c )d e
+--R             + 
+--R                       3 7
+--R               18424B c d
+--R          *
+--R              3
+--R             m
+--R         + 
+--R                       3 3 4               2            3  4 3
+--R               48860A b d e  + (- 146580A b c - 48860B b )d e
+--R             + 
+--R                           2            2   5 2
+--R               (146580A b c  + 146580B b c)d e
+--R             + 
+--R                          3              2  6            3 7
+--R               (- 48860A c  - 146580B b c )d e + 48860B c d
+--R          *
+--R              2
+--R             m
+--R         + 
+--R                       3 3 4               2            3  4 3
+--R               69264A b d e  + (- 207792A b c - 69264B b )d e
+--R             + 
+--R                           2            2   5 2
+--R               (207792A b c  + 207792B b c)d e
+--R             + 
+--R                          3              2  6            3 7
+--R               (- 69264A c  - 207792B b c )d e + 69264B c d
+--R          *
+--R             m
+--R         + 
+--R                   3 3 4               2            3  4 3
+--R           40320A b d e  + (- 120960A b c - 40320B b )d e
+--R         + 
+--R                       2            2   5 2              3              2  6
+--R           (120960A b c  + 120960B b c)d e  + (- 40320A c  - 120960B b c )d e
+--R         + 
+--R                   3 7
+--R           40320B c d
+--R      *
+--R                  m + 1
+--R         (e x + d)
+--R  /
+--R        8 8      8 7       8 6        8 5         8 4         8 3          8 2
+--R       e m  + 36e m  + 546e m  + 4536e m  + 22449e m  + 67284e m  + 118124e m
+--R     + 
+--R              8          8
+--R       109584e m + 40320e
+--R                                                    Type: Expression(Integer)
+--E 124
+
+--S 125 of 1457
+d0:=normalize(D(m0,x))
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 1457
+t0:=(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R        3 4 11        3         2  4       3   3  10
+--R     B c e x   + ((A c  + 3B b c )e  + 4B c d e )x
+--R   + 
+--R             2       2   4        3          2    3       3 2 2  9
+--R     ((3A b c  + 3B b c)e  + (4A c  + 12B b c )d e  + 6B c d e )x
+--R   + 
+--R              2       3  4           2        2     3        3          2  2 2
+--R         (3A b c + B b )e  + (12A b c  + 12B b c)d e  + (6A c  + 18B b c )d e
+--R       + 
+--R             3 3
+--R         4B c d e
+--R    *
+--R        8
+--R       x
+--R   + 
+--R            3 4         2        3    3           2        2   2 2
+--R         A b e  + (12A b c + 4B b )d e  + (18A b c  + 18B b c)d e
+--R       + 
+--R              3          2  3       3 4
+--R         (4A c  + 12B b c )d e + B c d
+--R    *
+--R        7
+--R       x
+--R   + 
+--R             3   3         2        3  2 2           2        2   3
+--R         4A b d e  + (18A b c + 6B b )d e  + (12A b c  + 12B b c)d e
+--R       + 
+--R             3         2  4
+--R         (A c  + 3B b c )d
+--R    *
+--R        6
+--R       x
+--R   + 
+--R          3 2 2         2        3  3           2       2   4  5
+--R     (6A b d e  + (12A b c + 4B b )d e + (3A b c  + 3B b c)d )x
+--R   + 
+--R          3 3         2       3  4  4      3 4 3
+--R     (4A b d e + (3A b c + B b )d )x  + A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 126
+
+--S 127 of 1457
+r0:=1/4*A*b^3*d^4*x^4+1/5*b^2*d^3*(b*B*d+3*A*c*d+4*A*b*e)*x^5+1/6*b*d^2*_
+     (3*A*c^2*d^2+2*b^2*e*(2*B*d+3*A*e)+3*b*c*d*(B*d+4*A*e))*x^6+1/7*d*_
+     (A*c^3*d^3+2*b^3*e^2*(3*B*d+2*A*e)+6*b^2*c*d*e*(2*B*d+3*A*e)+3*b*_
+     c^2*d^2*(B*d+4*A*e))*x^7+1/8*(A*e*(4*c^3*d^3+18*b*c^2*d^2*e+12*_
+     b^2*c*d*e^2+b^3*e^3)+B*d*(c^3*d^3+12*b*c^2*d^2*e+18*b^2*c*d*e^2+4*_
+     b^3*e^3))*x^8+1/9*e*(3*A*c*e*(2*c^2*d^2+4*b*c*d*e+b^2*e^2)+B*_
+     (4*c^3*d^3+18*b*c^2*d^2*e+12*b^2*c*d*e^2+b^3*e^3))*x^9+1/10*c*e^2*_
+     (A*c*e*(4*c*d+3*b*e)+3*B*(2*c^2*d^2+4*b*c*d*e+b^2*e^2))*x^10+1/11*_
+     c^2*e^3*(4*B*c*d+3*b*B*e+A*c*e)*x^11+1/12*B*c^3*e^4*x^12
+--R 
+--R
+--R   (2)
+--R      1    3 4 12      1    3    3      2  4    4    3   3  11
+--R     -- B c e x   + ((-- A c  + -- B b c )e  + -- B c d e )x
+--R     12               11        11             11
+--R   + 
+--R        3      2    3    2   4    2    3   6      2    3   3    3 2 2  10
+--R     ((-- A b c  + -- B b c)e  + (- A c  + - B b c )d e  + - B c d e )x
+--R       10          10             5        5               5
+--R   + 
+--R          1    2    1    3  4    4      2   4    2     3
+--R         (- A b c + - B b )e  + (- A b c  + - B b c)d e
+--R          3         9            3          3
+--R       + 
+--R          2    3         2  2 2   4    3 3
+--R         (- A c  + 2B b c )d e  + - B c d e
+--R          3                       9
+--R    *
+--R        9
+--R       x
+--R   + 
+--R         1    3 4    3    2    1    3    3    9      2   9    2   2 2
+--R         - A b e  + (- A b c + - B b )d e  + (- A b c  + - B b c)d e
+--R         8           2         2              4          4
+--R       + 
+--R          1    3   3      2  3    1    3 4
+--R         (- A c  + - B b c )d e + - B c d
+--R          2        2              8
+--R    *
+--R        8
+--R       x
+--R   + 
+--R         4    3   3    18    2    6    3  2 2    12      2   12    2   3
+--R         - A b d e  + (-- A b c + - B b )d e  + (-- A b c  + -- B b c)d e
+--R         7              7         7               7           7
+--R       + 
+--R          1    3   3      2  4
+--R         (- A c  + - B b c )d
+--R          7        7
+--R    *
+--R        7
+--R       x
+--R   + 
+--R         3 2 2        2    2    3  3     1      2   1    2   4  6
+--R     (A b d e  + (2A b c + - B b )d e + (- A b c  + - B b c)d )x
+--R                           3             2          2
+--R   + 
+--R      4    3 3     3    2    1    3  4  5   1    3 4 4
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      5            5         5              4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 127
+
+--S 128 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R      1    3 4 12      1    3    3      2  4    4    3   3  11
+--R     -- B c e x   + ((-- A c  + -- B b c )e  + -- B c d e )x
+--R     12               11        11             11
+--R   + 
+--R        3      2    3    2   4    2    3   6      2    3   3    3 2 2  10
+--R     ((-- A b c  + -- B b c)e  + (- A c  + - B b c )d e  + - B c d e )x
+--R       10          10             5        5               5
+--R   + 
+--R          1    2    1    3  4    4      2   4    2     3
+--R         (- A b c + - B b )e  + (- A b c  + - B b c)d e
+--R          3         9            3          3
+--R       + 
+--R          2    3         2  2 2   4    3 3
+--R         (- A c  + 2B b c )d e  + - B c d e
+--R          3                       9
+--R    *
+--R        9
+--R       x
+--R   + 
+--R         1    3 4    3    2    1    3    3    9      2   9    2   2 2
+--R         - A b e  + (- A b c + - B b )d e  + (- A b c  + - B b c)d e
+--R         8           2         2              4          4
+--R       + 
+--R          1    3   3      2  3    1    3 4
+--R         (- A c  + - B b c )d e + - B c d
+--R          2        2              8
+--R    *
+--R        8
+--R       x
+--R   + 
+--R         4    3   3    18    2    6    3  2 2    12      2   12    2   3
+--R         - A b d e  + (-- A b c + - B b )d e  + (-- A b c  + -- B b c)d e
+--R         7              7         7               7           7
+--R       + 
+--R          1    3   3      2  4
+--R         (- A c  + - B b c )d
+--R          7        7
+--R    *
+--R        7
+--R       x
+--R   + 
+--R         3 2 2        2    2    3  3     1      2   1    2   4  6
+--R     (A b d e  + (2A b c + - B b )d e + (- A b c  + - B b c)d )x
+--R                           3             2          2
+--R   + 
+--R      4    3 3     3    2    1    3  4  5   1    3 4 4
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      5            5         5              4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 128
+
+--S 129 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 129
+
+--S 130 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 130
+
+)clear all
+
+--S 131 of 1457
+t0:=(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R        3 3 10        3         2  3       3   2  9
+--R     B c e x   + ((A c  + 3B b c )e  + 3B c d e )x
+--R   + 
+--R             2       2   3        3         2    2       3 2   8
+--R     ((3A b c  + 3B b c)e  + (3A c  + 9B b c )d e  + 3B c d e)x
+--R   + 
+--R              2       3  3          2       2     2        3         2  2
+--R         (3A b c + B b )e  + (9A b c  + 9B b c)d e  + (3A c  + 9B b c )d e
+--R       + 
+--R            3 3
+--R         B c d
+--R    *
+--R        7
+--R       x
+--R   + 
+--R            3 3        2        3    2          2       2   2
+--R         A b e  + (9A b c + 3B b )d e  + (9A b c  + 9B b c)d e
+--R       + 
+--R             3         2  3
+--R         (A c  + 3B b c )d
+--R    *
+--R        6
+--R       x
+--R   + 
+--R          3   2        2        3  2           2       2   3  5
+--R     (3A b d e  + (9A b c + 3B b )d e + (3A b c  + 3B b c)d )x
+--R   + 
+--R          3 2         2       3  3  4      3 3 3
+--R     (3A b d e + (3A b c + B b )d )x  + A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 131
+
+--S 132 of 1457
+r0:=1/4*A*b^3*d^3*x^4+1/5*b^2*d^2*(b*B*d+3*A*c*d+3*A*b*e)*x^5+1/2*b*d*_
+     (A*c^2*d^2+b^2*e*(B*d+A*e)+b*c*d*(B*d+3*A*e))*x^6+1/7*(A*c^3*d^3+_
+     9*b^2*c*d*e*(B*d+A*e)+b^3*e^2*(3*B*d+A*e)+3*b*c^2*d^2*(B*d+3*A*e))*_
+     x^7+1/8*(3*A*c*e*(c^2*d^2+3*b*c*d*e+b^2*e^2)+B*(c^3*d^3+9*b*c^2*d^2*e+_
+     9*b^2*c*d*e^2+b^3*e^3))*x^8+1/3*c*e*(A*c*e*(c*d+b*e)+B*(c^2*d^2+_
+     3*b*c*d*e+b^2*e^2))*x^9+1/10*c^2*e^2*(A*c*e+3*B*(c*d+b*e))*x^10+_
+     1/11*B*c^3*e^3*x^11
+--R 
+--R
+--R   (2)
+--R      1    3 3 11      1    3    3      2  3    3    3   2  10
+--R     -- B c e x   + ((-- A c  + -- B b c )e  + -- B c d e )x
+--R     11               10        10             10
+--R   + 
+--R       1      2   1    2   3    1    3        2    2   1    3 2   9
+--R     ((- A b c  + - B b c)e  + (- A c  + B b c )d e  + - B c d e)x
+--R       3          3             3                      3
+--R   + 
+--R          3    2    1    3  3    9      2   9    2     2
+--R         (- A b c + - B b )e  + (- A b c  + - B b c)d e
+--R          8         8            8          8
+--R       + 
+--R          3    3   9      2  2    1    3 3
+--R         (- A c  + - B b c )d e + - B c d
+--R          8        8              8
+--R    *
+--R        8
+--R       x
+--R   + 
+--R         1    3 3    9    2    3    3    2    9      2   9    2   2
+--R         - A b e  + (- A b c + - B b )d e  + (- A b c  + - B b c)d e
+--R         7           7         7              7          7
+--R       + 
+--R          1    3   3      2  3
+--R         (- A c  + - B b c )d
+--R          7        7
+--R    *
+--R        7
+--R       x
+--R   + 
+--R      1    3   2    3    2    1    3  2     1      2   1    2   3  6
+--R     (- A b d e  + (- A b c + - B b )d e + (- A b c  + - B b c)d )x
+--R      2             2         2             2          2
+--R   + 
+--R      3    3 2     3    2    1    3  3  5   1    3 3 4
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      5            5         5              4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 132
+
+--S 133 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R      1    3 3 11      1    3    3      2  3    3    3   2  10
+--R     -- B c e x   + ((-- A c  + -- B b c )e  + -- B c d e )x
+--R     11               10        10             10
+--R   + 
+--R       1      2   1    2   3    1    3        2    2   1    3 2   9
+--R     ((- A b c  + - B b c)e  + (- A c  + B b c )d e  + - B c d e)x
+--R       3          3             3                      3
+--R   + 
+--R          3    2    1    3  3    9      2   9    2     2
+--R         (- A b c + - B b )e  + (- A b c  + - B b c)d e
+--R          8         8            8          8
+--R       + 
+--R          3    3   9      2  2    1    3 3
+--R         (- A c  + - B b c )d e + - B c d
+--R          8        8              8
+--R    *
+--R        8
+--R       x
+--R   + 
+--R         1    3 3    9    2    3    3    2    9      2   9    2   2
+--R         - A b e  + (- A b c + - B b )d e  + (- A b c  + - B b c)d e
+--R         7           7         7              7          7
+--R       + 
+--R          1    3   3      2  3
+--R         (- A c  + - B b c )d
+--R          7        7
+--R    *
+--R        7
+--R       x
+--R   + 
+--R      1    3   2    3    2    1    3  2     1      2   1    2   3  6
+--R     (- A b d e  + (- A b c + - B b )d e + (- A b c  + - B b c)d )x
+--R      2             2         2             2          2
+--R   + 
+--R      3    3 2     3    2    1    3  3  5   1    3 3 4
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      5            5         5              4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 133
+
+--S 134 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 134
+
+--S 135 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 135
+
+)clear all
+
+--S 136 of 1457
+t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R        3 2 9        3         2  2       3     8
+--R     B c e x  + ((A c  + 3B b c )e  + 2B c d e)x
+--R   + 
+--R             2       2   2        3         2          3 2  7
+--R     ((3A b c  + 3B b c)e  + (2A c  + 6B b c )d e + B c d )x
+--R   + 
+--R           2       3  2          2       2            3         2  2  6
+--R     ((3A b c + B b )e  + (6A b c  + 6B b c)d e + (A c  + 3B b c )d )x
+--R   + 
+--R         3 2        2        3              2       2   2  5
+--R     (A b e  + (6A b c + 2B b )d e + (3A b c  + 3B b c)d )x
+--R   + 
+--R          3           2       3  2  4      3 2 3
+--R     (2A b d e + (3A b c + B b )d )x  + A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 136
+
+--S 137 of 1457
+r0:=1/4*A*b^3*d^2*x^4+1/5*b^2*d*(b*B*d+3*A*c*d+2*A*b*e)*x^5+1/6*b*_
+     (3*A*c^2*d^2+b^2*e*(2*B*d+A*e)+3*b*c*d*(B*d+2*A*e))*x^6+1/7*_
+     (A*c^3*d^2+b^3*B*e^2+3*b^2*c*e*(2*B*d+A*e)+3*b*c^2*d*(B*d+2*A*e))*x^7+_
+     1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^8+_
+     1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+1/10*B*c^3*e^2*x^10
+--R 
+--R
+--R   (2)
+--R      1    3 2 10     1    3   1      2  2   2    3     9
+--R     -- B c e x   + ((- A c  + - B b c )e  + - B c d e)x
+--R     10               9        3             9
+--R   + 
+--R       3      2   3    2   2    1    3   3      2       1    3 2  8
+--R     ((- A b c  + - B b c)e  + (- A c  + - B b c )d e + - B c d )x
+--R       8          8             4        4              8
+--R   + 
+--R       3    2    1    3  2    6      2   6    2         1    3   3      2  2  7
+--R     ((- A b c + - B b )e  + (- A b c  + - B b c)d e + (- A c  + - B b c )d )x
+--R       7         7            7          7              7        7
+--R   + 
+--R      1    3 2       2    1    3        1      2   1    2   2  6
+--R     (- A b e  + (A b c + - B b )d e + (- A b c  + - B b c)d )x
+--R      6                   3             2          2
+--R   + 
+--R      2    3       3    2    1    3  2  5   1    3 2 4
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      5            5         5              4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 137
+
+--S 138 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R      1    3 2 10     1    3   1      2  2   2    3     9
+--R     -- B c e x   + ((- A c  + - B b c )e  + - B c d e)x
+--R     10               9        3             9
+--R   + 
+--R       3      2   3    2   2    1    3   3      2       1    3 2  8
+--R     ((- A b c  + - B b c)e  + (- A c  + - B b c )d e + - B c d )x
+--R       8          8             4        4              8
+--R   + 
+--R       3    2    1    3  2    6      2   6    2         1    3   3      2  2  7
+--R     ((- A b c + - B b )e  + (- A b c  + - B b c)d e + (- A c  + - B b c )d )x
+--R       7         7            7          7              7        7
+--R   + 
+--R      1    3 2       2    1    3        1      2   1    2   2  6
+--R     (- A b e  + (A b c + - B b )d e + (- A b c  + - B b c)d )x
+--R      6                   3             2          2
+--R   + 
+--R      2    3       3    2    1    3  2  5   1    3 2 4
+--R     (- A b d e + (- A b c + - B b )d )x  + - A b d x
+--R      5            5         5              4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 138
+
+--S 139 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 139
+
+--S 140 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 140
+
+)clear all
+
+--S 141 of 1457
+t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R        3   8        3         2        3   7
+--R     B c e x  + ((A c  + 3B b c )e + B c d)x
+--R   + 
+--R             2       2          3         2    6
+--R     ((3A b c  + 3B b c)e + (A c  + 3B b c )d)x
+--R   + 
+--R           2       3            2       2     5       3         2       3    4
+--R     ((3A b c + B b )e + (3A b c  + 3B b c)d)x  + (A b e + (3A b c + B b )d)x
+--R   + 
+--R        3   3
+--R     A b d x
+--R                                                    Type: Polynomial(Integer)
+--E 141
+
+--S 142 of 1457
+r0:=1/4*A*b^3*d*x^4+1/5*b^2*(b*B*d+3*A*c*d+A*b*e)*x^5+1/6*b*(3*A*c^2*d+_
+     b^2*B*e+3*b*c*(B*d+A*e))*x^6+1/7*c*(A*c^2*d+3*b^2*B*e+3*b*c*(B*d+_
+     A*e))*x^7+1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9
+--R 
+--R
+--R   (2)
+--R     1    3   9     1    3   3      2     1    3   8
+--R     - B c e x  + ((- A c  + - B b c )e + - B c d)x
+--R     9              8        8            8
+--R   + 
+--R       3      2   3    2       1    3   3      2    7
+--R     ((- A b c  + - B b c)e + (- A c  + - B b c )d)x
+--R       7          7            7        7
+--R   + 
+--R       1    2    1    3      1      2   1    2     6
+--R     ((- A b c + - B b )e + (- A b c  + - B b c)d)x
+--R       2         6           2          2
+--R   + 
+--R      1    3     3    2    1    3    5   1    3   4
+--R     (- A b e + (- A b c + - B b )d)x  + - A b d x
+--R      5          5         5             4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 142
+
+--S 143 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1    3   9     1    3   3      2     1    3   8
+--R     - B c e x  + ((- A c  + - B b c )e + - B c d)x
+--R     9              8        8            8
+--R   + 
+--R       3      2   3    2       1    3   3      2    7
+--R     ((- A b c  + - B b c)e + (- A c  + - B b c )d)x
+--R       7          7            7        7
+--R   + 
+--R       1    2    1    3      1      2   1    2     6
+--R     ((- A b c + - B b )e + (- A b c  + - B b c)d)x
+--R       2         6           2          2
+--R   + 
+--R      1    3     3    2    1    3    5   1    3   4
+--R     (- A b e + (- A b c + - B b )d)x  + - A b d x
+--R      5          5         5             4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 143
+
+--S 144 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 144
+
+--S 145 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 145
+
+)clear all
+
+--S 146 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R        3 7       3         2  6          2       2   5        2       3  4
+--R     B c x  + (A c  + 3B b c )x  + (3A b c  + 3B b c)x  + (3A b c + B b )x
+--R   + 
+--R        3 3
+--R     A b x
+--R                                                    Type: Polynomial(Integer)
+--E 146
+
+--S 147 of 1457
+r0:=1/4*A*b^3*x^4+1/5*b^2*(b*B+3*A*c)*x^5+1/2*b*c*(b*B+A*c)*x^6+_
+     1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8
+--R 
+--R
+--R   (2)
+--R     1    3 8    1    3   3      2  7    1      2   1    2   6
+--R     - B c x  + (- A c  + - B b c )x  + (- A b c  + - B b c)x
+--R     8           7        7              2          2
+--R   + 
+--R      3    2    1    3  5   1    3 4
+--R     (- A b c + - B b )x  + - A b x
+--R      5         5           4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 147
+
+--S 148 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R     1    3 8    1    3   3      2  7    1      2   1    2   6
+--R     - B c x  + (- A c  + - B b c )x  + (- A b c  + - B b c)x
+--R     8           7        7              2          2
+--R   + 
+--R      3    2    1    3  5   1    3 4
+--R     (- A b c + - B b )x  + - A b x
+--R      5         5           4
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 148
+
+--S 149 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 149
+
+--S 150 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                          Type: Polynomial(Fraction(Integer))
+--E 150
+
+)clear all
+
+--S 151 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)
+--R 
+--R
+--R   (1)
+--R          3 7       3         2  6          2       2   5        2       3  4
+--R       B c x  + (A c  + 3B b c )x  + (3A b c  + 3B b c)x  + (3A b c + B b )x
+--R     + 
+--R          3 3
+--R       A b x
+--R  /
+--R     e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 1457
+r0:=d^2*(B*d-A*e)*(c*d-b*e)^3*x/e^7-1/2*d*(B*d-A*e)*(c*d-b*e)^3*x^2/e^6+_
+     1/3*(B*d-A*e)*(c*d-b*e)^3*x^3/e^5-1/4*(B*(c*d-b*e)^3-A*c*e*(c^2*d^2-_
+     3*b*c*d*e+3*b^2*e^2))*x^4/e^4-1/5*c*(A*c*e*(c*d-3*b*e)-B*(c^2*d^2-_
+     3*b*c*d*e+3*b^2*e^2))*x^5/e^3-1/6*c^2*(B*c*d-3*b*B*e-A*c*e)*x^6/e^2+_
+     1/7*B*c^3*x^7/e-d^3*(B*d-A*e)*(c*d-b*e)^3*log(d+e*x)/e^8
+--R 
+--R
+--R   (2)
+--R                   3 3 4           2          3  4 3
+--R           - 420A b d e  + (1260A b c + 420B b )d e
+--R         + 
+--R                     2          2   5 2          3            2  6          3 7
+--R         (- 1260A b c  - 1260B b c)d e  + (420A c  + 1260B b c )d e - 420B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R            3 7 7          3           2  7        3   6  6
+--R       60B c e x  + ((70A c  + 210B b c )e  - 70B c d e )x
+--R     + 
+--R                 2         2   7           3           2    6        3 2 5  5
+--R       ((252A b c  + 252B b c)e  + (- 84A c  - 252B b c )d e  + 84B c d e )x
+--R     + 
+--R                  2          3  7              2         2     6
+--R           (315A b c + 105B b )e  + (- 315A b c  - 315B b c)d e
+--R         + 
+--R                  3           2  2 5         3 3 4
+--R           (105A c  + 315B b c )d e  - 105B c d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                 3 7            2          3    6            2         2   2 5
+--R           140A b e  + (- 420A b c - 140B b )d e  + (420A b c  + 420B b c)d e
+--R         + 
+--R                    3           2  3 4         3 4 3
+--R           (- 140A c  - 420B b c )d e  + 140B c d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                   3   6          2          3  2 5
+--R           - 210A b d e  + (630A b c + 210B b )d e
+--R         + 
+--R                    2         2   3 4          3           2  4 3         3 5 2
+--R         (- 630A b c  - 630B b c)d e  + (210A c  + 630B b c )d e  - 210B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                 3 2 5             2          3  3 4
+--R           420A b d e  + (- 1260A b c - 420B b )d e
+--R         + 
+--R                     2          2   4 3            3            2  5 2
+--R           (1260A b c  + 1260B b c)d e  + (- 420A c  - 1260B b c )d e
+--R         + 
+--R                 3 6
+--R           420B c d e
+--R      *
+--R         x
+--R  /
+--R         8
+--R     420e
+--R                                                    Type: Expression(Integer)
+--E 152
+
+--S 153 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                   3 3 4           2          3  4 3
+--R           - 420A b d e  + (1260A b c + 420B b )d e
+--R         + 
+--R                     2          2   5 2          3            2  6          3 7
+--R         (- 1260A b c  - 1260B b c)d e  + (420A c  + 1260B b c )d e - 420B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R            3 7 7          3           2  7        3   6  6
+--R       60B c e x  + ((70A c  + 210B b c )e  - 70B c d e )x
+--R     + 
+--R                 2         2   7           3           2    6        3 2 5  5
+--R       ((252A b c  + 252B b c)e  + (- 84A c  - 252B b c )d e  + 84B c d e )x
+--R     + 
+--R                  2          3  7              2         2     6
+--R           (315A b c + 105B b )e  + (- 315A b c  - 315B b c)d e
+--R         + 
+--R                  3           2  2 5         3 3 4
+--R           (105A c  + 315B b c )d e  - 105B c d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                 3 7            2          3    6            2         2   2 5
+--R           140A b e  + (- 420A b c - 140B b )d e  + (420A b c  + 420B b c)d e
+--R         + 
+--R                    3           2  3 4         3 4 3
+--R           (- 140A c  - 420B b c )d e  + 140B c d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                   3   6          2          3  2 5
+--R           - 210A b d e  + (630A b c + 210B b )d e
+--R         + 
+--R                    2         2   3 4          3           2  4 3         3 5 2
+--R         (- 630A b c  - 630B b c)d e  + (210A c  + 630B b c )d e  - 210B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                 3 2 5             2          3  3 4
+--R           420A b d e  + (- 1260A b c - 420B b )d e
+--R         + 
+--R                     2          2   4 3            3            2  5 2
+--R           (1260A b c  + 1260B b c)d e  + (- 420A c  - 1260B b c )d e
+--R         + 
+--R                 3 6
+--R           420B c d e
+--R      *
+--R         x
+--R  /
+--R         8
+--R     420e
+--R                                         Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 154
+
+--S 155 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^2
+--R 
+--R
+--R   (1)
+--R          3 7       3         2  6          2       2   5        2       3  4
+--R       B c x  + (A c  + 3B b c )x  + (3A b c  + 3B b c)x  + (3A b c + B b )x
+--R     + 
+--R          3 3
+--R       A b x
+--R  /
+--R      2 2             2
+--R     e x  + 2d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 1457
+r0:=d*(c*d-b*e)^2*(A*e*(5*c*d-2*b*e)-3*B*d*(2*c*d-b*e))*x/e^7+_
+     1/2*(c*d-b*e)^2*(B*d*(5*c*d-2*b*e)-A*e*(4*c*d-b*e))*x^2/e^6-_
+     1/3*(c*d-b*e)^2*(4*B*c*d-b*B*e-3*A*c*e)*x^3/e^5-1/4*c*(A*c*e*_
+     (2*c*d-3*b*e)-3*B*(c*d-b*e)^2)*x^4/e^4-1/5*c^2*(2*B*c*d-3*b*B*e-_
+     A*c*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*_
+     (d+e*x))+d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*_
+     log(d+e*x)/e^8
+--R 
+--R
+--R   (2)
+--R                     3 2 5            2          3  3 4
+--R               180A b d e  + (- 720A b c - 240B b )d e
+--R             + 
+--R                        2         2   4 3            3            2  5 2
+--R               (900A b c  + 900B b c)d e  + (- 360A c  - 1080B b c )d e
+--R             + 
+--R                     3 6
+--R               420B c d e
+--R          *
+--R             x
+--R         + 
+--R                 3 3 4            2          3  4 3            2         2   5 2
+--R           180A b d e  + (- 720A b c - 240B b )d e  + (900A b c  + 900B b c)d e
+--R         + 
+--R                    3            2  6          3 7
+--R           (- 360A c  - 1080B b c )d e + 420B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R            3 7 7          3          2  7        3   6  6
+--R       10B c e x  + ((12A c  + 36B b c )e  - 14B c d e )x
+--R     + 
+--R                2        2   7           3          2    6        3 2 5  5
+--R       ((45A b c  + 45B b c)e  + (- 18A c  - 54B b c )d e  + 21B c d e )x
+--R     + 
+--R                 2         3  7             2        2     6
+--R           (60A b c + 20B b )e  + (- 75A b c  - 75B b c)d e
+--R         + 
+--R                 3          2  2 5        3 3 4
+--R           (30A c  + 90B b c )d e  - 35B c d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                3 7            2         3    6            2         2   2 5
+--R           30A b e  + (- 120A b c - 40B b )d e  + (150A b c  + 150B b c)d e
+--R         + 
+--R                   3           2  3 4        3 4 3
+--R           (- 60A c  - 180B b c )d e  + 70B c d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                  3   6          2          3  2 5
+--R           - 90A b d e  + (360A b c + 120B b )d e
+--R         + 
+--R                    2         2   3 4          3           2  4 3         3 5 2
+--R         (- 450A b c  - 450B b c)d e  + (180A c  + 540B b c )d e  - 210B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                   3 2 5          2          3  3 4
+--R           - 120A b d e  + (540A b c + 180B b )d e
+--R         + 
+--R                    2         2   4 3          3           2  5 2         3 6
+--R         (- 720A b c  - 720B b c)d e  + (300A c  + 900B b c )d e  - 360B c d e
+--R      *
+--R         x
+--R     + 
+--R            3 3 4            2         3  4 3            2         2   5 2
+--R       60A b d e  + (- 180A b c - 60B b )d e  + (180A b c  + 180B b c)d e
+--R     + 
+--R               3           2  6         3 7
+--R       (- 60A c  - 180B b c )d e + 60B c d
+--R  /
+--R        9         8
+--R     60e x + 60d e
+--R                                                    Type: Expression(Integer)
+--E 157
+
+--S 158 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                     3 2 5            2          3  3 4
+--R               180A b d e  + (- 720A b c - 240B b )d e
+--R             + 
+--R                        2         2   4 3            3            2  5 2
+--R               (900A b c  + 900B b c)d e  + (- 360A c  - 1080B b c )d e
+--R             + 
+--R                     3 6
+--R               420B c d e
+--R          *
+--R             x
+--R         + 
+--R                 3 3 4            2          3  4 3            2         2   5 2
+--R           180A b d e  + (- 720A b c - 240B b )d e  + (900A b c  + 900B b c)d e
+--R         + 
+--R                    3            2  6          3 7
+--R           (- 360A c  - 1080B b c )d e + 420B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R            3 7 7          3          2  7        3   6  6
+--R       10B c e x  + ((12A c  + 36B b c )e  - 14B c d e )x
+--R     + 
+--R                2        2   7           3          2    6        3 2 5  5
+--R       ((45A b c  + 45B b c)e  + (- 18A c  - 54B b c )d e  + 21B c d e )x
+--R     + 
+--R                 2         3  7             2        2     6
+--R           (60A b c + 20B b )e  + (- 75A b c  - 75B b c)d e
+--R         + 
+--R                 3          2  2 5        3 3 4
+--R           (30A c  + 90B b c )d e  - 35B c d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                3 7            2         3    6            2         2   2 5
+--R           30A b e  + (- 120A b c - 40B b )d e  + (150A b c  + 150B b c)d e
+--R         + 
+--R                   3           2  3 4        3 4 3
+--R           (- 60A c  - 180B b c )d e  + 70B c d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                  3   6          2          3  2 5
+--R           - 90A b d e  + (360A b c + 120B b )d e
+--R         + 
+--R                    2         2   3 4          3           2  4 3         3 5 2
+--R         (- 450A b c  - 450B b c)d e  + (180A c  + 540B b c )d e  - 210B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                   3 2 5          2          3  3 4
+--R           - 120A b d e  + (540A b c + 180B b )d e
+--R         + 
+--R                    2         2   4 3          3           2  5 2         3 6
+--R         (- 720A b c  - 720B b c)d e  + (300A c  + 900B b c )d e  - 360B c d e
+--R      *
+--R         x
+--R     + 
+--R            3 3 4            2         3  4 3            2         2   5 2
+--R       60A b d e  + (- 180A b c - 60B b )d e  + (180A b c  + 180B b c)d e
+--R     + 
+--R               3           2  6         3 7
+--R       (- 60A c  - 180B b c )d e + 60B c d
+--R  /
+--R        9         8
+--R     60e x + 60d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 159
+
+--S 160 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^3
+--R 
+--R
+--R   (1)
+--R          3 7       3         2  6          2       2   5        2       3  4
+--R       B c x  + (A c  + 3B b c )x  + (3A b c  + 3B b c)x  + (3A b c + B b )x
+--R     + 
+--R          3 3
+--R       A b x
+--R  /
+--R      3 3       2 2     2       3
+--R     e x  + 3d e x  + 3d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 1457
+r0:=-(c*d-b*e)*(A*e*(10*c^2*d^2-8*b*c*d*e+b^2*e^2)-3*B*d*(5*c^2*d^2-_
+     5*b*c*d*e+b^2*e^2))*x/e^7+1/2*(c*d-b*e)*(3*A*c*e*(2*c*d-b*e)-_
+     B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*x^2/e^6+c*(c*d-b*e)*(2*B*c*d-b*B*e-_
+     A*c*e)*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*x^4/e^4+1/5*B*c^3*_
+     x^5/e^3+1/2*d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*(d+e*x)^2)-d^2*_
+     (c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))/(e^8*(d+e*x))+_
+     3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-_
+     8*b*c*d*e+2*b^2*e^2))*log(d+e*x)/e^8
+--R 
+--R
+--R   (2)
+--R                      3   6          2          3  2 5
+--R               - 60A b d e  + (360A b c + 120B b )d e
+--R             + 
+--R                          2         2   3 4          3           2  4 3
+--R               (- 600A b c  - 600B b c)d e  + (300A c  + 900B b c )d e
+--R             + 
+--R                       3 5 2
+--R               - 420B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                       3 2 5          2          3  3 4
+--R               - 120A b d e  + (720A b c + 240B b )d e
+--R             + 
+--R                           2          2   4 3          3            2  5 2
+--R               (- 1200A b c  - 1200B b c)d e  + (600A c  + 1800B b c )d e
+--R             + 
+--R                       3 6
+--R               - 840B c d e
+--R          *
+--R             x
+--R         + 
+--R                  3 3 4          2          3  4 3
+--R           - 60A b d e  + (360A b c + 120B b )d e
+--R         + 
+--R                      2         2   5 2          3           2  6          3 7
+--R           (- 600A b c  - 600B b c)d e  + (300A c  + 900B b c )d e - 420B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           3 7 7         3          2  7       3   6  6
+--R       4B c e x  + ((5A c  + 15B b c )e  - 7B c d e )x
+--R     + 
+--R                2        2   7           3          2    6        3 2 5  5
+--R       ((20A b c  + 20B b c)e  + (- 10A c  - 30B b c )d e  + 14B c d e )x
+--R     + 
+--R                 2         3  7             2        2     6
+--R           (30A b c + 10B b )e  + (- 50A b c  - 50B b c)d e
+--R         + 
+--R                 3          2  2 5        3 3 4
+--R           (25A c  + 75B b c )d e  - 35B c d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                3 7            2         3    6            2         2   2 5
+--R           20A b e  + (- 120A b c - 40B b )d e  + (200A b c  + 200B b c)d e
+--R         + 
+--R                    3           2  3 4         3 4 3
+--R           (- 100A c  - 300B b c )d e  + 140B c d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                3   6            2          3  2 5            2         2   3 4
+--R           40A b d e  + (- 330A b c - 110B b )d e  + (630A b c  + 630B b c)d e
+--R         + 
+--R                    3            2  4 3         3 5 2
+--R           (- 340A c  - 1020B b c )d e  + 500B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                  3 2 5         2         3  3 4           2        2   4 3
+--R           - 40A b d e  + (60A b c + 20B b )d e  + (60A b c  + 60B b c)d e
+--R         + 
+--R                   3           2  5 2         3 6
+--R           (- 80A c  - 240B b c )d e  + 160B c d e
+--R      *
+--R         x
+--R     + 
+--R              3 3 4          2         3  4 3              2         2   5 2
+--R       - 50A b d e  + (210A b c + 70B b )d e  + (- 270A b c  - 270B b c)d e
+--R     + 
+--R              3           2  6          3 7
+--R       (110A c  + 330B b c )d e - 130B c d
+--R  /
+--R        10 2        9       2 8
+--R     20e  x  + 40d e x + 20d e
+--R                                                    Type: Expression(Integer)
+--E 162
+
+--S 163 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                      3   6          2          3  2 5
+--R               - 60A b d e  + (360A b c + 120B b )d e
+--R             + 
+--R                          2         2   3 4          3           2  4 3
+--R               (- 600A b c  - 600B b c)d e  + (300A c  + 900B b c )d e
+--R             + 
+--R                       3 5 2
+--R               - 420B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                       3 2 5          2          3  3 4
+--R               - 120A b d e  + (720A b c + 240B b )d e
+--R             + 
+--R                           2          2   4 3          3            2  5 2
+--R               (- 1200A b c  - 1200B b c)d e  + (600A c  + 1800B b c )d e
+--R             + 
+--R                       3 6
+--R               - 840B c d e
+--R          *
+--R             x
+--R         + 
+--R                  3 3 4          2          3  4 3
+--R           - 60A b d e  + (360A b c + 120B b )d e
+--R         + 
+--R                      2         2   5 2          3           2  6          3 7
+--R           (- 600A b c  - 600B b c)d e  + (300A c  + 900B b c )d e - 420B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           3 7 7         3          2  7       3   6  6
+--R       4B c e x  + ((5A c  + 15B b c )e  - 7B c d e )x
+--R     + 
+--R                2        2   7           3          2    6        3 2 5  5
+--R       ((20A b c  + 20B b c)e  + (- 10A c  - 30B b c )d e  + 14B c d e )x
+--R     + 
+--R                 2         3  7             2        2     6
+--R           (30A b c + 10B b )e  + (- 50A b c  - 50B b c)d e
+--R         + 
+--R                 3          2  2 5        3 3 4
+--R           (25A c  + 75B b c )d e  - 35B c d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                3 7            2         3    6            2         2   2 5
+--R           20A b e  + (- 120A b c - 40B b )d e  + (200A b c  + 200B b c)d e
+--R         + 
+--R                    3           2  3 4         3 4 3
+--R           (- 100A c  - 300B b c )d e  + 140B c d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                3   6            2          3  2 5            2         2   3 4
+--R           40A b d e  + (- 330A b c - 110B b )d e  + (630A b c  + 630B b c)d e
+--R         + 
+--R                    3            2  4 3         3 5 2
+--R           (- 340A c  - 1020B b c )d e  + 500B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                  3 2 5         2         3  3 4           2        2   4 3
+--R           - 40A b d e  + (60A b c + 20B b )d e  + (60A b c  + 60B b c)d e
+--R         + 
+--R                   3           2  5 2         3 6
+--R           (- 80A c  - 240B b c )d e  + 160B c d e
+--R      *
+--R         x
+--R     + 
+--R              3 3 4          2         3  4 3              2         2   5 2
+--R       - 50A b d e  + (210A b c + 70B b )d e  + (- 270A b c  - 270B b c)d e
+--R     + 
+--R              3           2  6          3 7
+--R       (110A c  + 330B b c )d e - 130B c d
+--R  /
+--R        10 2        9       2 8
+--R     20e  x  + 40d e x + 20d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 164
+
+--S 165 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^4
+--R 
+--R
+--R   (1)
+--R          3 7       3         2  6          2       2   5        2       3  4
+--R       B c x  + (A c  + 3B b c )x  + (3A b c  + 3B b c)x  + (3A b c + B b )x
+--R     + 
+--R          3 3
+--R       A b x
+--R  /
+--R      4 4       3 3     2 2 2     3       4
+--R     e x  + 4d e x  + 6d e x  + 4d e x + d
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 1457
+r0:=(A*c*e*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2)-B*(20*c^3*d^3-30*b*c^2*d^2*e+_
+     12*b^2*c*d*e^2-b^3*e^3))*x/e^7-1/2*c*(A*c*e*(4*c*d-3*b*e)-_
+     B*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*x^2/e^6-1/3*c^2*(4*B*c*d-_
+     3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*d^3*(B*d-A*e)*_
+     (c*d-b*e)^3/(e^8*(d+e*x)^3)-1/2*d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-_
+     3*A*e*(2*c*d-b*e))/(e^8*(d+e*x)^2)-3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-_
+     5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-8*b*c*d*e+2*b^2*e^2))/(e^8*_
+     (d+e*x))+(B*d*(35*c^3*d^3-60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-_
+     A*e*(20*c^3*d^3-30*b*c^2*d^2*e+12*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/e^8
+--R 
+--R
+--R   (2)
+--R                    3 7            2         3    6            2         2   2 5
+--R               12A b e  + (- 144A b c - 48B b )d e  + (360A b c  + 360B b c)d e
+--R             + 
+--R                        3           2  3 4         3 4 3
+--R               (- 240A c  - 720B b c )d e  + 420B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                    3   6            2          3  2 5
+--R               36A b d e  + (- 432A b c - 144B b )d e
+--R             + 
+--R                         2          2   3 4            3            2  4 3
+--R               (1080A b c  + 1080B b c)d e  + (- 720A c  - 2160B b c )d e
+--R             + 
+--R                      3 5 2
+--R               1260B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    3 2 5            2          3  3 4
+--R               36A b d e  + (- 432A b c - 144B b )d e
+--R             + 
+--R                         2          2   4 3            3            2  5 2
+--R               (1080A b c  + 1080B b c)d e  + (- 720A c  - 2160B b c )d e
+--R             + 
+--R                      3 6
+--R               1260B c d e
+--R          *
+--R             x
+--R         + 
+--R                3 3 4            2         3  4 3            2         2   5 2
+--R           12A b d e  + (- 144A b c - 48B b )d e  + (360A b c  + 360B b c)d e
+--R         + 
+--R                    3           2  6          3 7
+--R           (- 240A c  - 720B b c )d e + 420B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           3 7 7         3          2  7       3   6  6
+--R       3B c e x  + ((4A c  + 12B b c )e  - 7B c d e )x
+--R     + 
+--R                2        2   7           3          2    6        3 2 5  5
+--R       ((18A b c  + 18B b c)e  + (- 12A c  - 36B b c )d e  + 21B c d e )x
+--R     + 
+--R                 2         3  7             2        2     6
+--R           (36A b c + 12B b )e  + (- 90A b c  - 90B b c)d e
+--R         + 
+--R                 3           2  2 5         3 3 4
+--R           (60A c  + 180B b c )d e  - 105B c d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                  2         3    6              2         2   2 5
+--R           (108A b c + 36B b )d e  + (- 378A b c  - 378B b c)d e
+--R         + 
+--R                  3           2  3 4         3 4 3
+--R           (292A c  + 876B b c )d e  - 556B c d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                3   6            2         3  2 5             2        2   3 4
+--R           36A b d e  + (- 108A b c - 36B b )d e  + (- 54A b c  - 54B b c)d e
+--R         + 
+--R                  3           2  4 3         3 5 2
+--R           (156A c  + 468B b c )d e  - 408B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                3 2 5            2          3  3 4            2         2   4 3
+--R           54A b d e  + (- 324A b c - 108B b )d e  + (486A b c  + 486B b c)d e
+--R         + 
+--R                    3           2  5 2         3 6
+--R           (- 204A c  - 612B b c )d e  + 222B c d e
+--R      *
+--R         x
+--R     + 
+--R            3 3 4            2         3  4 3            2         2   5 2
+--R       22A b d e  + (- 156A b c - 52B b )d e  + (282A b c  + 282B b c)d e
+--R     + 
+--R                3           2  6          3 7
+--R       (- 148A c  - 444B b c )d e + 214B c d
+--R  /
+--R        11 3        10 2      2 9       3 8
+--R     12e  x  + 36d e  x  + 36d e x + 12d e
+--R                                                    Type: Expression(Integer)
+--E 167
+
+--S 168 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                    3 7            2         3    6            2         2   2 5
+--R               12A b e  + (- 144A b c - 48B b )d e  + (360A b c  + 360B b c)d e
+--R             + 
+--R                        3           2  3 4         3 4 3
+--R               (- 240A c  - 720B b c )d e  + 420B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                    3   6            2          3  2 5
+--R               36A b d e  + (- 432A b c - 144B b )d e
+--R             + 
+--R                         2          2   3 4            3            2  4 3
+--R               (1080A b c  + 1080B b c)d e  + (- 720A c  - 2160B b c )d e
+--R             + 
+--R                      3 5 2
+--R               1260B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    3 2 5            2          3  3 4
+--R               36A b d e  + (- 432A b c - 144B b )d e
+--R             + 
+--R                         2          2   4 3            3            2  5 2
+--R               (1080A b c  + 1080B b c)d e  + (- 720A c  - 2160B b c )d e
+--R             + 
+--R                      3 6
+--R               1260B c d e
+--R          *
+--R             x
+--R         + 
+--R                3 3 4            2         3  4 3            2         2   5 2
+--R           12A b d e  + (- 144A b c - 48B b )d e  + (360A b c  + 360B b c)d e
+--R         + 
+--R                    3           2  6          3 7
+--R           (- 240A c  - 720B b c )d e + 420B c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R           3 7 7         3          2  7       3   6  6
+--R       3B c e x  + ((4A c  + 12B b c )e  - 7B c d e )x
+--R     + 
+--R                2        2   7           3          2    6        3 2 5  5
+--R       ((18A b c  + 18B b c)e  + (- 12A c  - 36B b c )d e  + 21B c d e )x
+--R     + 
+--R                 2         3  7             2        2     6
+--R           (36A b c + 12B b )e  + (- 90A b c  - 90B b c)d e
+--R         + 
+--R                 3           2  2 5         3 3 4
+--R           (60A c  + 180B b c )d e  - 105B c d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                  2         3    6              2         2   2 5
+--R           (108A b c + 36B b )d e  + (- 378A b c  - 378B b c)d e
+--R         + 
+--R                  3           2  3 4         3 4 3
+--R           (292A c  + 876B b c )d e  - 556B c d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                3   6            2         3  2 5             2        2   3 4
+--R           36A b d e  + (- 108A b c - 36B b )d e  + (- 54A b c  - 54B b c)d e
+--R         + 
+--R                  3           2  4 3         3 5 2
+--R           (156A c  + 468B b c )d e  - 408B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                3 2 5            2          3  3 4            2         2   4 3
+--R           54A b d e  + (- 324A b c - 108B b )d e  + (486A b c  + 486B b c)d e
+--R         + 
+--R                    3           2  5 2         3 6
+--R           (- 204A c  - 612B b c )d e  + 222B c d e
+--R      *
+--R         x
+--R     + 
+--R            3 3 4            2         3  4 3            2         2   5 2
+--R       22A b d e  + (- 156A b c - 52B b )d e  + (282A b c  + 282B b c)d e
+--R     + 
+--R                3           2  6          3 7
+--R       (- 148A c  - 444B b c )d e + 214B c d
+--R  /
+--R        11 3        10 2      2 9       3 8
+--R     12e  x  + 36d e  x  + 36d e x + 12d e
+--R                                         Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 169
+
+--S 170 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 1457
+t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R          4 5       4         3  4          3       2 2  3
+--R       B e x  + (A e  + 4B d e )x  + (4A d e  + 6B d e )x
+--R     + 
+--R            2 2       3   2        3       4        4
+--R       (6A d e  + 4B d e)x  + (4A d e + B d )x + A d
+--R  /
+--R        2
+--R     c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 1457
+r0:=e*(A*c*e*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)+B*(4*c^3*d^3-6*b*c^2*d^2*e+_
+     4*b^2*c*d*e^2-b^3*e^3))*x/c^4+1/2*e^2*(A*c*e*(4*c*d-b*e)+B*_
+     (6*c^2*d^2-4*b*c*d*e+b^2*e^2))*x^2/c^3+1/3*e^3*(4*B*c*d-b*B*e+_
+     A*c*e)*x^3/c^2+1/4*B*e^4*x^4/c+A*d^4*log(x)/b+(b*B-A*c)*_
+     (c*d-b*e)^4*log(b+c*x)/(b*c^5)
+--R 
+--R
+--R   (2)
+--R                   4         5  4         3 2        4     3
+--R           (- 12A b c + 12B b )e  + (48A b c  - 48B b c)d e
+--R         + 
+--R                   2 3        3 2  2 2           4        2 3  3
+--R           (- 72A b c  + 72B b c )d e  + (48A b c  - 48B b c )d e
+--R         + 
+--R                   5          4  4
+--R           (- 12A c  + 12B b c )d
+--R      *
+--R         log(c x + b)
+--R     + 
+--R            5 4               4 4 4           4       2 3  4          4   3  3
+--R       12A c d log(x) + 3B b c e x  + ((4A b c  - 4B b c )e  + 16B b c d e )x
+--R     + 
+--R               2 3       3 2  4           4        2 3    3          4 2 2  2
+--R       ((- 6A b c  + 6B b c )e  + (24A b c  - 24B b c )d e  + 36B b c d e )x
+--R     + 
+--R                 3 2        4   4           2 3        3 2    3
+--R           (12A b c  - 12B b c)e  + (- 48A b c  + 48B b c )d e
+--R         + 
+--R                   4        2 3  2 2          4 3
+--R           (72A b c  - 72B b c )d e  + 48B b c d e
+--R      *
+--R         x
+--R  /
+--R          5
+--R     12b c
+--R                                                    Type: Expression(Integer)
+--E 172
+
+--S 173 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                   4         5  4         3 2        4     3
+--R           (- 12A b c + 12B b )e  + (48A b c  - 48B b c)d e
+--R         + 
+--R                   2 3        3 2  2 2           4        2 3  3
+--R           (- 72A b c  + 72B b c )d e  + (48A b c  - 48B b c )d e
+--R         + 
+--R                   5          4  4
+--R           (- 12A c  + 12B b c )d
+--R      *
+--R         log(c x + b)
+--R     + 
+--R            5 4               4 4 4           4       2 3  4          4   3  3
+--R       12A c d log(x) + 3B b c e x  + ((4A b c  - 4B b c )e  + 16B b c d e )x
+--R     + 
+--R               2 3       3 2  4           4        2 3    3          4 2 2  2
+--R       ((- 6A b c  + 6B b c )e  + (24A b c  - 24B b c )d e  + 36B b c d e )x
+--R     + 
+--R                 3 2        4   4           2 3        3 2    3
+--R           (12A b c  - 12B b c)e  + (- 48A b c  + 48B b c )d e
+--R         + 
+--R                   4        2 3  2 2          4 3
+--R           (72A b c  - 72B b c )d e  + 48B b c d e
+--R      *
+--R         x
+--R  /
+--R          5
+--R     12b c
+--R                                         Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 174
+
+--S 175 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 1457
+t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R      3 4       3         2  3          2       2   2        2       3        3
+--R   B e x  + (A e  + 3B d e )x  + (3A d e  + 3B d e)x  + (3A d e + B d )x + A d
+--R   ----------------------------------------------------------------------------
+--R                                       2
+--R                                    c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 1457
+r0:=e*(A*c*e*(3*c*d-b*e)+B*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*x/c^3+_
+     1/2*e^2*(3*B*c*d-b*B*e+A*c*e)*x^2/c^2+1/3*B*e^3*x^3/c+A*d^3*_
+     log(x)/b+(b*B-A*c)*(c*d-b*e)^3*log(b+c*x)/(b*c^4)
+--R 
+--R
+--R   (2)
+--R                3        4  3           2 2        3     2
+--R           (6A b c - 6B b )e  + (- 18A b c  + 18B b c)d e
+--R         + 
+--R                   3        2 2  2           4         3  3
+--R           (18A b c  - 18B b c )d e + (- 6A c  + 6B b c )d
+--R      *
+--R         log(c x + b)
+--R     + 
+--R           4 3               3 3 3           3       2 2  3         3   2  2
+--R       6A c d log(x) + 2B b c e x  + ((3A b c  - 3B b c )e  + 9B b c d e )x
+--R     + 
+--R               2 2       3   3           3        2 2    2          3 2
+--R       ((- 6A b c  + 6B b c)e  + (18A b c  - 18B b c )d e  + 18B b c d e)x
+--R  /
+--R         4
+--R     6b c
+--R                                                    Type: Expression(Integer)
+--E 177
+
+--S 178 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                3        4  3           2 2        3     2
+--R           (6A b c - 6B b )e  + (- 18A b c  + 18B b c)d e
+--R         + 
+--R                   3        2 2  2           4         3  3
+--R           (18A b c  - 18B b c )d e + (- 6A c  + 6B b c )d
+--R      *
+--R         log(c x + b)
+--R     + 
+--R           4 3               3 3 3           3       2 2  3         3   2  2
+--R       6A c d log(x) + 2B b c e x  + ((3A b c  - 3B b c )e  + 9B b c d e )x
+--R     + 
+--R               2 2       3   3           3        2 2    2          3 2
+--R       ((- 6A b c  + 6B b c)e  + (18A b c  - 18B b c )d e  + 18B b c d e)x
+--R  /
+--R         4
+--R     6b c
+--R                                         Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 179
+
+--S 180 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 1457
+t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)
+--R 
+--R
+--R           2 3       2           2                2        2
+--R        B e x  + (A e  + 2B d e)x  + (2A d e + B d )x + A d
+--R   (1)  ----------------------------------------------------
+--R                                2
+--R                             c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 1457
+r0:=e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+A*d^2*log(x)/b+_
+     (b*B-A*c)*(c*d-b*e)^2*log(b+c*x)/(b*c^3)
+--R 
+--R
+--R   (2)
+--R                 2        3  2          2       2               3         2  2
+--R         ((- 2A b c + 2B b )e  + (4A b c  - 4B b c)d e + (- 2A c  + 2B b c )d )
+--R      *
+--R         log(c x + b)
+--R     + 
+--R           3 2              2 2 2           2       2   2         2
+--R       2A c d log(x) + B b c e x  + ((2A b c  - 2B b c)e  + 4B b c d e)x
+--R  /
+--R         3
+--R     2b c
+--R                                                    Type: Expression(Integer)
+--E 182
+
+--S 183 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                 2        3  2          2       2               3         2  2
+--R         ((- 2A b c + 2B b )e  + (4A b c  - 4B b c)d e + (- 2A c  + 2B b c )d )
+--R      *
+--R         log(c x + b)
+--R     + 
+--R           3 2              2 2 2           2       2   2         2
+--R       2A c d log(x) + B b c e x  + ((2A b c  - 2B b c)e  + 4B b c d e)x
+--R  /
+--R         3
+--R     2b c
+--R                                         Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 184
+
+--S 185 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 1457
+t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)
+--R 
+--R
+--R             2
+--R        B e x  + (A e + B d)x + A d
+--R   (1)  ---------------------------
+--R                    2
+--R                 c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 1457
+r0:=B*e*x/c+A*d*log(x)/b+(b*B-A*c)*(c*d-b*e)*log(b+c*x)/(b*c^2)
+--R 
+--R
+--R   (2)
+--R                2           2                             2
+--R   ((A b c - B b )e + (- A c  + B b c)d)log(c x + b) + A c d log(x) + B b c e x
+--R   ----------------------------------------------------------------------------
+--R                                          2
+--R                                       b c
+--R                                                    Type: Expression(Integer)
+--E 187
+
+--S 188 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                2           2                             2
+--R   ((A b c - B b )e + (- A c  + B b c)d)log(c x + b) + A c d log(x) + B b c e x
+--R   ----------------------------------------------------------------------------
+--R                                          2
+--R                                       b c
+--R                                         Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 189
+
+--S 190 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 1457
+t0:=(A+B*x)/(b*x+c*x^2)
+--R 
+--R
+--R          B x + A
+--R   (1)  ----------
+--R           2
+--R        c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 1457
+r0:=A*log(x)/b+(b*B-A*c)*log(b+c*x)/(b*c)
+--R 
+--R
+--R        (- A c + B b)log(c x + b) + A c log(x)
+--R   (2)  --------------------------------------
+--R                          b c
+--R                                                    Type: Expression(Integer)
+--E 192
+
+--S 193 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R        (- A c + B b)log(c x + b) + A c log(x)
+--R   (3)  --------------------------------------
+--R                          b c
+--R                                         Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 194
+
+--S 195 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 1457
+t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2))
+--R 
+--R
+--R                    B x + A
+--R   (1)  ------------------------------
+--R             3               2
+--R        c e x  + (b e + c d)x  + b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 1457
+r0:=A*log(x)/(b*d)+(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e))-_
+     (B*d-A*e)*log(d+e*x)/(d*(c*d-b*e))
+--R 
+--R
+--R   (2)
+--R       (- A b e + B b d)log(e x + d) + (A c - B b)d log(c x + b)
+--R     + 
+--R       (A b e - A c d)log(x)
+--R  /
+--R      2           2
+--R     b d e - b c d
+--R                                                    Type: Expression(Integer)
+--E 197
+
+--S 198 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R       (- A b e + B b d)log(e x + d) + (A c - B b)d log(c x + b)
+--R     + 
+--R       (A b e - A c d)log(x)
+--R  /
+--R      2           2
+--R     b d e - b c d
+--R                                         Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 199
+
+--S 200 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 1457
+t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2))
+--R 
+--R
+--R                                B x + A
+--R   (1)  ------------------------------------------------------
+--R           2 4       2           3                2  2      2
+--R        c e x  + (b e  + 2c d e)x  + (2b d e + c d )x  + b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 1457
+r0:=(B*d-A*e)/(d*(c*d-b*e)*(d+e*x))+A*log(x)/(b*d^2)+c*(b*B-A*c)*_
+     log(b+c*x)/(b*(c*d-b*e)^2)-(B*c*d^2-A*e*(2*c*d-b*e))*log(d+e*x)/_
+     (d^2*(c*d-b*e)^2)
+--R 
+--R
+--R   (2)
+--R                 2 3             2          2         2   2           2
+--R           (- A b e  + 2A b c d e  - B b c d e)x - A b d e  + 2A b c d e
+--R         + 
+--R                    3
+--R           - B b c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R              2          2            2          3
+--R       ((- A c  + B b c)d e x + (- A c  + B b c)d )log(c x + b)
+--R     + 
+--R              2 3             2      2 2         2   2           2       2 3
+--R         ((A b e  - 2A b c d e  + A c d e)x + A b d e  - 2A b c d e + A c d )
+--R      *
+--R         log(x)
+--R     + 
+--R          2   2                 2  2           3
+--R       A b d e  + (- A b c - B b )d e + B b c d
+--R  /
+--R       3 2 3     2   3 2      2 4       3 3 2     2   4       2 5
+--R     (b d e  - 2b c d e  + b c d e)x + b d e  - 2b c d e + b c d
+--R                                                    Type: Expression(Integer)
+--E 202
+
+--S 203 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                 2 3             2          2         2   2           2
+--R           (- A b e  + 2A b c d e  - B b c d e)x - A b d e  + 2A b c d e
+--R         + 
+--R                    3
+--R           - B b c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R              2          2            2          3
+--R       ((- A c  + B b c)d e x + (- A c  + B b c)d )log(c x + b)
+--R     + 
+--R              2 3             2      2 2         2   2           2       2 3
+--R         ((A b e  - 2A b c d e  + A c d e)x + A b d e  - 2A b c d e + A c d )
+--R      *
+--R         log(x)
+--R     + 
+--R          2   2                 2  2           3
+--R       A b d e  + (- A b c - B b )d e + B b c d
+--R  /
+--R       3 2 3     2   3 2      2 4       3 3 2     2   4       2 5
+--R     (b d e  - 2b c d e  + b c d e)x + b d e  - 2b c d e + b c d
+--R                                         Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 204
+
+--S 205 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 1457
+t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2))
+--R 
+--R
+--R   (1)
+--R     B x + A
+--R  /
+--R          3 5       3         2  4          2       2   3        2       3  2
+--R       c e x  + (b e  + 3c d e )x  + (3b d e  + 3c d e)x  + (3b d e + c d )x
+--R     + 
+--R          3
+--R       b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 1457
+r0:=1/2*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^2)+(B*c*d^2-A*e*(2*c*d-b*e))/_
+     (d^2*(c*d-b*e)^2*(d+e*x))+A*log(x)/(b*d^3)+c^2*(b*B-A*c)*_
+     log(b+c*x)/(b*(c*d-b*e)^3)-(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_
+     b^2*e^2))*log(d+e*x)/(d^3*(c*d-b*e)^3)
+--R 
+--R
+--R   (2)
+--R                  3 5       2     4         2 2 3         2 3 2  2
+--R           (- 2A b e  + 6A b c d e  - 6A b c d e  + 2B b c d e )x
+--R         + 
+--R                  3   4        2   2 3          2 3 2         2 4          3 2 3
+--R           (- 4A b d e  + 12A b c d e  - 12A b c d e  + 4B b c d e)x - 2A b d e
+--R         + 
+--R               2   3 2         2 4          2 5
+--R           6A b c d e  - 6A b c d e + 2B b c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R                  3         2  3 2 2        3         2  4
+--R             (2A c  - 2B b c )d e x  + (4A c  - 4B b c )d e x
+--R           + 
+--R                  3         2  5
+--R             (2A c  - 2B b c )d
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                3 5       2     4         2 2 3       3 3 2  2
+--R           (2A b e  - 6A b c d e  + 6A b c d e  - 2A c d e )x
+--R         + 
+--R                3   4        2   2 3          2 3 2       3 4          3 2 3
+--R           (4A b d e  - 12A b c d e  + 12A b c d e  - 4A c d e)x + 2A b d e
+--R         + 
+--R                 2   3 2         2 4        3 5
+--R           - 6A b c d e  + 6A b c d e - 2A c d
+--R      *
+--R         log(x)
+--R     + 
+--R            3   4       2   2 3          2       2   3 2         2 4
+--R       (2A b d e  - 6A b c d e  + (4A b c  + 2B b c)d e  - 2B b c d e)x
+--R     + 
+--R           3 2 3          2       3  3 2          2       2   4          2 5
+--R       3A b d e  + (- 8A b c - B b )d e  + (5A b c  + 4B b c)d e - 3B b c d
+--R  /
+--R          4 3 5     3   4 4     2 2 5 3       3 6 2  2
+--R       (2b d e  - 6b c d e  + 6b c d e  - 2b c d e )x
+--R     + 
+--R          4 4 4      3   5 3      2 2 6 2       3 7        4 5 3     3   6 2
+--R       (4b d e  - 12b c d e  + 12b c d e  - 4b c d e)x + 2b d e  - 6b c d e
+--R     + 
+--R         2 2 7        3 8
+--R       6b c d e - 2b c d
+--R                                                    Type: Expression(Integer)
+--E 207
+
+--S 208 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  3 5       2     4         2 2 3         2 3 2  2
+--R           (- 2A b e  + 6A b c d e  - 6A b c d e  + 2B b c d e )x
+--R         + 
+--R                  3   4        2   2 3          2 3 2         2 4          3 2 3
+--R           (- 4A b d e  + 12A b c d e  - 12A b c d e  + 4B b c d e)x - 2A b d e
+--R         + 
+--R               2   3 2         2 4          2 5
+--R           6A b c d e  - 6A b c d e + 2B b c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R                  3         2  3 2 2        3         2  4
+--R             (2A c  - 2B b c )d e x  + (4A c  - 4B b c )d e x
+--R           + 
+--R                  3         2  5
+--R             (2A c  - 2B b c )d
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                3 5       2     4         2 2 3       3 3 2  2
+--R           (2A b e  - 6A b c d e  + 6A b c d e  - 2A c d e )x
+--R         + 
+--R                3   4        2   2 3          2 3 2       3 4          3 2 3
+--R           (4A b d e  - 12A b c d e  + 12A b c d e  - 4A c d e)x + 2A b d e
+--R         + 
+--R                 2   3 2         2 4        3 5
+--R           - 6A b c d e  + 6A b c d e - 2A c d
+--R      *
+--R         log(x)
+--R     + 
+--R            3   4       2   2 3          2       2   3 2         2 4
+--R       (2A b d e  - 6A b c d e  + (4A b c  + 2B b c)d e  - 2B b c d e)x
+--R     + 
+--R           3 2 3          2       3  3 2          2       2   4          2 5
+--R       3A b d e  + (- 8A b c - B b )d e  + (5A b c  + 4B b c)d e - 3B b c d
+--R  /
+--R          4 3 5     3   4 4     2 2 5 3       3 6 2  2
+--R       (2b d e  - 6b c d e  + 6b c d e  - 2b c d e )x
+--R     + 
+--R          4 4 4      3   5 3      2 2 6 2       3 7        4 5 3     3   6 2
+--R       (4b d e  - 12b c d e  + 12b c d e  - 4b c d e)x + 2b d e  - 6b c d e
+--R     + 
+--R         2 2 7        3 8
+--R       6b c d e - 2b c d
+--R                                         Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 209
+
+--S 210 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 1457
+t0:=(A+B*x)/((d+e*x)^4*(b*x+c*x^2))
+--R 
+--R
+--R   (1)
+--R     B x + A
+--R  /
+--R          4 6       4         3  5          3       2 2  4
+--R       c e x  + (b e  + 4c d e )x  + (4b d e  + 6c d e )x
+--R     + 
+--R            2 2       3   3        3       4  2      4
+--R       (6b d e  + 4c d e)x  + (4b d e + c d )x  + b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 211
+
+--S 212 of 1457
+r0:=1/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^3)+1/2*(B*c*d^2-A*e*(2*c*d-b*e))/_
+     (d^2*(c*d-b*e)^2*(d+e*x)^2)+(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+_
+     b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x))+A*log(x)/(b*d^4)+c^3*(b*B-A*c)*_
+     log(b+c*x)/(b*(c*d-b*e)^4)-(B*c^3*d^4-A*e*(4*c^3*d^3-_
+     6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/(d^4*(c*d-b*e)^4)
+--R 
+--R
+--R   (2)
+--R                     4 7        3     6        2 2 2 5          3 3 4
+--R               - 6A b e  + 24A b c d e  - 36A b c d e  + 24A b c d e
+--R             + 
+--R                       3 4 3
+--R               - 6B b c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      4   6        3   2 5         2 2 3 4          3 4 3
+--R               - 18A b d e  + 72A b c d e  - 108A b c d e  + 72A b c d e
+--R             + 
+--R                        3 5 2
+--R               - 18B b c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      4 2 5        3   3 4         2 2 4 3          3 5 2
+--R               - 18A b d e  + 72A b c d e  - 108A b c d e  + 72A b c d e
+--R             + 
+--R                        3 6
+--R               - 18B b c d e
+--R          *
+--R             x
+--R         + 
+--R                 4 3 4        3   4 3        2 2 5 2          3 6          3 7
+--R           - 6A b d e  + 24A b c d e  - 36A b c d e  + 24A b c d e - 6B b c d
+--R      *
+--R         log(e x + d)
+--R     + 
+--R                  4         3  4 3 3           4          3  5 2 2
+--R           (- 6A c  + 6B b c )d e x  + (- 18A c  + 18B b c )d e x
+--R         + 
+--R                   4          3  6             4         3  7
+--R           (- 18A c  + 18B b c )d e x + (- 6A c  + 6B b c )d
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                4 7        3     6        2 2 2 5          3 3 4       4 4 3  3
+--R           (6A b e  - 24A b c d e  + 36A b c d e  - 24A b c d e  + 6A c d e )x
+--R         + 
+--R                    4   6        3   2 5         2 2 3 4          3 4 3
+--R               18A b d e  - 72A b c d e  + 108A b c d e  - 72A b c d e
+--R             + 
+--R                    4 5 2
+--R               18A c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    4 2 5        3   3 4         2 2 4 3          3 5 2
+--R               18A b d e  - 72A b c d e  + 108A b c d e  - 72A b c d e
+--R             + 
+--R                    4 6
+--R               18A c d e
+--R          *
+--R             x
+--R         + 
+--R               4 3 4        3   4 3        2 2 5 2          3 6        4 7
+--R           6A b d e  - 24A b c d e  + 36A b c d e  - 24A b c d e + 6A c d
+--R      *
+--R         log(x)
+--R     + 
+--R               4   6        3   2 5        2 2 3 4             3       2 2  4 3
+--R           6A b d e  - 24A b c d e  + 36A b c d e  + (- 18A b c  - 6B b c )d e
+--R         + 
+--R                 3 5 2
+--R           6B b c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                4 2 5        3   3 4         2 2       3   4 3
+--R           15A b d e  - 60A b c d e  + (87A b c  + 3B b c)d e
+--R         + 
+--R                     3        2 2  5 2          3 6
+--R           (- 42A b c  - 18B b c )d e  + 15B b c d e
+--R      *
+--R         x
+--R     + 
+--R            4 3 4           3        4  4 3         2 2       3   5 2
+--R       11A b d e  + (- 42A b c - 2B b )d e  + (57A b c  + 9B b c)d e
+--R     + 
+--R                 3        2 2  6           3 7
+--R       (- 26A b c  - 18B b c )d e + 11B b c d
+--R  /
+--R          5 4 7      4   5 6      3 2 6 5      2 3 7 4       4 8 3  3
+--R       (6b d e  - 24b c d e  + 36b c d e  - 24b c d e  + 6b c d e )x
+--R     + 
+--R           5 5 6      4   6 5       3 2 7 4      2 3 8 3        4 9 2  2
+--R       (18b d e  - 72b c d e  + 108b c d e  - 72b c d e  + 18b c d e )x
+--R     + 
+--R           5 6 5      4   7 4       3 2 8 3      2 3 9 2        4 10
+--R       (18b d e  - 72b c d e  + 108b c d e  - 72b c d e  + 18b c d  e)x
+--R     + 
+--R         5 7 4      4   8 3      3 2 9 2      2 3 10        4 11
+--R       6b d e  - 24b c d e  + 36b c d e  - 24b c d  e + 6b c d
+--R                                                    Type: Expression(Integer)
+--E 212
+
+--S 213 of 1457
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 1457
+--m0:=a0-r0
+--E 214
+
+--S 215 of 1457
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 1457
+t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R          4 5       4         3  4          3       2 2  3
+--R       B e x  + (A e  + 4B d e )x  + (4A d e  + 6B d e )x
+--R     + 
+--R            2 2       3   2        3       4        4
+--R       (6A d e  + 4B d e)x  + (4A d e + B d )x + A d
+--R  /
+--R      2 4         3    2 2
+--R     c x  + 2b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 216
+
+--S 217 of 1457
+r0:=-A*d^4/(b^2*x)+e^3*(4*B*c*d-2*b*B*e+A*c*e)*x/c^3+1/2*B*e^4*x^2/c^2+_
+     (b*B-A*c)*(c*d-b*e)^4/(b^2*c^4*(b+c*x))+d^3*(b*B*d-2*A*c*d+_
+     4*A*b*e)*log(x)/b^3+(c*d-b*e)^3*(2*A*c^2*d-3*b^2*B*e-b*c*(B*d-_
+     2*A*e))*log(b+c*x)/(b^3*c^4)
+--R 
+--R
+--R   (2)
+--R                      4 2       5   4        3 3        4 2    3        3 3 2 2
+--R               (- 4A b c  + 6B b c)e  + (8A b c  - 16B b c )d e  + 12B b c d e
+--R             + 
+--R                       5 3         6         5  4
+--R               - 8A b c d e + (4A c  - 2B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      5        6  4        4 2        5     3        4 2 2 2
+--R               (- 4A b c + 6B b )e  + (8A b c  - 16B b c)d e  + 12B b c d e
+--R             + 
+--R                     2 4 3           5       2 4  4
+--R               - 8A b c d e + (4A b c  - 2B b c )d
+--R          *
+--R             x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                  5 3           6         5  4  2
+--R           (8A b c d e + (- 4A c  + 2B b c )d )x
+--R         + 
+--R                2 4 3             5       2 4  4
+--R           (8A b c d e + (- 4A b c  + 2B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R          3 3 4 4         3 3       4 2  4       3 3   3  3
+--R       B b c e x  + ((2A b c  - 3B b c )e  + 8B b c d e )x
+--R     + 
+--R             4 2       5   4       4 2   3  2
+--R       ((2A b c  - 4B b c)e  + 8B b c d e )x
+--R     + 
+--R                  5        6  4        4 2       5     3
+--R           (- 2A b c + 2B b )e  + (8A b c  - 8B b c)d e
+--R         + 
+--R                   3 3        4 2  2 2        2 4       3 3  3
+--R           (- 12A b c  + 12B b c )d e  + (8A b c  - 8B b c )d e
+--R         + 
+--R                    5       2 4  4
+--R           (- 4A b c  + 2B b c )d
+--R      *
+--R         x
+--R     + 
+--R             2 4 4
+--R       - 2A b c d
+--R  /
+--R       3 5 2     4 4
+--R     2b c x  + 2b c x
+--R                                                    Type: Expression(Integer)
+--E 217
+
+--S 218 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                      4 2       5   4        3 3        4 2    3        3 3 2 2
+--R               (- 4A b c  + 6B b c)e  + (8A b c  - 16B b c )d e  + 12B b c d e
+--R             + 
+--R                       5 3         6         5  4
+--R               - 8A b c d e + (4A c  - 2B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      5        6  4        4 2        5     3        4 2 2 2
+--R               (- 4A b c + 6B b )e  + (8A b c  - 16B b c)d e  + 12B b c d e
+--R             + 
+--R                     2 4 3           5       2 4  4
+--R               - 8A b c d e + (4A b c  - 2B b c )d
+--R          *
+--R             x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                  5 3           6         5  4  2
+--R           (8A b c d e + (- 4A c  + 2B b c )d )x
+--R         + 
+--R                2 4 3             5       2 4  4
+--R           (8A b c d e + (- 4A b c  + 2B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R          3 3 4 4         3 3       4 2  4       3 3   3  3
+--R       B b c e x  + ((2A b c  - 3B b c )e  + 8B b c d e )x
+--R     + 
+--R             4 2       5   4       4 2   3  2
+--R       ((2A b c  - 4B b c)e  + 8B b c d e )x
+--R     + 
+--R                  5        6  4        4 2       5     3
+--R           (- 2A b c + 2B b )e  + (8A b c  - 8B b c)d e
+--R         + 
+--R                   3 3        4 2  2 2        2 4       3 3  3
+--R           (- 12A b c  + 12B b c )d e  + (8A b c  - 8B b c )d e
+--R         + 
+--R                    5       2 4  4
+--R           (- 4A b c  + 2B b c )d
+--R      *
+--R         x
+--R     + 
+--R             2 4 4
+--R       - 2A b c d
+--R  /
+--R       3 5 2     4 4
+--R     2b c x  + 2b c x
+--R                                         Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 219
+
+--S 220 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 1457
+t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R      3 4       3         2  3          2       2   2        2       3        3
+--R   B e x  + (A e  + 3B d e )x  + (3A d e  + 3B d e)x  + (3A d e + B d )x + A d
+--R   ----------------------------------------------------------------------------
+--R                                2 4         3    2 2
+--R                               c x  + 2b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 221
+
+--S 222 of 1457
+r0:=-A*d^3/(b^2*x)+B*e^3*x/c^2+(b*B-A*c)*(c*d-b*e)^3/(b^2*c^3*(b+c*x))+_
+     d^2*(b*B*d-2*A*c*d+3*A*b*e)*log(x)/b^3-(c*d-b*e)^2*(b*B*c*d-_
+     2*A*c^2*d+2*b^2*B*e-A*b*c*e)*log(b+c*x)/(b^3*c^3)
+--R 
+--R
+--R   (2)
+--R                     3 2       4   3       3 2   2         4 2
+--R                 (A b c  - 2B b c)e  + 3B b c d e  - 3A b c d e
+--R               + 
+--R                      5        4  3
+--R                 (2A c  - B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R              4        5  3       4     2       2 3 2           4      2 3  3
+--R         ((A b c - 2B b )e  + 3B b c d e  - 3A b c d e + (2A b c  - B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                  4 2           5        4  3  2
+--R           (3A b c d e + (- 2A c  + B b c )d )x
+--R         + 
+--R                2 3 2             4      2 3  3
+--R           (3A b c d e + (- 2A b c  + B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R          3 2 3 3      4   3 2
+--R       B b c e x  + B b c e x
+--R     + 
+--R               4       5  3          3 2       4     2        2 3       3 2  2
+--R           (A b c - B b )e  + (- 3A b c  + 3B b c)d e  + (3A b c  - 3B b c )d e
+--R         + 
+--R                    4      2 3  3
+--R           (- 2A b c  + B b c )d
+--R      *
+--R         x
+--R     + 
+--R            2 3 3
+--R       - A b c d
+--R  /
+--R      3 4 2    4 3
+--R     b c x  + b c x
+--R                                                    Type: Expression(Integer)
+--E 222
+
+--S 223 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                     3 2       4   3       3 2   2         4 2
+--R                 (A b c  - 2B b c)e  + 3B b c d e  - 3A b c d e
+--R               + 
+--R                      5        4  3
+--R                 (2A c  - B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R              4        5  3       4     2       2 3 2           4      2 3  3
+--R         ((A b c - 2B b )e  + 3B b c d e  - 3A b c d e + (2A b c  - B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                  4 2           5        4  3  2
+--R           (3A b c d e + (- 2A c  + B b c )d )x
+--R         + 
+--R                2 3 2             4      2 3  3
+--R           (3A b c d e + (- 2A b c  + B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R          3 2 3 3      4   3 2
+--R       B b c e x  + B b c e x
+--R     + 
+--R               4       5  3          3 2       4     2        2 3       3 2  2
+--R           (A b c - B b )e  + (- 3A b c  + 3B b c)d e  + (3A b c  - 3B b c )d e
+--R         + 
+--R                    4      2 3  3
+--R           (- 2A b c  + B b c )d
+--R      *
+--R         x
+--R     + 
+--R            2 3 3
+--R       - A b c d
+--R  /
+--R      3 4 2    4 3
+--R     b c x  + b c x
+--R                                         Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 224
+
+--S 225 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 1457
+t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^2
+--R 
+--R
+--R           2 3       2           2                2        2
+--R        B e x  + (A e  + 2B d e)x  + (2A d e + B d )x + A d
+--R   (1)  ----------------------------------------------------
+--R                         2 4         3    2 2
+--R                        c x  + 2b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 226
+
+--S 227 of 1457
+r0:=-A*d^2/(b^2*x)+(b*B-A*c)*(c*d-b*e)^2/(b^2*c^2*(b+c*x))+d*_
+     (b*B*d-2*A*c*d+2*A*b*e)*log(x)/b^3-(c*d-b*e)*(b*B*c*d-2*A*c^2*d+_
+     b^2*B*e)*log(b+c*x)/(b^3*c^2)
+--R 
+--R
+--R   (2)
+--R               3   2         3           4        3  2  2
+--R           (B b c e  - 2A b c d e + (2A c  - B b c )d )x
+--R         + 
+--R               4 2       2 2             3      2 2  2
+--R           (B b e  - 2A b c d e + (2A b c  - B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                  3             4        3  2  2
+--R           (2A b c d e + (- 2A c  + B b c )d )x
+--R         + 
+--R                2 2               3      2 2  2
+--R           (2A b c d e + (- 2A b c  + B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R              3       4  2        2 2       3                 3      2 2  2
+--R       ((- A b c + B b )e  + (2A b c  - 2B b c)d e + (- 2A b c  + B b c )d )x
+--R     + 
+--R            2 2 2
+--R       - A b c d
+--R  /
+--R      3 3 2    4 2
+--R     b c x  + b c x
+--R                                                    Type: Expression(Integer)
+--E 227
+
+--S 228 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R               3   2         3           4        3  2  2
+--R           (B b c e  - 2A b c d e + (2A c  - B b c )d )x
+--R         + 
+--R               4 2       2 2             3      2 2  2
+--R           (B b e  - 2A b c d e + (2A b c  - B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                  3             4        3  2  2
+--R           (2A b c d e + (- 2A c  + B b c )d )x
+--R         + 
+--R                2 2               3      2 2  2
+--R           (2A b c d e + (- 2A b c  + B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R              3       4  2        2 2       3                 3      2 2  2
+--R       ((- A b c + B b )e  + (2A b c  - 2B b c)d e + (- 2A b c  + B b c )d )x
+--R     + 
+--R            2 2 2
+--R       - A b c d
+--R  /
+--R      3 3 2    4 2
+--R     b c x  + b c x
+--R                                         Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 229
+
+--S 230 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 1457
+t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^2
+--R 
+--R
+--R             2
+--R        B e x  + (A e + B d)x + A d
+--R   (1)  ---------------------------
+--R            2 4         3    2 2
+--R           c x  + 2b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 1457
+r0:=-A*d/(b^2*x)+(b*B-A*c)*(c*d-b*e)/(b^2*c*(b+c*x))+(b*B*d-2*A*c*d+A*b*e)*_
+     log(x)/b^3-(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^3
+--R 
+--R
+--R   (2)
+--R                  2         3        2    2         2             2      2
+--R         ((- A b c e + (2A c  - B b c )d)x  + (- A b c e + (2A b c  - B b c)d)x)
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                2           3        2    2       2               2      2
+--R         ((A b c e + (- 2A c  + B b c )d)x  + (A b c e + (- 2A b c  + B b c)d)x)
+--R      *
+--R         log(x)
+--R     + 
+--R            2       3              2      2           2
+--R       ((A b c - B b )e + (- 2A b c  + B b c)d)x - A b c d
+--R  /
+--R      3 2 2    4
+--R     b c x  + b c x
+--R                                                    Type: Expression(Integer)
+--E 232
+
+--S 233 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  2         3        2    2         2             2      2
+--R         ((- A b c e + (2A c  - B b c )d)x  + (- A b c e + (2A b c  - B b c)d)x)
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                2           3        2    2       2               2      2
+--R         ((A b c e + (- 2A c  + B b c )d)x  + (A b c e + (- 2A b c  + B b c)d)x)
+--R      *
+--R         log(x)
+--R     + 
+--R            2       3              2      2           2
+--R       ((A b c - B b )e + (- 2A b c  + B b c)d)x - A b c d
+--R  /
+--R      3 2 2    4
+--R     b c x  + b c x
+--R                                         Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 234
+
+--S 235 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 1457
+t0:=(A+B*x)/(b*x+c*x^2)^2
+--R 
+--R
+--R               B x + A
+--R   (1)  ---------------------
+--R         2 4         3    2 2
+--R        c x  + 2b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 1457
+r0:=-A/(b^2*x)+(b*B-A*c)/(b^2*(b+c*x))+(b*B-2*A*c)*log(x)/b^3-(b*B-2*A*c)*_
+     log(b+c*x)/b^3
+--R 
+--R
+--R   (2)
+--R             2          2                2
+--R       ((2A c  - B b c)x  + (2A b c - B b )x)log(c x + b)
+--R     + 
+--R               2          2                  2                           2
+--R       ((- 2A c  + B b c)x  + (- 2A b c + B b )x)log(x) + (- 2A b c + B b )x
+--R     + 
+--R            2
+--R       - A b
+--R  /
+--R      3   2    4
+--R     b c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 237
+
+--S 238 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R             2          2                2
+--R       ((2A c  - B b c)x  + (2A b c - B b )x)log(c x + b)
+--R     + 
+--R               2          2                  2                           2
+--R       ((- 2A c  + B b c)x  + (- 2A b c + B b )x)log(x) + (- 2A b c + B b )x
+--R     + 
+--R            2
+--R       - A b
+--R  /
+--R      3   2    4
+--R     b c x  + b x
+--R                                         Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 239
+
+--S 240 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 1457
+t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^2)
+--R 
+--R
+--R                               B x + A
+--R   (1)  -----------------------------------------------------
+--R         2   5              2   4     2            3    2   2
+--R        c e x  + (2b c e + c d)x  + (b e + 2b c d)x  + b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 1457
+r0:=-A/(b^2*d*x)+c*(b*B-A*c)/(b^2*(c*d-b*e)*(b+c*x))+(b*B*d-2*A*c*d-A*b*e)*_
+     log(x)/(b^3*d^2)+c*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+3*A*e))*log(b+c*x)/_
+     (b^3*(c*d-b*e)^2)-e^2*(B*d-A*e)*log(d+e*x)/(d^2*(c*d-b*e)^2)
+--R 
+--R
+--R   (2)
+--R            3   3      3     2  2       4 3      4   2
+--R       ((A b c e  - B b c d e )x  + (A b e  - B b d e )x)log(e x + d)
+--R     + 
+--R                     3       2 2  2         4        3  3  2
+--R           ((- 3A b c  + 2B b c )d e + (2A c  - B b c )d )x
+--R         + 
+--R                   2 2       3   2           3      2 2  3
+--R           ((- 3A b c  + 2B b c)d e + (2A b c  - B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                    3   3      3     2          3       2 2  2
+--R               - A b c e  + B b c d e  + (3A b c  - 2B b c )d e
+--R             + 
+--R                      4        3  3
+--R               (- 2A c  + B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R               4 3      4   2        2 2       3   2             3      2 2  3
+--R         (- A b e  + B b d e  + (3A b c  - 2B b c)d e + (- 2A b c  + B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R             3     2        2 2      3   2             3      2 2  3
+--R       (- A b c d e  + (3A b c  - B b c)d e + (- 2A b c  + B b c )d )x
+--R     + 
+--R            4   2       3   2       2 2 3
+--R       - A b d e  + 2A b c d e - A b c d
+--R  /
+--R       5   2 2     4 2 3     3 3 4  2     6 2 2     5   3     4 2 4
+--R     (b c d e  - 2b c d e + b c d )x  + (b d e  - 2b c d e + b c d )x
+--R                                                    Type: Expression(Integer)
+--E 242
+
+--S 243 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R            3   3      3     2  2       4 3      4   2
+--R       ((A b c e  - B b c d e )x  + (A b e  - B b d e )x)log(e x + d)
+--R     + 
+--R                     3       2 2  2         4        3  3  2
+--R           ((- 3A b c  + 2B b c )d e + (2A c  - B b c )d )x
+--R         + 
+--R                   2 2       3   2           3      2 2  3
+--R           ((- 3A b c  + 2B b c)d e + (2A b c  - B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                    3   3      3     2          3       2 2  2
+--R               - A b c e  + B b c d e  + (3A b c  - 2B b c )d e
+--R             + 
+--R                      4        3  3
+--R               (- 2A c  + B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R               4 3      4   2        2 2       3   2             3      2 2  3
+--R         (- A b e  + B b d e  + (3A b c  - 2B b c)d e + (- 2A b c  + B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R             3     2        2 2      3   2             3      2 2  3
+--R       (- A b c d e  + (3A b c  - B b c)d e + (- 2A b c  + B b c )d )x
+--R     + 
+--R            4   2       3   2       2 2 3
+--R       - A b d e  + 2A b c d e - A b c d
+--R  /
+--R       5   2 2     4 2 3     3 3 4  2     6 2 2     5   3     4 2 4
+--R     (b c d e  - 2b c d e + b c d )x  + (b d e  - 2b c d e + b c d )x
+--R                                         Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 244
+
+--S 245 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 1457
+t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^2)
+--R 
+--R
+--R   (1)
+--R     B x + A
+--R  /
+--R        2 2 6          2     2     5     2 2               2 2  4
+--R       c e x  + (2b c e  + 2c d e)x  + (b e  + 4b c d e + c d )x
+--R     + 
+--R          2            2  3    2 2 2
+--R       (2b d e + 2b c d )x  + b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 1457
+r0:=-A/(b^2*d^2*x)+c^2*(b*B-A*c)/(b^2*(c*d-b*e)^2*(b+c*x))+e^2*(B*d-A*e)/_
+     (d^2*(c*d-b*e)^2*(d+e*x))+(b*B*d-2*A*c*d-2*A*b*e)*log(x)/(b^3*d^3)+_
+     c^2*(2*A*c^2*d+3*b^2*B*e-b*c*(B*d+4*A*e))*log(b+c*x)/(b^3*_
+     (c*d-b*e)^3)+e^2*(2*A*e*(2*c*d-b*e)-B*d*(3*c*d-b*e))*log(d+e*x)/_
+     (d^3*(c*d-b*e)^3)
+--R 
+--R
+--R   (2)
+--R                4   5          3 2      4     4       3 2 2 3  3
+--R           (2A b c e  + (- 4A b c  - B b c)d e  + 3B b c d e )x
+--R         + 
+--R                   5 5          4       5    4          3 2       4   2 3
+--R               2A b e  + (- 2A b c - B b )d e  + (- 4A b c  + 2B b c)d e
+--R             + 
+--R                   3 2 3 2
+--R               3B b c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                5   4          4       5  2 3       4   3 2
+--R           (2A b d e  + (- 4A b c - B b )d e  + 3B b c d e )x
+--R      *
+--R         log(e x + d)
+--R     + 
+--R                   4       2 3  3 2          5        4  4   3
+--R           ((4A b c  - 3B b c )d e  + (- 2A c  + B b c )d e)x
+--R         + 
+--R                    2 3       3 2  3 2          4       2 3  4
+--R               (4A b c  - 3B b c )d e  + (2A b c  - 2B b c )d e
+--R             + 
+--R                      5        4  5
+--R               (- 2A c  + B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                 2 3       3 2  4             4      2 3  5
+--R           ((4A b c  - 3B b c )d e + (- 2A b c  + B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                     4   5        3 2      4     4       3 2 2 3
+--R               - 2A b c e  + (4A b c  + B b c)d e  - 3B b c d e
+--R             + 
+--R                        4       2 3  3 2        5        4  4
+--R               (- 4A b c  + 3B b c )d e  + (2A c  - B b c )d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                     5 5        4       5    4        3 2       4   2 3
+--R               - 2A b e  + (2A b c + B b )d e  + (4A b c  - 2B b c)d e
+--R             + 
+--R                     2 3 3 2            4       2 3  4         5        4  5
+--R               - 4A b c d e  + (- 2A b c  + 2B b c )d e + (2A c  - B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                     5   4        4       5  2 3       4   3 2
+--R               - 2A b d e  + (4A b c + B b )d e  - 3B b c d e
+--R             + 
+--R                      2 3       3 2  4           4      2 3  5
+--R               (- 4A b c  + 3B b c )d e + (2A b c  - B b c )d
+--R          *
+--R             x
+--R      *
+--R         log(x)
+--R     + 
+--R                 4     4        3 2      4   2 3       2 3 3 2
+--R           - 2A b c d e  + (4A b c  + B b c)d e  - 4A b c d e
+--R         + 
+--R                  4      2 3  4
+--R           (2A b c  - B b c )d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                 5   4        4       5  2 3      4   3 2
+--R           - 2A b d e  + (3A b c + B b )d e  - B b c d e
+--R         + 
+--R                  2 3      3 2  4           4      2 3  5
+--R           (- 3A b c  + B b c )d e + (2A b c  - B b c )d
+--R      *
+--R         x
+--R     + 
+--R            5 2 3       4   3 2       3 2 4       2 3 5
+--R       - A b d e  + 3A b c d e  - 3A b c d e + A b c d
+--R  /
+--R         6   3 4     5 2 4 3     4 3 5 2    3 4 6   3
+--R       (b c d e  - 3b c d e  + 3b c d e  - b c d e)x
+--R     + 
+--R         7 3 4     6   4 3     4 3 6     3 4 7  2
+--R       (b d e  - 2b c d e  + 2b c d e - b c d )x
+--R     + 
+--R         7 4 3     6   5 2     5 2 6     4 3 7
+--R       (b d e  - 3b c d e  + 3b c d e - b c d )x
+--R                                                    Type: Expression(Integer)
+--E 247
+
+--S 248 of 1457
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 1457
+--m0:=a0-r0
+--E 249
+
+--S 250 of 1457
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 1457
+t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^2)
+--R 
+--R
+--R   (1)
+--R     B x + A
+--R  /
+--R        2 3 7          3     2   2  6     2 3           2     2 2   5
+--R       c e x  + (2b c e  + 3c d e )x  + (b e  + 6b c d e  + 3c d e)x
+--R     + 
+--R          2   2         2     2 3  4      2 2          3  3    2 3 2
+--R       (3b d e  + 6b c d e + c d )x  + (3b d e + 2b c d )x  + b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 1457
+r0:=-A/(b^2*d^3*x)+c^3*(b*B-A*c)/(b^2*(c*d-b*e)^3*(b+c*x))+1/2*e^2*_
+     (B*d-A*e)/(d^2*(c*d-b*e)^2*(d+e*x)^2)-e^2*(2*A*e*(2*c*d-b*e)-B*d*_
+     (3*c*d-b*e))/(d^3*(c*d-b*e)^3*(d+e*x))+(b*B*d-2*A*c*d-3*A*b*e)*_
+     log(x)/(b^3*d^4)+c^3*(2*A*c^2*d+4*b^2*B*e-b*c*(B*d+5*A*e))*log(b+_
+     c*x)/(b^3*(c*d-b*e)^4)-e^2*(B*d*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)-_
+     A*e*(10*c^2*d^2-10*b*c*d*e+3*b^2*e^2))*log(d+e*x)/(d^4*(c*d-b*e)^4)
+--R 
+--R
+--R   (2)
+--R                   5   7           4 2       5     6         3 3       4 2  2 5
+--R               6A b c e  + (- 20A b c  - 2B b c)d e  + (20A b c  + 8B b c )d e
+--R             + 
+--R                      3 3 3 4
+--R               - 12B b c d e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                   6 7          5        6    6           4 2       5   2 5
+--R               6A b e  + (- 8A b c - 2B b )d e  + (- 20A b c  + 4B b c)d e
+--R             + 
+--R                     3 3       4 2  3 4        3 3 4 3
+--R               (40A b c  + 4B b c )d e  - 24B b c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                    6   6           5        6  2 5         4 2        5   3 4
+--R               12A b d e  + (- 34A b c - 4B b )d e  + (20A b c  + 14B b c)d e
+--R             + 
+--R                     3 3        4 2  4 3        3 3 5 2
+--R               (20A b c  - 16B b c )d e  - 12B b c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                   6 2 5           5        6  3 4         4 2       5   4 3
+--R               6A b d e  + (- 20A b c - 2B b )d e  + (20A b c  + 8B b c)d e
+--R             + 
+--R                      4 2 5 2
+--R               - 12B b c d e
+--R          *
+--R             x
+--R      *
+--R         log(e x + d)
+--R     + 
+--R                      5       2 4  4 3        6         5  5 2  4
+--R           ((- 10A b c  + 8B b c )d e  + (4A c  - 2B b c )d e )x
+--R         + 
+--R                       2 4       3 3  4 3             5        2 4  5 2
+--R               (- 10A b c  + 8B b c )d e  + (- 16A b c  + 14B b c )d e
+--R             + 
+--R                    6         5  6
+--R               (8A c  - 4B b c )d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                       2 4        3 3  5 2            5       2 4  6
+--R               (- 20A b c  + 16B b c )d e  + (- 2A b c  + 4B b c )d e
+--R             + 
+--R                    6         5  7
+--R               (4A c  - 2B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    2 4       3 3  6           5       2 4  7
+--R           ((- 10A b c  + 8B b c )d e + (4A b c  - 2B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                     5   7         4 2       5     6
+--R               - 6A b c e  + (20A b c  + 2B b c)d e
+--R             + 
+--R                       3 3       4 2  2 5        3 3 3 4
+--R               (- 20A b c  - 8B b c )d e  + 12B b c d e
+--R             + 
+--R                       5       2 4  4 3          6         5  5 2
+--R               (10A b c  - 8B b c )d e  + (- 4A c  + 2B b c )d e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                     6 7        5        6    6         4 2       5   2 5
+--R               - 6A b e  + (8A b c + 2B b )d e  + (20A b c  - 4B b c)d e
+--R             + 
+--R                       3 3       4 2  3 4         2 4        3 3  4 3
+--R               (- 40A b c  - 4B b c )d e  + (10A b c  + 16B b c )d e
+--R             + 
+--R                       5        2 4  5 2          6         5  6
+--R               (16A b c  - 14B b c )d e  + (- 8A c  + 4B b c )d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      6   6         5        6  2 5           4 2        5   3 4
+--R               - 12A b d e  + (34A b c + 4B b )d e  + (- 20A b c  - 14B b c)d e
+--R             + 
+--R                       3 3        4 2  4 3         2 4       3 3  5 2
+--R               (- 20A b c  + 16B b c )d e  + (20A b c  - 4B b c )d e
+--R             + 
+--R                      5       2 4  6           6         5  7
+--R               (2A b c  - 4B b c )d e + (- 4A c  + 2B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                     6 2 5         5        6  3 4           4 2       5   4 3
+--R               - 6A b d e  + (20A b c + 2B b )d e  + (- 20A b c  - 8B b c)d e
+--R             + 
+--R                    4 2 5 2         2 4       3 3  6             5       2 4  7
+--R               12B b c d e  + (10A b c  - 8B b c )d e + (- 4A b c  + 2B b c )d
+--R          *
+--R             x
+--R      *
+--R         log(x)
+--R     + 
+--R                 5     6         4 2       5   2 5           3 3       4 2  3 4
+--R           - 6A b c d e  + (20A b c  + 2B b c)d e  + (- 20A b c  - 8B b c )d e
+--R         + 
+--R                 2 4       3 3  4 3            5       2 4  5 2
+--R           (10A b c  + 4B b c )d e  + (- 4A b c  + 2B b c )d e
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                 6   6         5        6  2 5         4 2       5   3 4
+--R           - 6A b d e  + (11A b c + 2B b )d e  + (10A b c  - 5B b c)d e
+--R         + 
+--R                   3 3       4 2  4 3         2 4       3 3  5 2
+--R           (- 25A b c  - 4B b c )d e  + (18A b c  + 3B b c )d e
+--R         + 
+--R                    5       2 4  6
+--R           (- 8A b c  + 4B b c )d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                 6 2 5         5        6  3 4           4 2        5   4 3
+--R           - 9A b d e  + (28A b c + 3B b )d e  + (- 25A b c  - 10B b c)d e
+--R         + 
+--R                3 3       4 2  5 2        2 4       3 3  6
+--R           (4A b c  + 7B b c )d e  + (6A b c  - 2B b c )d e
+--R         + 
+--R                    5       2 4  7
+--R           (- 4A b c  + 2B b c )d
+--R      *
+--R         x
+--R     + 
+--R             6 3 4       5   4 3        4 2 5 2       3 3 6        2 4 7
+--R       - 2A b d e  + 8A b c d e  - 12A b c d e  + 8A b c d e - 2A b c d
+--R  /
+--R          7   4 6     6 2 5 5      5 3 6 4     4 4 7 3     3 5 8 2  4
+--R       (2b c d e  - 8b c d e  + 12b c d e  - 8b c d e  + 2b c d e )x
+--R     + 
+--R          8 4 6     7   5 5     6 2 6 4      5 3 7 3      4 4 8 2     3 5 9   3
+--R       (2b d e  - 4b c d e  - 4b c d e  + 16b c d e  - 14b c d e  + 4b c d e)x
+--R     + 
+--R          8 5 5      7   6 4      6 2 7 3     5 3 8 2     4 4 9      3 5 10  2
+--R       (4b d e  - 14b c d e  + 16b c d e  - 4b c d e  - 4b c d e + 2b c d  )x
+--R     + 
+--R          8 6 4     7   7 3      6 2 8 2     5 3 9      4 4 10
+--R       (2b d e  - 8b c d e  + 12b c d e  - 8b c d e + 2b c d  )x
+--R                                                    Type: Expression(Integer)
+--E 252
+
+--S 253 of 1457
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 1457
+--m0:=a0-r0
+--E 254
+
+--S 255 of 1457
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 1457
+t0:=(A+B*x)*(d+e*x)^5/(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R          5 6       5         4  5          4        2 3  4
+--R       B e x  + (A e  + 5B d e )x  + (5A d e  + 10B d e )x
+--R     + 
+--R           2 3        3 2  3         3 2       4   2        4       5        5
+--R     (10A d e  + 10B d e )x  + (10A d e  + 5B d e)x  + (5A d e + B d )x + A d
+--R  /
+--R      3 6       2 5     2   4    3 3
+--R     c x  + 3b c x  + 3b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 1457
+r0:=-1/2*A*d^5/(b^3*x^2)-d^4*(b*B*d-3*A*c*d+5*A*b*e)/(b^4*x)+B*e^5*x/c^3-_
+     1/2*(b*B-A*c)*(c*d-b*e)^5/(b^3*c^4*(b+c*x)^2)-(c*d-b*e)^4*(2*b*B*c*d-_
+     3*A*c^2*d+3*b^2*B*e-2*A*b*c*e)/(b^4*c^4*(b+c*x))+d^3*(6*A*c^2*d^2+_
+     5*b^2*e*(B*d+2*A*e)-3*b*c*d*(B*d+5*A*e))*log(x)/b^5-(c*d-b*e)^3*_
+     (6*A*c^3*d^2-3*b^3*B*e^2-3*b*c^2*d*(B*d-A*e)-b^2*c*e*(4*B*d-A*e))*_
+     log(b+c*x)/(b^5*c^4)
+--R 
+--R
+--R   (2)
+--R                    5 3       6 2  5        5 3   4        2 6 3 2
+--R               (2A b c  - 6B b c )e  + 10B b c d e  - 20A b c d e
+--R             + 
+--R                       7        2 6  4            8         7  5
+--R               (30A b c  - 10B b c )d e + (- 12A c  + 6B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                    6 2        7   5        6 2   4        3 5 3 2
+--R               (4A b c  - 12B b c)e  + 20B b c d e  - 40A b c d e
+--R             + 
+--R                     2 6        3 5  4              7        2 6  5
+--R               (60A b c  - 20B b c )d e + (- 24A b c  + 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                    7        8  5        7     4        4 4 3 2
+--R               (2A b c - 6B b )e  + 10B b c d e  - 20A b c d e
+--R             + 
+--R                     3 5        4 4  4            2 6       3 5  5
+--R               (30A b c  - 10B b c )d e + (- 12A b c  + 6B b c )d
+--R          *
+--R              2
+--R             x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                 2 6 3 2             7        2 6  4          8         7  5  4
+--R           (20A b c d e  + (- 30A b c  + 10B b c )d e + (12A c  - 6B b c )d )x
+--R         + 
+--R                      3 5 3 2           2 6        3 5  4
+--R                 40A b c d e  + (- 60A b c  + 20B b c )d e
+--R               + 
+--R                         7        2 6  5
+--R                 (24A b c  - 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R               4 4 3 2           3 5        4 4  4          2 6       3 5  5  2
+--R         (20A b c d e  + (- 30A b c  + 10B b c )d e + (12A b c  - 6B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R           5 3 5 5       6 2 5 4
+--R       2B b c e x  + 4B b c e x
+--R     + 
+--R                6 2       7   5           5 3        6 2    4        5 3 2 3
+--R           (4A b c  - 4B b c)e  + (- 10A b c  + 20B b c )d e  - 20B b c d e
+--R         + 
+--R                3 5 3 2           2 6        3 5  4            7       2 6  5
+--R           20A b c d e  + (- 30A b c  + 10B b c )d e + (12A b c  - 6B b c )d
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                7        8  5          6 2        7     4
+--R           (3A b c - 5B b )e  + (- 5A b c  + 15B b c)d e
+--R         + 
+--R                   5 3        6 2  2 3         4 4        5 3  3 2
+--R           (- 10A b c  - 10B b c )d e  + (30A b c  - 10B b c )d e
+--R         + 
+--R                   3 5        4 4  4          2 6       3 5  5
+--R           (- 45A b c  + 15B b c )d e + (18A b c  - 9B b c )d
+--R      *
+--R          2
+--R         x
+--R     + 
+--R               4 4 4         3 5       4 4  5        4 4 5
+--R       (- 10A b c d e + (4A b c  - 2B b c )d )x - A b c d
+--R  /
+--R       5 6 4     6 5 3     7 4 2
+--R     2b c x  + 4b c x  + 2b c x
+--R                                                    Type: Expression(Integer)
+--E 257
+
+--S 258 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                    5 3       6 2  5        5 3   4        2 6 3 2
+--R               (2A b c  - 6B b c )e  + 10B b c d e  - 20A b c d e
+--R             + 
+--R                       7        2 6  4            8         7  5
+--R               (30A b c  - 10B b c )d e + (- 12A c  + 6B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                    6 2        7   5        6 2   4        3 5 3 2
+--R               (4A b c  - 12B b c)e  + 20B b c d e  - 40A b c d e
+--R             + 
+--R                     2 6        3 5  4              7        2 6  5
+--R               (60A b c  - 20B b c )d e + (- 24A b c  + 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                    7        8  5        7     4        4 4 3 2
+--R               (2A b c - 6B b )e  + 10B b c d e  - 20A b c d e
+--R             + 
+--R                     3 5        4 4  4            2 6       3 5  5
+--R               (30A b c  - 10B b c )d e + (- 12A b c  + 6B b c )d
+--R          *
+--R              2
+--R             x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                 2 6 3 2             7        2 6  4          8         7  5  4
+--R           (20A b c d e  + (- 30A b c  + 10B b c )d e + (12A c  - 6B b c )d )x
+--R         + 
+--R                      3 5 3 2           2 6        3 5  4
+--R                 40A b c d e  + (- 60A b c  + 20B b c )d e
+--R               + 
+--R                         7        2 6  5
+--R                 (24A b c  - 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R               4 4 3 2           3 5        4 4  4          2 6       3 5  5  2
+--R         (20A b c d e  + (- 30A b c  + 10B b c )d e + (12A b c  - 6B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R           5 3 5 5       6 2 5 4
+--R       2B b c e x  + 4B b c e x
+--R     + 
+--R                6 2       7   5           5 3        6 2    4        5 3 2 3
+--R           (4A b c  - 4B b c)e  + (- 10A b c  + 20B b c )d e  - 20B b c d e
+--R         + 
+--R                3 5 3 2           2 6        3 5  4            7       2 6  5
+--R           20A b c d e  + (- 30A b c  + 10B b c )d e + (12A b c  - 6B b c )d
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                7        8  5          6 2        7     4
+--R           (3A b c - 5B b )e  + (- 5A b c  + 15B b c)d e
+--R         + 
+--R                   5 3        6 2  2 3         4 4        5 3  3 2
+--R           (- 10A b c  - 10B b c )d e  + (30A b c  - 10B b c )d e
+--R         + 
+--R                   3 5        4 4  4          2 6       3 5  5
+--R           (- 45A b c  + 15B b c )d e + (18A b c  - 9B b c )d
+--R      *
+--R          2
+--R         x
+--R     + 
+--R               4 4 4         3 5       4 4  5        4 4 5
+--R       (- 10A b c d e + (4A b c  - 2B b c )d )x - A b c d
+--R  /
+--R       5 6 4     6 5 3     7 4 2
+--R     2b c x  + 4b c x  + 2b c x
+--R                                         Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 259
+
+--S 260 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 1457
+t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R          4 5       4         3  4          3       2 2  3
+--R       B e x  + (A e  + 4B d e )x  + (4A d e  + 6B d e )x
+--R     + 
+--R            2 2       3   2        3       4        4
+--R       (6A d e  + 4B d e)x  + (4A d e + B d )x + A d
+--R  /
+--R      3 6       2 5     2   4    3 3
+--R     c x  + 3b c x  + 3b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 1457
+r0:=-1/2*A*d^4/(b^3*x^2)-d^3*(b*B*d-3*A*c*d+4*A*b*e)/(b^4*x)-1/2*(b*B-_
+     A*c)*(c*d-b*e)^4/(b^3*c^3*(b+c*x)^2)+(c*d-b*e)^3*(3*A*c^2*d-2*b^2*_
+     B*e-b*c*(2*B*d-A*e))/(b^4*c^3*(b+c*x))+d^2*(6*A*c^2*d^2+2*b^2*e*_
+     (2*B*d+3*A*e)-3*b*c*d*(B*d+4*A*e))*log(x)/b^5+(c*d-b*e)^2*(3*b*B*_
+     c^2*d^2-6*A*c^3*d^2+2*b^2*B*c*d*e+b^3*B*e^2)*log(b+c*x)/(b^5*c^3)
+--R 
+--R
+--R   (2)
+--R                   5 2 4        2 5 2 2           6       2 5  3
+--R               2B b c e  - 12A b c d e  + (24A b c  - 8B b c )d e
+--R             + 
+--R                       7         6  4
+--R               (- 12A c  + 6B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                   6   4        3 4 2 2         2 5        3 4  3
+--R               4B b c e  - 24A b c d e  + (48A b c  - 16B b c )d e
+--R             + 
+--R                         6        2 5  4
+--R               (- 24A b c  + 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                   7 4        4 3 2 2         3 4       4 3  3
+--R               2B b e  - 12A b c d e  + (24A b c  - 8B b c )d e
+--R             + 
+--R                       2 5       3 4  4
+--R               (- 12A b c  + 6B b c )d
+--R          *
+--R              2
+--R             x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                 2 5 2 2             6       2 5  3          7         6  4  4
+--R           (12A b c d e  + (- 24A b c  + 8B b c )d e + (12A c  - 6B b c )d )x
+--R         + 
+--R                      3 4 2 2           2 5        3 4  3
+--R                 24A b c d e  + (- 48A b c  + 16B b c )d e
+--R               + 
+--R                         6        2 5  4
+--R                 (24A b c  - 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R               4 3 2 2           3 4       4 3  3          2 5       3 4  4  2
+--R         (12A b c d e  + (- 24A b c  + 8B b c )d e + (12A b c  - 6B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R                  5 2       6   4       5 2   3        3 4 2 2
+--R           (- 2A b c  + 4B b c)e  - 8B b c d e  + 12A b c d e
+--R         + 
+--R                   2 5       3 4  3            6       2 5  4
+--R           (- 24A b c  + 8B b c )d e + (12A b c  - 6B b c )d
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                 6        7  4          5 2       6     3
+--R           (- A b c + 3B b )e  + (- 4A b c  - 4B b c)d e
+--R         + 
+--R                 4 3       5 2  2 2           3 4        4 3  3
+--R           (18A b c  - 6B b c )d e  + (- 36A b c  + 12B b c )d e
+--R         + 
+--R                 2 5       3 4  4
+--R           (18A b c  - 9B b c )d
+--R      *
+--R          2
+--R         x
+--R     + 
+--R              4 3 3         3 4       4 3  4        4 3 4
+--R       (- 8A b c d e + (4A b c  - 2B b c )d )x - A b c d
+--R  /
+--R       5 5 4     6 4 3     7 3 2
+--R     2b c x  + 4b c x  + 2b c x
+--R                                                    Type: Expression(Integer)
+--E 262
+
+--S 263 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                   5 2 4        2 5 2 2           6       2 5  3
+--R               2B b c e  - 12A b c d e  + (24A b c  - 8B b c )d e
+--R             + 
+--R                       7         6  4
+--R               (- 12A c  + 6B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                   6   4        3 4 2 2         2 5        3 4  3
+--R               4B b c e  - 24A b c d e  + (48A b c  - 16B b c )d e
+--R             + 
+--R                         6        2 5  4
+--R               (- 24A b c  + 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                   7 4        4 3 2 2         3 4       4 3  3
+--R               2B b e  - 12A b c d e  + (24A b c  - 8B b c )d e
+--R             + 
+--R                       2 5       3 4  4
+--R               (- 12A b c  + 6B b c )d
+--R          *
+--R              2
+--R             x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                 2 5 2 2             6       2 5  3          7         6  4  4
+--R           (12A b c d e  + (- 24A b c  + 8B b c )d e + (12A c  - 6B b c )d )x
+--R         + 
+--R                      3 4 2 2           2 5        3 4  3
+--R                 24A b c d e  + (- 48A b c  + 16B b c )d e
+--R               + 
+--R                         6        2 5  4
+--R                 (24A b c  - 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R               4 3 2 2           3 4       4 3  3          2 5       3 4  4  2
+--R         (12A b c d e  + (- 24A b c  + 8B b c )d e + (12A b c  - 6B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R                  5 2       6   4       5 2   3        3 4 2 2
+--R           (- 2A b c  + 4B b c)e  - 8B b c d e  + 12A b c d e
+--R         + 
+--R                   2 5       3 4  3            6       2 5  4
+--R           (- 24A b c  + 8B b c )d e + (12A b c  - 6B b c )d
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                 6        7  4          5 2       6     3
+--R           (- A b c + 3B b )e  + (- 4A b c  - 4B b c)d e
+--R         + 
+--R                 4 3       5 2  2 2           3 4        4 3  3
+--R           (18A b c  - 6B b c )d e  + (- 36A b c  + 12B b c )d e
+--R         + 
+--R                 2 5       3 4  4
+--R           (18A b c  - 9B b c )d
+--R      *
+--R          2
+--R         x
+--R     + 
+--R              4 3 3         3 4       4 3  4        4 3 4
+--R       (- 8A b c d e + (4A b c  - 2B b c )d )x - A b c d
+--R  /
+--R       5 5 4     6 4 3     7 3 2
+--R     2b c x  + 4b c x  + 2b c x
+--R                                         Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 264
+
+--S 265 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 1457
+t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^3
+--R 
+--R
+--R   (1)
+--R      3 4       3         2  3          2       2   2        2       3        3
+--R   B e x  + (A e  + 3B d e )x  + (3A d e  + 3B d e)x  + (3A d e + B d )x + A d
+--R   ----------------------------------------------------------------------------
+--R                           3 6       2 5     2   4    3 3
+--R                          c x  + 3b c x  + 3b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 1457
+r0:=-1/2*A*d^3/(b^3*x^2)-d^2*(b*B*d-3*A*c*d+3*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_
+     (c*d-b*e)^3/(b^3*c^2*(b+c*x)^2)-(c*d-b*e)^2*(2*b*B*c*d-3*A*c^2*d+_
+     b^2*B*e)/(b^4*c^2*(b+c*x))-3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*_
+     log(x)/b^5+3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^5
+--R 
+--R
+--R   (2)
+--R                  2 4   2           5       2 4  2            6         5  3  4
+--R           (- 6A b c d e  + (18A b c  - 6B b c )d e + (- 12A c  + 6B b c )d )x
+--R         + 
+--R                      3 3   2         2 4        3 3  2
+--R               - 12A b c d e  + (36A b c  - 12B b c )d e
+--R             + 
+--R                         5        2 4  3
+--R               (- 24A b c  + 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                4 2   2         3 3       4 2  2            2 4       3 3  3  2
+--R         (- 6A b c d e  + (18A b c  - 6B b c )d e + (- 12A b c  + 6B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                2 4   2             5       2 4  2          6         5  3  4
+--R           (6A b c d e  + (- 18A b c  + 6B b c )d e + (12A c  - 6B b c )d )x
+--R         + 
+--R                      3 3   2           2 4        3 3  2
+--R                 12A b c d e  + (- 36A b c  + 12B b c )d e
+--R               + 
+--R                         5        2 4  3
+--R                 (24A b c  - 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                4 2   2           3 3       4 2  2          2 4       3 3  3  2
+--R           (6A b c d e  + (- 18A b c  + 6B b c )d e + (12A b c  - 6B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R                 5   3       3 3   2           2 4       3 3  2
+--R           - 2B b c e  + 6A b c d e  + (- 18A b c  + 6B b c )d e
+--R         + 
+--R                   5       2 4  3
+--R           (12A b c  - 6B b c )d
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                 5       6  3        4 2       5     2
+--R           (- A b c - B b )e  + (9A b c  - 3B b c)d e
+--R         + 
+--R                   3 3       4 2  2          2 4       3 3  3
+--R           (- 27A b c  + 9B b c )d e + (18A b c  - 9B b c )d
+--R      *
+--R          2
+--R         x
+--R     + 
+--R              4 2 2         3 3       4 2  3        4 2 3
+--R       (- 6A b c d e + (4A b c  - 2B b c )d )x - A b c d
+--R  /
+--R       5 4 4     6 3 3     7 2 2
+--R     2b c x  + 4b c x  + 2b c x
+--R                                                    Type: Expression(Integer)
+--E 267
+
+--S 268 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  2 4   2           5       2 4  2            6         5  3  4
+--R           (- 6A b c d e  + (18A b c  - 6B b c )d e + (- 12A c  + 6B b c )d )x
+--R         + 
+--R                      3 3   2         2 4        3 3  2
+--R               - 12A b c d e  + (36A b c  - 12B b c )d e
+--R             + 
+--R                         5        2 4  3
+--R               (- 24A b c  + 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                4 2   2         3 3       4 2  2            2 4       3 3  3  2
+--R         (- 6A b c d e  + (18A b c  - 6B b c )d e + (- 12A b c  + 6B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                2 4   2             5       2 4  2          6         5  3  4
+--R           (6A b c d e  + (- 18A b c  + 6B b c )d e + (12A c  - 6B b c )d )x
+--R         + 
+--R                      3 3   2           2 4        3 3  2
+--R                 12A b c d e  + (- 36A b c  + 12B b c )d e
+--R               + 
+--R                         5        2 4  3
+--R                 (24A b c  - 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                4 2   2           3 3       4 2  2          2 4       3 3  3  2
+--R           (6A b c d e  + (- 18A b c  + 6B b c )d e + (12A b c  - 6B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R                 5   3       3 3   2           2 4       3 3  2
+--R           - 2B b c e  + 6A b c d e  + (- 18A b c  + 6B b c )d e
+--R         + 
+--R                   5       2 4  3
+--R           (12A b c  - 6B b c )d
+--R      *
+--R          3
+--R         x
+--R     + 
+--R                 5       6  3        4 2       5     2
+--R           (- A b c - B b )e  + (9A b c  - 3B b c)d e
+--R         + 
+--R                   3 3       4 2  2          2 4       3 3  3
+--R           (- 27A b c  + 9B b c )d e + (18A b c  - 9B b c )d
+--R      *
+--R          2
+--R         x
+--R     + 
+--R              4 2 2         3 3       4 2  3        4 2 3
+--R       (- 6A b c d e + (4A b c  - 2B b c )d )x - A b c d
+--R  /
+--R       5 4 4     6 3 3     7 2 2
+--R     2b c x  + 4b c x  + 2b c x
+--R                                         Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 269
+
+--S 270 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 1457
+t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^3
+--R 
+--R
+--R           2 3       2           2                2        2
+--R        B e x  + (A e  + 2B d e)x  + (2A d e + B d )x + A d
+--R   (1)  ----------------------------------------------------
+--R                    3 6       2 5     2   4    3 3
+--R                   c x  + 3b c x  + 3b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 1457
+r0:=-1/2*A*d^2/(b^3*x^2)-d*(b*B*d-3*A*c*d+2*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_
+     (c*d-b*e)^2/(b^3*c*(b+c*x)^2)-(c*d-b*e)*(2*b*B*d-3*A*c*d+A*b*e)/_
+     (b^4*(b+c*x))+(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_
+     log(x)/b^5-(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*_
+     log(b+c*x)/b^5
+--R 
+--R
+--R   (2)
+--R                  2 3 2           4       2 3               5         4  2  4
+--R           (- 2A b c e  + (12A b c  - 4B b c )d e + (- 12A c  + 6B b c )d )x
+--R         + 
+--R                  3 2 2         2 3       3 2                 4        2 3  2  3
+--R           (- 4A b c e  + (24A b c  - 8B b c )d e + (- 24A b c  + 12B b c )d )x
+--R         + 
+--R                  4   2         3 2       4                2 3       3 2  2  2
+--R           (- 2A b c e  + (12A b c  - 4B b c)d e + (- 12A b c  + 6B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                2 3 2             4       2 3             5         4  2  4
+--R           (2A b c e  + (- 12A b c  + 4B b c )d e + (12A c  - 6B b c )d )x
+--R         + 
+--R                3 2 2           2 3       3 2               4        2 3  2  3
+--R           (4A b c e  + (- 24A b c  + 8B b c )d e + (24A b c  - 12B b c )d )x
+--R         + 
+--R                4   2           3 2       4              2 3       3 2  2  2
+--R           (2A b c e  + (- 12A b c  + 4B b c)d e + (12A b c  - 6B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R            3 2 2           2 3       3 2               4       2 3  2  3
+--R       (2A b c e  + (- 12A b c  + 4B b c )d e + (12A b c  - 6B b c )d )x
+--R     + 
+--R             4       5  2           3 2       4              2 3       3 2  2  2
+--R       ((3A b c - B b )e  + (- 18A b c  + 6B b c)d e + (18A b c  - 9B b c )d )x
+--R     + 
+--R              4             3 2       4   2        4   2
+--R       (- 4A b c d e + (4A b c  - 2B b c)d )x - A b c d
+--R  /
+--R       5 3 4     6 2 3     7   2
+--R     2b c x  + 4b c x  + 2b c x
+--R                                                    Type: Expression(Integer)
+--E 272
+
+--S 273 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  2 3 2           4       2 3               5         4  2  4
+--R           (- 2A b c e  + (12A b c  - 4B b c )d e + (- 12A c  + 6B b c )d )x
+--R         + 
+--R                  3 2 2         2 3       3 2                 4        2 3  2  3
+--R           (- 4A b c e  + (24A b c  - 8B b c )d e + (- 24A b c  + 12B b c )d )x
+--R         + 
+--R                  4   2         3 2       4                2 3       3 2  2  2
+--R           (- 2A b c e  + (12A b c  - 4B b c)d e + (- 12A b c  + 6B b c )d )x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                2 3 2             4       2 3             5         4  2  4
+--R           (2A b c e  + (- 12A b c  + 4B b c )d e + (12A c  - 6B b c )d )x
+--R         + 
+--R                3 2 2           2 3       3 2               4        2 3  2  3
+--R           (4A b c e  + (- 24A b c  + 8B b c )d e + (24A b c  - 12B b c )d )x
+--R         + 
+--R                4   2           3 2       4              2 3       3 2  2  2
+--R           (2A b c e  + (- 12A b c  + 4B b c)d e + (12A b c  - 6B b c )d )x
+--R      *
+--R         log(x)
+--R     + 
+--R            3 2 2           2 3       3 2               4       2 3  2  3
+--R       (2A b c e  + (- 12A b c  + 4B b c )d e + (12A b c  - 6B b c )d )x
+--R     + 
+--R             4       5  2           3 2       4              2 3       3 2  2  2
+--R       ((3A b c - B b )e  + (- 18A b c  + 6B b c)d e + (18A b c  - 9B b c )d )x
+--R     + 
+--R              4             3 2       4   2        4   2
+--R       (- 4A b c d e + (4A b c  - 2B b c)d )x - A b c d
+--R  /
+--R       5 3 4     6 2 3     7   2
+--R     2b c x  + 4b c x  + 2b c x
+--R                                         Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 274
+
+--S 275 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 1457
+t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^3
+--R 
+--R
+--R               2
+--R          B e x  + (A e + B d)x + A d
+--R   (1)  -------------------------------
+--R         3 6       2 5     2   4    3 3
+--R        c x  + 3b c x  + 3b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 1457
+r0:=-1/2*A*d/(b^3*x^2)+(-b*B*d+3*A*c*d-A*b*e)/(b^4*x)-1/2*(b*B-A*c)*_
+     (c*d-b*e)/(b^3*(b+c*x)^2)+(3*A*c^2*d+b^2*B*e-2*b*c*(B*d+A*e))/_
+     (b^4*(b+c*x))+(6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(x)/b^5-_
+     (6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(b+c*x)/b^5
+--R 
+--R
+--R   (2)
+--R                   3       2 2             4         3    4
+--R           ((6A b c  - 2B b c )e + (- 12A c  + 6B b c )d)x
+--R         + 
+--R                  2 2       3                3        2 2    3
+--R           ((12A b c  - 4B b c)e + (- 24A b c  + 12B b c )d)x
+--R         + 
+--R                 3        4             2 2       3     2
+--R           ((6A b c - 2B b )e + (- 12A b c  + 6B b c)d)x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                     3       2 2           4         3    4
+--R           ((- 6A b c  + 2B b c )e + (12A c  - 6B b c )d)x
+--R         + 
+--R                    2 2       3              3        2 2    3
+--R           ((- 12A b c  + 4B b c)e + (24A b c  - 12B b c )d)x
+--R         + 
+--R                   3        4           2 2       3     2
+--R           ((- 6A b c + 2B b )e + (12A b c  - 6B b c)d)x
+--R      *
+--R         log(x)
+--R     + 
+--R               2 2       3              3       2 2    3
+--R       ((- 6A b c  + 2B b c)e + (12A b c  - 6B b c )d)x
+--R     + 
+--R               3        4           2 2       3     2
+--R       ((- 9A b c + 3B b )e + (18A b c  - 9B b c)d)x
+--R     + 
+--R              4         3        4          4
+--R       (- 2A b e + (4A b c - 2B b )d)x - A b d
+--R  /
+--R       5 2 4     6   3     7 2
+--R     2b c x  + 4b c x  + 2b x
+--R                                                    Type: Expression(Integer)
+--E 277
+
+--S 278 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                   3       2 2             4         3    4
+--R           ((6A b c  - 2B b c )e + (- 12A c  + 6B b c )d)x
+--R         + 
+--R                  2 2       3                3        2 2    3
+--R           ((12A b c  - 4B b c)e + (- 24A b c  + 12B b c )d)x
+--R         + 
+--R                 3        4             2 2       3     2
+--R           ((6A b c - 2B b )e + (- 12A b c  + 6B b c)d)x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                     3       2 2           4         3    4
+--R           ((- 6A b c  + 2B b c )e + (12A c  - 6B b c )d)x
+--R         + 
+--R                    2 2       3              3        2 2    3
+--R           ((- 12A b c  + 4B b c)e + (24A b c  - 12B b c )d)x
+--R         + 
+--R                   3        4           2 2       3     2
+--R           ((- 6A b c + 2B b )e + (12A b c  - 6B b c)d)x
+--R      *
+--R         log(x)
+--R     + 
+--R               2 2       3              3       2 2    3
+--R       ((- 6A b c  + 2B b c)e + (12A b c  - 6B b c )d)x
+--R     + 
+--R               3        4           2 2       3     2
+--R       ((- 9A b c + 3B b )e + (18A b c  - 9B b c)d)x
+--R     + 
+--R              4         3        4          4
+--R       (- 2A b e + (4A b c - 2B b )d)x - A b d
+--R  /
+--R       5 2 4     6   3     7 2
+--R     2b c x  + 4b c x  + 2b x
+--R                                         Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 279
+
+--S 280 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 1457
+t0:=(A+B*x)/(b*x+c*x^2)^3
+--R 
+--R
+--R                    B x + A
+--R   (1)  -------------------------------
+--R         3 6       2 5     2   4    3 3
+--R        c x  + 3b c x  + 3b c x  + b x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 1457
+r0:=-1/2*A/(b^3*x^2)+(-b*B+3*A*c)/(b^4*x)-1/2*c*(b*B-A*c)/(b^3*(b+c*x)^2)-_
+     c*(2*b*B-3*A*c)/(b^4*(b+c*x))-3*c*(b*B-2*A*c)*log(x)/b^5+3*c*(b*B-_
+     2*A*c)*log(b+c*x)/b^5
+--R 
+--R
+--R   (2)
+--R                   4         3  4             3        2 2  3
+--R           (- 12A c  + 6B b c )x  + (- 24A b c  + 12B b c )x
+--R         + 
+--R                   2 2       3   2
+--R           (- 12A b c  + 6B b c)x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                   4         3  4           3        2 2  3
+--R             (12A c  - 6B b c )x  + (24A b c  - 12B b c )x
+--R           + 
+--R                   2 2       3   2
+--R             (12A b c  - 6B b c)x
+--R      *
+--R         log(x)
+--R     + 
+--R             3       2 2  3         2 2       3   2        3        4        4
+--R     (12A b c  - 6B b c )x  + (18A b c  - 9B b c)x  + (4A b c - 2B b )x - A b
+--R  /
+--R       5 2 4     6   3     7 2
+--R     2b c x  + 4b c x  + 2b x
+--R                                                    Type: Expression(Integer)
+--E 282
+
+--S 283 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                   4         3  4             3        2 2  3
+--R           (- 12A c  + 6B b c )x  + (- 24A b c  + 12B b c )x
+--R         + 
+--R                   2 2       3   2
+--R           (- 12A b c  + 6B b c)x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                   4         3  4           3        2 2  3
+--R             (12A c  - 6B b c )x  + (24A b c  - 12B b c )x
+--R           + 
+--R                   2 2       3   2
+--R             (12A b c  - 6B b c)x
+--R      *
+--R         log(x)
+--R     + 
+--R             3       2 2  3         2 2       3   2        3        4        4
+--R     (12A b c  - 6B b c )x  + (18A b c  - 9B b c)x  + (4A b c - 2B b )x - A b
+--R  /
+--R       5 2 4     6   3     7 2
+--R     2b c x  + 4b c x  + 2b x
+--R                                         Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 284
+
+--S 285 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 1457
+t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^3)
+--R 
+--R
+--R   (1)
+--R                                     B x + A
+--R   ---------------------------------------------------------------------------
+--R    3   7        2     3   6      2          2   5     3      2     4    3   3
+--R   c e x  + (3b c e + c d)x  + (3b c e + 3b c d)x  + (b e + 3b c d)x  + b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 1457
+r0:=-1/2*A/(b^3*d*x^2)+(-b*B*d+3*A*c*d+A*b*e)/(b^4*d^2*x)-1/2*c^2*(b*B-_
+     A*c)/(b^3*(c*d-b*e)*(b+c*x)^2)+c^2*(3*A*c^2*d+3*b^2*B*e-2*b*c*(B*d+_
+     2*A*e))/(b^4*(c*d-b*e)^2*(b+c*x))+(6*A*c^2*d^2-3*b*c*d*(B*d-A*e)-_
+     b^2*e*(B*d-A*e))*log(x)/(b^5*d^3)-c^2*(6*A*c^3*d^2-6*b^3*B*e^2-_
+     3*b*c^2*d*(B*d+5*A*e)+2*b^2*c*e*(4*B*d+5*A*e))*log(b+c*x)/(b^5*(c*d-_
+     b*e)^3)-e^4*(B*d-A*e)*log(d+e*x)/(d^3*(c*d-b*e)^3)
+--R 
+--R
+--R   (2)
+--R                  5 2 5       5 2   4  4          6   5       6     4  3
+--R           (- 2A b c e  + 2B b c d e )x  + (- 4A b c e  + 4B b c d e )x
+--R         + 
+--R                  7 5       7   4  2
+--R           (- 2A b e  + 2B b d e )x
+--R      *
+--R         log(e x + d)
+--R     + 
+--R                     2 5        3 4  3 2             6        2 5  4
+--R               (20A b c  - 12B b c )d e  + (- 30A b c  + 16B b c )d e
+--R             + 
+--R                     7         6  5
+--R               (12A c  - 6B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                     3 4        4 3  3 2           2 5        3 4  4
+--R               (40A b c  - 24B b c )d e  + (- 60A b c  + 32B b c )d e
+--R             + 
+--R                       6        2 5  5
+--R               (24A b c  - 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                     4 3        5 2  3 2           3 4        4 3  4
+--R               (20A b c  - 12B b c )d e  + (- 30A b c  + 16B b c )d e
+--R             + 
+--R                     2 5       3 4  5
+--R               (12A b c  - 6B b c )d
+--R          *
+--R              2
+--R             x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                   5 2 5       5 2   4           2 5        3 4  3 2
+--R               2A b c e  - 2B b c d e  + (- 20A b c  + 12B b c )d e
+--R             + 
+--R                       6        2 5  4            7         6  5
+--R               (30A b c  - 16B b c )d e + (- 12A c  + 6B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                   6   5       6     4           3 4        4 3  3 2
+--R               4A b c e  - 4B b c d e  + (- 40A b c  + 24B b c )d e
+--R             + 
+--R                     2 5        3 4  4              6        2 5  5
+--R               (60A b c  - 32B b c )d e + (- 24A b c  + 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                   7 5       7   4           4 3        5 2  3 2
+--R               2A b e  - 2B b d e  + (- 20A b c  + 12B b c )d e
+--R             + 
+--R                     3 4        4 3  4            2 5       3 4  5
+--R               (30A b c  - 16B b c )d e + (- 12A b c  + 6B b c )d
+--R          *
+--R              2
+--R             x
+--R      *
+--R         log(x)
+--R     + 
+--R               5 2   4       5 2 2 3           3 4        4 3  3 2
+--R           2A b c d e  - 2B b c d e  + (- 20A b c  + 12B b c )d e
+--R         + 
+--R                 2 5        3 4  4              6       2 5  5
+--R           (30A b c  - 16B b c )d e + (- 12A b c  + 6B b c )d
+--R      *
+--R          3
+--R         x
+--R     + 
+--R               6     4         5 2       6   2 3           4 3        5 2  3 2
+--R           4A b c d e  + (- A b c  - 4B b c)d e  + (- 30A b c  + 19B b c )d e
+--R         + 
+--R                 3 4        4 3  4            2 5       3 4  5
+--R           (45A b c  - 24B b c )d e + (- 18A b c  + 9B b c )d
+--R      *
+--R          2
+--R         x
+--R     + 
+--R               7   4          6        7  2 3          5 2       6   3 2
+--R           2A b d e  + (- 2A b c - 2B b )d e  + (- 6A b c  + 6B b c)d e
+--R         + 
+--R                 4 3       5 2  4           3 4       4 3  5
+--R           (10A b c  - 6B b c )d e + (- 4A b c  + 2B b c )d
+--R      *
+--R         x
+--R     + 
+--R            7 2 3       6   3 2       5 2 4       4 3 5
+--R       - A b d e  + 3A b c d e  - 3A b c d e + A b c d
+--R  /
+--R          8 2 3 3     7 3 4 2     6 4 5      5 5 6  4
+--R       (2b c d e  - 6b c d e  + 6b c d e - 2b c d )x
+--R     + 
+--R          9   3 3      8 2 4 2      7 3 5      6 4 6  3
+--R       (4b c d e  - 12b c d e  + 12b c d e - 4b c d )x
+--R     + 
+--R          10 3 3     9   4 2     8 2 5      7 3 6  2
+--R       (2b  d e  - 6b c d e  + 6b c d e - 2b c d )x
+--R                                                    Type: Expression(Integer)
+--E 287
+
+--S 288 of 1457
+--a0:=integrate(t0,x)
+--E 288
+
+--S 289 of 1457
+--m0:=a0-r0
+--E 289
+
+--S 290 of 1457
+--d0:=D(m0,x)
+--E 290
+
+)clear all
+
+--S 291 of 1457
+t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^3)
+--R 
+--R
+--R   (1)
+--R     B x + A
+--R  /
+--R        3 2 8        2 2     3     7      2   2       2       3 2  6
+--R       c e x  + (3b c e  + 2c d e)x  + (3b c e  + 6b c d e + c d )x
+--R     + 
+--R         3 2     2            2 2  5      3        2   2  4    3 2 3
+--R       (b e  + 6b c d e + 3b c d )x  + (2b d e + 3b c d )x  + b d x
+--R                                          Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 1457
+r0:=-1/2*A/(b^3*d^2*x^2)+(-b*B*d+3*A*c*d+2*A*b*e)/(b^4*d^3*x)-1/2*c^3*(b*B-_
+     A*c)/(b^3*(c*d-b*e)^2*(b+c*x)^2)-c^3*(2*b*B*c*d-3*A*c^2*d-4*b^2*B*e+_
+     5*A*b*c*e)/(b^4*(c*d-b*e)^3*(b+c*x))+e^4*(B*d-A*e)/(d^3*(c*d-b*e)^3*_
+     (d+e*x))+(6*A*c^2*d^2-b^2*e*(2*B*d-3*A*e)-3*b*c*d*(B*d-2*A*e))*_
+     log(x)/(b^5*d^4)-c^3*(6*A*c^3*d^2-10*b^3*B*e^2+5*b^2*c*e*(2*B*d+_
+     3*A*e)-3*b*c^2*d*(B*d+6*A*e))*log(b+c*x)/(b^5*(c*d-b*e)^4)-e^4*_
+     (B*d*(5*c*d-2*b*e)-3*A*e*(2*c*d-b*e))*log(d+e*x)/(d^4*(c*d-b*e)^4)
+--R 
+--R
+--R   (2)
+--R                  6 2 7         5 3       6 2    6        5 3 2 5  5
+--R           (- 6A b c e  + (12A b c  + 4B b c )d e  - 10B b c d e )x
+--R         + 
+--R                      7   7         6 2       7     6
+--R               - 12A b c e  + (18A b c  + 8B b c)d e
+--R             + 
+--R                     5 3        6 2  2 5        5 3 3 4
+--R               (12A b c  - 16B b c )d e  - 10B b c d e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                  8 7       8   6         6 2       7   2 5        6 2 3 4  3
+--R           (- 6A b e  + 4B b d e  + (24A b c  - 2B b c)d e  - 20B b c d e )x
+--R         + 
+--R                  8   6         7        8  2 5        7   3 4  2
+--R           (- 6A b d e  + (12A b c + 4B b )d e  - 10B b c d e )x
+--R      *
+--R         log(e x + d)
+--R     + 
+--R                       2 6        3 5  4 3           7        2 6  5 2
+--R               (- 30A b c  + 20B b c )d e  + (36A b c  - 20B b c )d e
+--R             + 
+--R                       8         7  6
+--R               (- 12A c  + 6B b c )d e
+--R          *
+--R              5
+--R             x
+--R         + 
+--R                       3 5        4 4  4 3         2 6        3 5  5 2
+--R               (- 60A b c  + 40B b c )d e  + (42A b c  - 20B b c )d e
+--R             + 
+--R                       7       2 6  6            8         7  7
+--R               (12A b c  - 8B b c )d e + (- 12A c  + 6B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                       4 4        5 3  4 3           3 5        4 4  5 2
+--R               (- 30A b c  + 20B b c )d e  + (- 24A b c  + 20B b c )d e
+--R             + 
+--R                     2 6        3 5  6              7        2 6  7
+--R               (60A b c  - 34B b c )d e + (- 24A b c  + 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                       4 4        5 3  5 2         3 5        4 4  6
+--R               (- 30A b c  + 20B b c )d e  + (36A b c  - 20B b c )d e
+--R             + 
+--R                       2 6       3 5  7
+--R               (- 12A b c  + 6B b c )d
+--R          *
+--R              2
+--R             x
+--R      *
+--R         log(c x + b)
+--R     + 
+--R                   6 2 7           5 3       6 2    6        5 3 2 5
+--R               6A b c e  + (- 12A b c  - 4B b c )d e  + 10B b c d e
+--R             + 
+--R                     2 6        3 5  4 3             7        2 6  5 2
+--R               (30A b c  - 20B b c )d e  + (- 36A b c  + 20B b c )d e
+--R             + 
+--R                     8         7  6
+--R               (12A c  - 6B b c )d e
+--R          *
+--R              5
+--R             x
+--R         + 
+--R                    7   7           6 2       7     6
+--R               12A b c e  + (- 18A b c  - 8B b c)d e
+--R             + 
+--R                       5 3        6 2  2 5        5 3 3 4
+--R               (- 12A b c  + 16B b c )d e  + 10B b c d e
+--R             + 
+--R                     3 5        4 4  4 3           2 6        3 5  5 2
+--R               (60A b c  - 40B b c )d e  + (- 42A b c  + 20B b c )d e
+--R             + 
+--R                         7       2 6  6          8         7  7
+--R               (- 12A b c  + 8B b c )d e + (12A c  - 6B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                   8 7       8   6           6 2       7   2 5        6 2 3 4
+--R               6A b e  - 4B b d e  + (- 24A b c  + 2B b c)d e  + 20B b c d e
+--R             + 
+--R                     4 4        5 3  4 3         3 5        4 4  5 2
+--R               (30A b c  - 20B b c )d e  + (24A b c  - 20B b c )d e
+--R             + 
+--R                       2 6        3 5  6            7        2 6  7
+--R               (- 60A b c  + 34B b c )d e + (24A b c  - 12B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                   8   6           7        8  2 5        7   3 4
+--R               6A b d e  + (- 12A b c - 4B b )d e  + 10B b c d e
+--R             + 
+--R                     4 4        5 3  5 2           3 5        4 4  6
+--R               (30A b c  - 20B b c )d e  + (- 36A b c  + 20B b c )d e
+--R             + 
+--R                     2 6       3 5  7
+--R               (12A b c  - 6B b c )d
+--R          *
+--R              2
+--R             x
+--R      *
+--R         log(x)
+--R     + 
+--R               6 2   6           5 3       6 2  2 5        5 3 3 4
+--R           6A b c d e  + (- 12A b c  - 4B b c )d e  + 10B b c d e
+--R         + 
+--R                 3 5        4 4  4 3           2 6        3 5  5 2
+--R           (30A b c  - 20B b c )d e  + (- 36A b c  + 20B b c )d e
+--R         + 
+--R                   7       2 6  6
+--R           (12A b c  - 6B b c )d e
+--R      *
+--R          4
+--R         x
+--R     + 
+--R                7     6           6 2       7   2 5          5 3        6 2  3 4
+--R           12A b c d e  + (- 21A b c  - 8B b c)d e  + (- 6A b c  + 18B b c )d e
+--R         + 
+--R                 4 4        5 3  4 3           3 5        4 4  5 2
+--R           (45A b c  - 25B b c )d e  + (- 24A b c  + 10B b c )d e
+--R         + 
+--R                   2 6        3 5  6            7       2 6  7
+--R           (- 18A b c  + 11B b c )d e + (12A b c  - 6B b c )d
+--R      *
+--R          3
+--R         x
+--R     + 
+--R               8   6          7        8  2 5           6 2       7   3 4
+--R           6A b d e  + (- 6A b c - 4B b )d e  + (- 13A b c  + 6B b c)d e
+--R         + 
+--R                 5 3       6 2  4 3         4 4        5 3  5 2
+--R           (12A b c  + 4B b c )d e  + (33A b c  - 25B b c )d e
+--R         + 
+--R                   3 5        4 4  6          2 6       3 5  7
+--R           (- 50A b c  + 28B b c )d e + (18A b c  - 9B b c )d
+--R      *
+--R          2
+--R         x
+--R     + 
+--R               8 2 5          7        8  3 4        6 2       7   4 3
+--R           3A b d e  + (- 8A b c - 2B b )d e  + (2A b c  + 8B b c)d e
+--R         + 
+--R                 5 3        6 2  5 2           4 4       5 3  6
+--R           (12A b c  - 12B b c )d e  + (- 13A b c  + 8B b c )d e
+--R         + 
+--R                3 5       4 4  7
+--R           (4A b c  - 2B b c )d
+--R      *
+--R         x
+--R     + 
+--R            8 3 4       7   4 3       6 2 5 2       5 3 6       4 4 7
+--R       - A b d e  + 4A b c d e  - 6A b c d e  + 4A b c d e - A b c d
+--R  /
+--R          9 2 4 5     8 3 5 4      7 4 6 3     6 5 7 2     5 6 8   5
+--R       (2b c d e  - 8b c d e  + 12b c d e  - 8b c d e  + 2b c d e)x
+--R     + 
+--R          10   4 5      9 2 5 4      8 3 6 3     7 4 7 2     6 5 8      5 6 9  4
+--R       (4b  c d e  - 14b c d e  + 16b c d e  - 4b c d e  - 4b c d e + 2b c d )x
+--R     + 
+--R          11 4 5     10   5 4     9 2 6 3      8 3 7 2      7 4 8      6 5 9  3
+--R       (2b  d e  - 4b  c d e  - 4b c d e  + 16b c d e  - 14b c d e + 4b c d )x
+--R     + 
+--R          11 5 4     10   6 3      9 2 7 2     8 3 8      7 4 9  2
+--R       (2b  d e  - 8b  c d e  + 12b c d e  - 8b c d e + 2b c d )x
+--R                                                    Type: Expression(Integer)
+--E 292
+
+--S 293 of 1457
+--a0:=integrate(t0,x)
+--E 293
+
+--S 294 of 1457
+--m0:=a0-r0
+--E 294
+
+--S 295 of 1457
+--d0:=D(m0,x)
+--E 295
+
+)clear all
+
+--S 296 of 1457
+t0:=(A+B*x)*(d+e*x)^3*sqrt(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R          3 4       3         2  3          2       2   2        2       3
+--R       B e x  + (A e  + 3B d e )x  + (3A d e  + 3B d e)x  + (3A d e + B d )x
+--R     + 
+--R          3
+--R       A d
+--R  *
+--R      +----------+
+--R      |   2
+--R     \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 296
+
+--S 297 of 1457
+r0:=1/960*(4*A*c*e*(132*c^2*d^2-132*b*c*d*e+35*b^2*e^2)+B*(64*c^3*d^3-_
+     360*b*c^2*d^2*e+366*b^2*c*d*e^2-105*b^3*e^3))*(b*x+c*x^2)^(3/2)/c^4+_
+     1/20*(2*B*c*d-3*b*B*e+4*A*c*e)*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c^2+_
+     1/6*B*(d+e*x)^3*(b*x+c*x^2)^(3/2)/c-1/160*e*(d*(16*b*B*c*d-40*A*c^2*d-_
+     9*b^2*B*e+12*A*b*c*e)-(28*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-36*b*c*d*e+_
+     21*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/c^3-1/512*b^2*(128*A*c^4*d^3+_
+     21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-28*b^3*c*e^2*(3*B*d+A*e)-_
+     64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+_
+     1/512*b*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_
+     28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/c^5+_
+     1/256*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-_
+     28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*x*sqrt(b*x+c*x^2)/c^4
+--R 
+--R
+--R   (2)
+--R                  5          6  3             4 2          5     2
+--R           (420A b c - 315B b )e  + (- 1800A b c  + 1260B b c)d e
+--R         + 
+--R                   3 3          4 2  2              2 4         3 3  3
+--R           (2880A b c  - 1800B b c )d e + (- 1920A b c  + 960B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                  5 3 5            5           4  3          5   2  4
+--R           1280B c e x  + ((1536A c  + 128B b c )e  + 4608B c d e )x
+--R         + 
+--R                        4         2 3  3           5           4    2
+--R               (192A b c  - 144B b c )e  + (5760A c  + 576B b c )d e
+--R             + 
+--R                      5 2
+--R               5760B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                        2 3         3 2  3            4         2 3    2
+--R               (- 224A b c  + 168B b c )e  + (960A b c  - 672B b c )d e
+--R             + 
+--R                       5           4  2           5 3
+--R               (7680A c  + 960B b c )d e + 2560B c d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      3 2         4   3             2 3         3 2    2
+--R               (280A b c  - 210B b c)e  + (- 1200A b c  + 840B b c )d e
+--R             + 
+--R                         4          2 3  2            5           4  3
+--R               (1920A b c  - 1200B b c )d e + (3840A c  + 640B b c )d
+--R          *
+--R             x
+--R         + 
+--R                    4          5  3           3 2          4     2
+--R           (- 420A b c + 315B b )e  + (1800A b c  - 1260B b c)d e
+--R         + 
+--R                     2 3          3 2  2              4         2 3  3
+--R           (- 2880A b c  + 1800B b c )d e + (1920A b c  - 960B b c )d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R          5 +-+
+--R     7680c \|c
+--R                                                    Type: Expression(Integer)
+--E 297
+
+--S 298 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                    5          6  3             4 2          5     2
+--R             (420A b c - 315B b )e  + (- 1800A b c  + 1260B b c)d e
+--R           + 
+--R                     3 3          4 2  2              2 4         3 3  3
+--R             (2880A b c  - 1800B b c )d e + (- 1920A b c  + 960B b c )d
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                    5 3 5            5           4  3          5   2  4
+--R             2560B c e x  + ((3072A c  + 256B b c )e  + 9216B c d e )x
+--R           + 
+--R                          4         2 3  3            5            4    2
+--R                 (384A b c  - 288B b c )e  + (11520A c  + 1152B b c )d e
+--R               + 
+--R                         5 2
+--R                 11520B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                          2 3         3 2  3             4          2 3    2
+--R                 (- 448A b c  + 336B b c )e  + (1920A b c  - 1344B b c )d e
+--R               + 
+--R                          5            4  2           5 3
+--R                 (15360A c  + 1920B b c )d e + 5120B c d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2         4   3             2 3          3 2    2
+--R                 (560A b c  - 420B b c)e  + (- 2400A b c  + 1680B b c )d e
+--R               + 
+--R                           4          2 3  2            5            4  3
+--R                 (3840A b c  - 2400B b c )d e + (7680A c  + 1280B b c )d
+--R            *
+--R               x
+--R           + 
+--R                      4          5  3           3 2          4     2
+--R             (- 840A b c + 630B b )e  + (3600A b c  - 2520B b c)d e
+--R           + 
+--R                       2 3          3 2  2              4          2 3  3
+--R             (- 5760A b c  + 3600B b c )d e + (3840A b c  - 1920B b c )d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R             5 +-+
+--R       15360c \|c
+--R     ,
+--R
+--R                    5          6  3             4 2          5     2
+--R             (420A b c - 315B b )e  + (- 1800A b c  + 1260B b c)d e
+--R           + 
+--R                     3 3          4 2  2              2 4         3 3  3
+--R             (2880A b c  - 1800B b c )d e + (- 1920A b c  + 960B b c )d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                    5 3 5            5           4  3          5   2  4
+--R             1280B c e x  + ((1536A c  + 128B b c )e  + 4608B c d e )x
+--R           + 
+--R                          4         2 3  3           5           4    2
+--R                 (192A b c  - 144B b c )e  + (5760A c  + 576B b c )d e
+--R               + 
+--R                        5 2
+--R                 5760B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                          2 3         3 2  3            4         2 3    2
+--R                 (- 224A b c  + 168B b c )e  + (960A b c  - 672B b c )d e
+--R               + 
+--R                         5           4  2           5 3
+--R                 (7680A c  + 960B b c )d e + 2560B c d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2         4   3             2 3         3 2    2
+--R                 (280A b c  - 210B b c)e  + (- 1200A b c  + 840B b c )d e
+--R               + 
+--R                           4          2 3  2            5           4  3
+--R                 (1920A b c  - 1200B b c )d e + (3840A c  + 640B b c )d
+--R            *
+--R               x
+--R           + 
+--R                      4          5  3           3 2          4     2
+--R             (- 420A b c + 315B b )e  + (1800A b c  - 1260B b c)d e
+--R           + 
+--R                       2 3          3 2  2              4         2 3  3
+--R             (- 2880A b c  + 1800B b c )d e + (1920A b c  - 960B b c )d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R            5 +---+
+--R       7680c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 298
+
+--S 299 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                 5         6  3            4 2        5     2
+--R           (28A b c - 21B b )e  + (- 120A b c  + 84B b c)d e
+--R         + 
+--R                  3 3         4 2  2             2 4        3 3  3
+--R           (192A b c  - 120B b c )d e + (- 128A b c  + 64B b c )d
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   5         6  3          4 2         5     2
+--R           (- 56A b c + 42B b )e  + (240A b c  - 168B b c)d e
+--R         + 
+--R                    3 3         4 2  2           2 4         3 3  3
+--R           (- 384A b c  + 240B b c )d e + (256A b c  - 128B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R  /
+--R          5 +-+
+--R     1024c \|c
+--R                                                    Type: Expression(Integer)
+--E 299
+
+--S 300 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 300
+
+--S 301 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                   5         6  3          4 2        5     2
+--R           (- 28A b c + 21B b )e  + (120A b c  - 84B b c)d e
+--R         + 
+--R                    3 3         4 2  2           2 4        3 3  3
+--R           (- 192A b c  + 120B b c )d e + (128A b c  - 64B b c )d
+--R      *
+--R                           +-+
+--R          +---+          x\|c
+--R         \|- c atanh(-------------)
+--R                      +----------+
+--R                      |   2
+--R                     \|c x  + b x
+--R     + 
+--R                 5         6  3            4 2        5     2
+--R           (28A b c - 21B b )e  + (- 120A b c  + 84B b c)d e
+--R         + 
+--R                  3 3         4 2  2             2 4        3 3  3
+--R           (192A b c  - 120B b c )d e + (- 128A b c  + 64B b c )d
+--R      *
+--R                         +----------+
+--R                   +---+ |   2
+--R          +-+     \|- c \|c x  + b x
+--R         \|c atan(-------------------)
+--R                          c x
+--R  /
+--R         5 +---+ +-+
+--R     512c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 301
+
+--S 302 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 302
+
+)clear all
+
+--S 303 of 1457
+t0:=(A+B*x)*(d+e*x)^2*sqrt(b*x+c*x^2)
+--R 
+--R
+--R                                                               +----------+
+--R            2 3       2           2                2        2  |   2
+--R   (1)  (B e x  + (A e  + 2B d e)x  + (2A d e + B d )x + A d )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 303
+
+--S 304 of 1457
+r0:=1/240*(50*A*c*e*(2*c*d-b*e)+B*(32*c^2*d^2-82*b*c*d*e+35*b^2*e^2))*_
+     (b*x+c*x^2)^(3/2)/c^3+1/5*B*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c-1/40*e*_
+     ((3*b*B-10*A*c)*d-(4*B*c*d-7*b*B*e+10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/c^2-_
+     1/128*b^2*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-_
+     16*b*c^2*d*(B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)+_
+     1/128*b*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*_
+     d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/c^4+1/64*(32*A*c^3*d^2-7*b^3*B*e^2+_
+     10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^3
+--R 
+--R
+--R   (2)
+--R                    4          5  2          3 2         4
+--R           (- 150A b c + 105B b )e  + (480A b c  - 300B b c)d e
+--R         + 
+--R                    2 3         3 2  2
+--R           (- 480A b c  + 240B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                 4 2 4           4          3  2         4     3
+--R           384B c e x  + ((480A c  + 48B b c )e  + 960B c d e)x
+--R         + 
+--R                    3        2 2  2           4           3             4 2  2
+--R           ((80A b c  - 56B b c )e  + (1280A c  + 160B b c )d e + 640B c d )x
+--R         + 
+--R                        2 2        3   2            3         2 2
+--R               (- 100A b c  + 70B b c)e  + (320A b c  - 200B b c )d e
+--R             + 
+--R                      4           3  2
+--R               (960A c  + 160B b c )d
+--R          *
+--R             x
+--R         + 
+--R                  3          4  2            2 2         3
+--R           (150A b c - 105B b )e  + (- 480A b c  + 300B b c)d e
+--R         + 
+--R                    3         2 2  2
+--R           (480A b c  - 240B b c )d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R          4 +-+
+--R     1920c \|c
+--R                                                    Type: Expression(Integer)
+--E 304
+
+--S 305 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                    4          5  2            3 2         4
+--R             (150A b c - 105B b )e  + (- 480A b c  + 300B b c)d e
+--R           + 
+--R                    2 3         3 2  2
+--R             (480A b c  - 240B b c )d
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                   4 2 4           4          3  2          4     3
+--R             768B c e x  + ((960A c  + 96B b c )e  + 1920B c d e)x
+--R           + 
+--R                          3         2 2  2           4           3
+--R                 (160A b c  - 112B b c )e  + (2560A c  + 320B b c )d e
+--R               + 
+--R                        4 2
+--R                 1280B c d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                          2 2         3   2            3         2 2
+--R                 (- 200A b c  + 140B b c)e  + (640A b c  - 400B b c )d e
+--R               + 
+--R                         4           3  2
+--R                 (1920A c  + 320B b c )d
+--R            *
+--R               x
+--R           + 
+--R                    3          4  2            2 2         3
+--R             (300A b c - 210B b )e  + (- 960A b c  + 600B b c)d e
+--R           + 
+--R                      3         2 2  2
+--R             (960A b c  - 480B b c )d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R            4 +-+
+--R       3840c \|c
+--R     ,
+--R
+--R                      4          5  2          3 2         4
+--R             (- 150A b c + 105B b )e  + (480A b c  - 300B b c)d e
+--R           + 
+--R                      2 3         3 2  2
+--R             (- 480A b c  + 240B b c )d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                   4 2 4           4          3  2         4     3
+--R             384B c e x  + ((480A c  + 48B b c )e  + 960B c d e)x
+--R           + 
+--R                      3        2 2  2           4           3             4 2  2
+--R             ((80A b c  - 56B b c )e  + (1280A c  + 160B b c )d e + 640B c d )x
+--R           + 
+--R                          2 2        3   2            3         2 2
+--R                 (- 100A b c  + 70B b c)e  + (320A b c  - 200B b c )d e
+--R               + 
+--R                        4           3  2
+--R                 (960A c  + 160B b c )d
+--R            *
+--R               x
+--R           + 
+--R                    3          4  2            2 2         3
+--R             (150A b c - 105B b )e  + (- 480A b c  + 300B b c)d e
+--R           + 
+--R                      3         2 2  2
+--R             (480A b c  - 240B b c )d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R            4 +---+
+--R       1920c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 305
+
+--S 306 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                 4        5  2           3 2        4
+--R           (10A b c - 7B b )e  + (- 32A b c  + 20B b c)d e
+--R         + 
+--R                 2 3        3 2  2
+--R           (32A b c  - 16B b c )d
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                 4         5  2           3 2        4
+--R           (20A b c - 14B b )e  + (- 64A b c  + 40B b c)d e
+--R         + 
+--R                 2 3        3 2  2
+--R           (64A b c  - 32B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R  /
+--R         4 +-+
+--R     256c \|c
+--R                                                    Type: Expression(Integer)
+--E 306
+
+--S 307 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 307
+
+--S 308 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                 4        5  2           3 2        4
+--R           (10A b c - 7B b )e  + (- 32A b c  + 20B b c)d e
+--R         + 
+--R                 2 3        3 2  2
+--R           (32A b c  - 16B b c )d
+--R      *
+--R                           +-+
+--R          +---+          x\|c
+--R         \|- c atanh(-------------)
+--R                      +----------+
+--R                      |   2
+--R                     \|c x  + b x
+--R     + 
+--R                   4        5  2         3 2        4
+--R           (- 10A b c + 7B b )e  + (32A b c  - 20B b c)d e
+--R         + 
+--R                   2 3        3 2  2
+--R           (- 32A b c  + 16B b c )d
+--R      *
+--R                         +----------+
+--R                   +---+ |   2
+--R          +-+     \|- c \|c x  + b x
+--R         \|c atan(-------------------)
+--R                          c x
+--R  /
+--R         4 +---+ +-+
+--R     128c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 308
+
+--S 309 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 309
+
+)clear all
+
+--S 310 of 1457
+t0:=(A+B*x)*(d+e*x)*sqrt(b*x+c*x^2)
+--R 
+--R
+--R                                      +----------+
+--R              2                       |   2
+--R   (1)  (B e x  + (A e + B d)x + A d)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 310
+
+--S 311 of 1457
+r0:=1/24*(2*B*c*d-5*b*B*e+8*A*c*e)*(b*x+c*x^2)^(3/2)/c^2+1/4*B*(d+e*x)*_
+     (b*x+c*x^2)^(3/2)/c-1/64*b^2*(16*A*c^2*d+5*b^2*B*e-8*b*c*(B*d+A*e))*_
+     atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/64*b*(16*A*c^2*d+5*b^2*B*e-_
+     8*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^3+1/32*(16*A*c^2*d+5*b^2*B*e-_
+     8*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^2
+--R 
+--R
+--R   (2)
+--R                                                                  +-+
+--R              3         4             2 2        3              x\|c
+--R       ((24A b c - 15B b )e + (- 48A b c  + 24B b c)d)atanh(-------------)
+--R                                                             +----------+
+--R                                                             |   2
+--R                                                            \|c x  + b x
+--R     + 
+--R                3   3          3         2          3   2
+--R           48B c e x  + ((64A c  + 8B b c )e + 64B c d)x
+--R         + 
+--R                    2        2            3          2
+--R           ((16A b c  - 10B b c)e + (96A c  + 16B b c )d)x
+--R         + 
+--R                   2         3             2        2
+--R           (- 24A b c + 15B b )e + (48A b c  - 24B b c)d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R         3 +-+
+--R     192c \|c
+--R                                                    Type: Expression(Integer)
+--E 311
+
+--S 312 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                  3         4             2 2        3
+--R           ((24A b c - 15B b )e + (- 48A b c  + 24B b c)d)
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                  3   3           3          2           3   2
+--R             96B c e x  + ((128A c  + 16B b c )e + 128B c d)x
+--R           + 
+--R                      2        2             3          2
+--R             ((32A b c  - 20B b c)e + (192A c  + 32B b c )d)x
+--R           + 
+--R                     2         3             2        2
+--R             (- 48A b c + 30B b )e + (96A b c  - 48B b c)d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R           3 +-+
+--R       384c \|c
+--R     ,
+--R
+--R                  3         4             2 2        3
+--R           ((24A b c - 15B b )e + (- 48A b c  + 24B b c)d)
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                  3   3          3         2          3   2
+--R             48B c e x  + ((64A c  + 8B b c )e + 64B c d)x
+--R           + 
+--R                      2        2            3          2
+--R             ((16A b c  - 10B b c)e + (96A c  + 16B b c )d)x
+--R           + 
+--R                     2         3             2        2
+--R             (- 24A b c + 15B b )e + (48A b c  - 24B b c)d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R           3 +---+
+--R       192c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 312
+
+--S 313 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R               3        4             2 2       3
+--R         ((8A b c - 5B b )e + (- 16A b c  + 8B b c)d)
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                                                  +-+
+--R                3         4           2 2        3              x\|c
+--R       ((- 16A b c + 10B b )e + (32A b c  - 16B b c)d)atanh(-------------)
+--R                                                             +----------+
+--R                                                             |   2
+--R                                                            \|c x  + b x
+--R  /
+--R         3 +-+
+--R     128c \|c
+--R                                                    Type: Expression(Integer)
+--E 313
+
+--S 314 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 314
+
+--S 315 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                                     +-+
+--R               3        4           2 2       3     +---+          x\|c
+--R       ((- 8A b c + 5B b )e + (16A b c  - 8B b c)d)\|- c atanh(-------------)
+--R                                                                +----------+
+--R                                                                |   2
+--R                                                               \|c x  + b x
+--R     + 
+--R                                                                 +----------+
+--R                                                           +---+ |   2
+--R           3        4             2 2       3     +-+     \|- c \|c x  + b x
+--R     ((8A b c - 5B b )e + (- 16A b c  + 8B b c)d)\|c atan(-------------------)
+--R                                                                  c x
+--R  /
+--R        3 +---+ +-+
+--R     64c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 315
+
+--S 316 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 316
+
+)clear all
+
+--S 317 of 1457
+t0:=(A+B*x)*sqrt(b*x+c*x^2)
+--R 
+--R
+--R                  +----------+
+--R                  |   2
+--R   (1)  (B x + A)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 317
+
+--S 318 of 1457
+r0:=1/3*B*(b*x+c*x^2)^(3/2)/c+1/8*b^2*(b*B-2*A*c)*atanh(x*sqrt(c)/_
+     sqrt(b*x+c*x^2))/c^(5/2)-1/8*b*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^2-_
+     1/4*(b*B-2*A*c)*x*sqrt(b*x+c*x^2)/c
+--R 
+--R
+--R   (2)
+--R                                     +-+
+--R              2        3           x\|c
+--R       (- 6A b c + 3B b )atanh(-------------)
+--R                                +----------+
+--R                                |   2
+--R                               \|c x  + b x
+--R     + 
+--R                                                           +----------+
+--R            2 2         2                           2  +-+ |   2
+--R       (8B c x  + (12A c  + 2B b c)x + 6A b c - 3B b )\|c \|c x  + b x
+--R  /
+--R        2 +-+
+--R     24c \|c
+--R                                                    Type: Expression(Integer)
+--E 318
+
+--S 319 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                                  +----------+
+--R              2        3          |   2                     +-+
+--R         (6A b c - 3B b )log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                                                               +----------+
+--R               2 2         2                            2  +-+ |   2
+--R         (16B c x  + (24A c  + 4B b c)x + 12A b c - 6B b )\|c \|c x  + b x
+--R    /
+--R          2 +-+
+--R       48c \|c
+--R     ,
+--R
+--R                                       +----------+
+--R                                 +---+ |   2
+--R                2        3      \|- c \|c x  + b x
+--R         (- 6A b c + 3B b )atan(-------------------)
+--R                                        c x
+--R       + 
+--R                                                               +----------+
+--R              2 2         2                           2  +---+ |   2
+--R         (8B c x  + (12A c  + 2B b c)x + 6A b c - 3B b )\|- c \|c x  + b x
+--R    /
+--R          2 +---+
+--R       24c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 319
+
+--S 320 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                               +----------+
+--R            2       3          |   2                     +-+
+--R       (2A b c - B b )log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                   +-+
+--R            2        3           x\|c
+--R       (4A b c - 2B b )atanh(-------------)
+--R                              +----------+
+--R                              |   2
+--R                             \|c x  + b x
+--R  /
+--R        2 +-+
+--R     16c \|c
+--R                                                    Type: Expression(Integer)
+--E 320
+
+--S 321 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 321
+
+--S 322 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                        +-+
+--R            2       3  +---+          x\|c
+--R       (2A b c - B b )\|- c atanh(-------------)
+--R                                   +----------+
+--R                                   |   2
+--R                                  \|c x  + b x
+--R     + 
+--R                                        +----------+
+--R                                  +---+ |   2
+--R              2       3  +-+     \|- c \|c x  + b x
+--R       (- 2A b c + B b )\|c atan(-------------------)
+--R                                         c x
+--R  /
+--R       2 +---+ +-+
+--R     8c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 322
+
+--S 323 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 323
+
+)clear all
+
+--S 324 of 1457
+t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)
+--R 
+--R
+--R                  +----------+
+--R                  |   2
+--R        (B x + A)\|c x  + b x
+--R   (1)  ----------------------
+--R                e x + d
+--R                                                    Type: Expression(Integer)
+--E 324
+
+--S 325 of 1457
+r0:=-1/4*(4*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-4*b*c*d*e-b^2*e^2))*atanh(x*_
+     sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^3)-(B*d-A*e)*atanh(1/2*(b*d+_
+     (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*_
+     sqrt(c*d-b*e)/e^3-1/4*(4*B*c*d-b*B*e-4*A*c*e-2*B*c*e*x)*sqrt(b*x+_
+     c*x^2)/(c*e^2)
+--R 
+--R
+--R   (2)
+--R                                                                        +-+
+--R                     2  2          2                    2 2           x\|c
+--R       ((4A b c - B b )e  + (- 8A c  - 4B b c)d e + 8B c d )atanh(-------------)
+--R                                                                   +----------+
+--R                                                                   |   2
+--R                                                                  \|c x  + b x
+--R     + 
+--R                             +-----------+ +-+ +-+
+--R         (- 4A c e + 4B c d)\|- b e + c d \|c \|d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                                  +----------+
+--R              2                 2             +-+ |   2
+--R       (2B c e x + (4A c + B b)e  - 4B c d e)\|c \|c x  + b x
+--R  /
+--R         3 +-+
+--R     4c e \|c
+--R                                                    Type: Expression(Integer)
+--E 325
+
+--S 326 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                             +--------------+
+--R                             |             2  +-+
+--R           (8A c e - 8B c d)\|- b d e + c d  \|c
+--R        *
+--R                 +--------------+ +----------+
+--R                 |             2  |   2
+--R               2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(-------------------------------------------------------)
+--R                                       e x + d
+--R       + 
+--R                         2  2          2                    2 2
+--R           ((4A b c - B b )e  + (- 8A c  - 4B b c)d e + 8B c d )
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                                                     +----------+
+--R                2                  2             +-+ |   2
+--R         (4B c e x + (8A c + 2B b)e  - 8B c d e)\|c \|c x  + b x
+--R    /
+--R           3 +-+
+--R       8c e \|c
+--R     ,
+--R
+--R                         2  2          2                    2 2
+--R           ((4A b c - B b )e  + (- 8A c  - 4B b c)d e + 8B c d )
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                                                       +----------+
+--R                                 +------------+        |   2
+--R                             +-+ |           2       d\|c x  + b x
+--R         (16A c e - 16B c d)\|c \|b d e - c d  atan(----------------)
+--R                                                      +------------+
+--R                                                      |           2
+--R                                                    x\|b d e - c d
+--R       + 
+--R                                                     +----------+
+--R                2                  2             +-+ |   2
+--R         (4B c e x + (8A c + 2B b)e  - 8B c d e)\|c \|c x  + b x
+--R    /
+--R           3 +-+
+--R       8c e \|c
+--R     ,
+--R
+--R                             +--------------+
+--R                             |             2  +---+
+--R           (4A c e - 4B c d)\|- b d e + c d  \|- c
+--R        *
+--R                 +--------------+ +----------+
+--R                 |             2  |   2
+--R               2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(-------------------------------------------------------)
+--R                                       e x + d
+--R       + 
+--R                         2  2          2                    2 2
+--R           ((4A b c - B b )e  + (- 8A c  - 4B b c)d e + 8B c d )
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                                                      +----------+
+--R                2                 2             +---+ |   2
+--R         (2B c e x + (4A c + B b)e  - 4B c d e)\|- c \|c x  + b x
+--R    /
+--R           3 +---+
+--R       4c e \|- c
+--R     ,
+--R
+--R                         2  2          2                    2 2
+--R           ((4A b c - B b )e  + (- 8A c  - 4B b c)d e + 8B c d )
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                                                       +----------+
+--R                                 +------------+        |   2
+--R                           +---+ |           2       d\|c x  + b x
+--R         (8A c e - 8B c d)\|- c \|b d e - c d  atan(----------------)
+--R                                                      +------------+
+--R                                                      |           2
+--R                                                    x\|b d e - c d
+--R       + 
+--R                                                      +----------+
+--R                2                 2             +---+ |   2
+--R         (2B c e x + (4A c + B b)e  - 4B c d e)\|- c \|c x  + b x
+--R    /
+--R           3 +---+
+--R       4c e \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 326
+
+--S 327 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                           +--------------+
+--R                           |             2  +-+
+--R         (8A c e - 8B c d)\|- b d e + c d  \|c
+--R      *
+--R               +--------------+ +----------+
+--R               |             2  |   2
+--R             2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R         log(-------------------------------------------------------)
+--R                                     e x + d
+--R     + 
+--R                       2  2          2                    2 2
+--R         ((4A b c - B b )e  + (- 8A c  - 4B b c)d e + 8B c d )
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                          2  2         2                     2 2
+--R         ((- 8A b c + 2B b )e  + (16A c  + 8B b c)d e - 16B c d )
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                           +-----------+ +-+ +-+
+--R         (8A c e - 8B c d)\|- b e + c d \|c \|d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R         3 +-+
+--R     8c e \|c
+--R                                                    Type: Expression(Integer)
+--E 327
+
+--S 328 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 328
+
+--S 329 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                       2  2          2                    2 2
+--R         ((4A b c - B b )e  + (- 8A c  - 4B b c)d e + 8B c d )
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                          2  2         2                     2 2
+--R         ((- 8A b c + 2B b )e  + (16A c  + 8B b c)d e - 16B c d )
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                           +-----------+ +-+ +-+
+--R         (8A c e - 8B c d)\|- b e + c d \|c \|d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                                     +----------+
+--R                               +------------+        |   2
+--R                           +-+ |           2       d\|c x  + b x
+--R       (16A c e - 16B c d)\|c \|b d e - c d  atan(----------------)
+--R                                                    +------------+
+--R                                                    |           2
+--R                                                  x\|b d e - c d
+--R  /
+--R         3 +-+
+--R     8c e \|c
+--R                                                    Type: Expression(Integer)
+--E 329
+
+--S 330 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 1457
+t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^2
+--R 
+--R
+--R                  +----------+
+--R                  |   2
+--R        (B x + A)\|c x  + b x
+--R   (1)  ----------------------
+--R           2 2             2
+--R          e x  + 2d e x + d
+--R                                                    Type: Expression(Integer)
+--E 331
+
+--S 332 of 1457
+r0:=-(4*B*c*d-b*B*e-2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^3*sqrt(c))+_
+     1/2*(B*d*(4*c*d-3*b*e)-A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_
+     (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^3*sqrt(d)*sqrt(c*d-b*e))+_
+     (2*B*d-A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                         2                                         2
+--R         (((4A c + 2B b)e  - 8B c d e)x + (4A c + 2B b)d e - 8B c d )
+--R      *
+--R                                       +-+
+--R          +-----------+ +-+          x\|c
+--R         \|- b e + c d \|d atanh(-------------)
+--R                                  +----------+
+--R                                  |   2
+--R                                 \|c x  + b x
+--R     + 
+--R                   3                   2         2             2
+--R           (- A b e  + (2A c + 3B b)d e  - 4B c d e)x - A b d e
+--R         + 
+--R                         2          3
+--R           (2A c + 3B b)d e - 4B c d
+--R      *
+--R          +-+             (b e - 2c d)x - b d
+--R         \|c atanh(--------------------------------)
+--R                                       +----------+
+--R                     +-----------+ +-+ |   2
+--R                   2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                                       +----------+
+--R            2        2           +-----------+ +-+ +-+ |   2
+--R       (2B e x - 2A e  + 4B d e)\|- b e + c d \|c \|d \|c x  + b x
+--R  /
+--R        4        3  +-----------+ +-+ +-+
+--R     (2e x + 2d e )\|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 332
+
+--S 333 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                          2                                        2
+--R           (((2A c + B b)e  - 4B c d e)x + (2A c + B b)d e - 4B c d )
+--R        *
+--R            +--------------+       +----------+
+--R            |             2        |   2                     +-+
+--R           \|- b d e + c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                   3                     2         2             2
+--R             (A b e  + (- 2A c - 3B b)d e  + 4B c d e)x + A b d e
+--R           + 
+--R                             2          3
+--R             (- 2A c - 3B b)d e + 4B c d
+--R        *
+--R            +-+
+--R           \|c
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                                   +--------------+     +----------+
+--R              2        2           |             2  +-+ |   2
+--R         (2B e x - 2A e  + 4B d e)\|- b d e + c d  \|c \|c x  + b x
+--R    /
+--R                      +--------------+
+--R          4        3  |             2  +-+
+--R       (2e x + 2d e )\|- b d e + c d  \|c
+--R     ,
+--R
+--R                          2                                        2
+--R           (((2A c + B b)e  - 4B c d e)x + (2A c + B b)d e - 4B c d )
+--R        *
+--R            +------------+       +----------+
+--R            |           2        |   2                     +-+
+--R           \|b d e - c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                      3                   2         2              2
+--R             (- 2A b e  + (4A c + 6B b)d e  - 8B c d e)x - 2A b d e
+--R           + 
+--R                           2          3
+--R             (4A c + 6B b)d e - 8B c d
+--R        *
+--R                     +------------+ +----------+
+--R                     |           2  |   2
+--R            +-+     \|b d e - c d  \|c x  + b x
+--R           \|c atan(----------------------------)
+--R                            (b e - c d)x
+--R       + 
+--R                                       +------------+ +----------+
+--R              2        2           +-+ |           2  |   2
+--R         (2B e x - 2A e  + 4B d e)\|c \|b d e - c d  \|c x  + b x
+--R    /
+--R                          +------------+
+--R          4        3  +-+ |           2
+--R       (2e x + 2d e )\|c \|b d e - c d
+--R     ,
+--R
+--R                   3                     2         2             2
+--R             (A b e  + (- 2A c - 3B b)d e  + 4B c d e)x + A b d e
+--R           + 
+--R                             2          3
+--R             (- 2A c - 3B b)d e + 4B c d
+--R        *
+--R            +---+
+--R           \|- c
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                           2                                         2
+--R           (((4A c + 2B b)e  - 8B c d e)x + (4A c + 2B b)d e - 8B c d )
+--R        *
+--R                                        +----------+
+--R            +--------------+      +---+ |   2
+--R            |             2      \|- c \|c x  + b x
+--R           \|- b d e + c d  atan(-------------------)
+--R                                         c x
+--R       + 
+--R                                   +--------------+       +----------+
+--R              2        2           |             2  +---+ |   2
+--R         (2B e x - 2A e  + 4B d e)\|- b d e + c d  \|- c \|c x  + b x
+--R    /
+--R                      +--------------+
+--R          4        3  |             2  +---+
+--R       (2e x + 2d e )\|- b d e + c d  \|- c
+--R     ,
+--R
+--R                     3                   2         2             2
+--R             (- A b e  + (2A c + 3B b)d e  - 4B c d e)x - A b d e
+--R           + 
+--R                           2          3
+--R             (2A c + 3B b)d e - 4B c d
+--R        *
+--R                       +------------+ +----------+
+--R                       |           2  |   2
+--R            +---+     \|b d e - c d  \|c x  + b x
+--R           \|- c atan(----------------------------)
+--R                              (b e - c d)x
+--R       + 
+--R                          2                                        2
+--R           (((2A c + B b)e  - 4B c d e)x + (2A c + B b)d e - 4B c d )
+--R        *
+--R                                      +----------+
+--R            +------------+      +---+ |   2
+--R            |           2      \|- c \|c x  + b x
+--R           \|b d e - c d  atan(-------------------)
+--R                                       c x
+--R       + 
+--R                                       +------------+ +----------+
+--R             2       2           +---+ |           2  |   2
+--R         (B e x - A e  + 2B d e)\|- c \|b d e - c d  \|c x  + b x
+--R    /
+--R                          +------------+
+--R         4       3  +---+ |           2
+--R       (e x + d e )\|- c \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 333
+
+--S 334 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                  +--------------+
+--R                                  |             2  +-----------+ +-+
+--R         ((2A c + B b)e - 4B c d)\|- b d e + c d  \|- b e + c d \|d
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R               2                              2  +-----------+ +-+ +-+
+--R         (A b e  + (- 2A c - 3B b)d e + 4B c d )\|- b e + c d \|c \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                     +--------------+
+--R                                     |             2  +-----------+ +-+
+--R         ((- 4A c - 2B b)e + 8B c d)\|- b d e + c d  \|- b e + c d \|d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                                                 +--------------+
+--R               2                              2  |             2  +-+
+--R         (A b e  + (- 2A c - 3B b)d e + 4B c d )\|- b d e + c d  \|c
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R         +--------------+
+--R       3 |             2  +-----------+ +-+ +-+
+--R     2e \|- b d e + c d  \|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 334
+
+--S 335 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 335
+
+--S 336 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                    +------------+
+--R                                  +-----------+ +-+ |           2
+--R         ((2A c + B b)e - 4B c d)\|- b e + c d \|d \|b d e - c d
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                                       +------------+
+--R                                     +-----------+ +-+ |           2
+--R         ((- 4A c - 2B b)e + 8B c d)\|- b e + c d \|d \|b d e - c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                                                     +------------+
+--R               2                              2  +-+ |           2
+--R         (A b e  + (- 2A c - 3B b)d e + 4B c d )\|c \|b d e - c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  2                            2  +-----------+ +-+ +-+
+--R         (- 2A b e  + (4A c + 6B b)d e - 8B c d )\|- b e + c d \|c \|d
+--R      *
+--R               +------------+ +----------+
+--R               |           2  |   2
+--R              \|b d e - c d  \|c x  + b x
+--R         atan(----------------------------)
+--R                      (b e - c d)x
+--R  /
+--R                               +------------+
+--R       3 +-----------+ +-+ +-+ |           2
+--R     2e \|- b e + c d \|c \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 336
+
+--S 337 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 337
+
+)clear all
+
+--S 338 of 1457
+t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^3
+--R 
+--R
+--R                     +----------+
+--R                     |   2
+--R           (B x + A)\|c x  + b x
+--R   (1)  ----------------------------
+--R         3 3       2 2     2       3
+--R        e x  + 3d e x  + 3d e x + d
+--R                                                    Type: Expression(Integer)
+--E 338
+
+--S 339 of 1457
+r0:=1/2*(B*d-A*e)*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^2)-1/8*(A*b^2*e^3+_
+     B*d*(8*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_
+     (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*e^3*(c*d-b*e)^(3/2))+_
+     2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^3+1/4*(A*b*e^2-B*d*_
+     (4*c*d-3*b*e)-2*c*e*(B*d-A*e)*x)*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                     3          2 2  2           2 2          3             3
+--R           (16B b d e  - 16B c d e )x  + (32B b d e  - 32B c d e)x + 16B b d e
+--R         + 
+--R                    4
+--R           - 16B c d
+--R      *
+--R                                           +-+
+--R          +-----------+ +-+ +-+          x\|c
+--R         \|- b e + c d \|c \|d atanh(-------------)
+--R                                      +----------+
+--R                                      |   2
+--R                                     \|c x  + b x
+--R     + 
+--R                 2 5       2   4            2 3       2 3 2  2
+--R           (- A b e  - 3B b d e  + 12B b c d e  - 8B c d e )x
+--R         + 
+--R                  2   4       2 2 3            3 2        2 4         2 2 3
+--R           (- 2A b d e  - 6B b d e  + 24B b c d e  - 16B c d e)x - A b d e
+--R         + 
+--R                 2 3 2            4        2 5
+--R           - 3B b d e  + 12B b c d e - 8B c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  4                      3          2 2             3
+--R           (2A b e  + (- 4A c - 10B b)d e  + 12B c d e )x - 2A b d e
+--R         + 
+--R                   2 2         3
+--R           - 6B b d e  + 8B c d e
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R               6       2 5  2         2 5        3 4         3 4       4 3
+--R       ((8b d e  - 8c d e )x  + (16b d e  - 16c d e )x + 8b d e  - 8c d e )
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 339
+
+--S 340 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                      3         2 2  2           2 2          3            3
+--R             (8B b d e  - 8B c d e )x  + (16B b d e  - 16B c d e)x + 8B b d e
+--R           + 
+--R                     4
+--R             - 8B c d
+--R        *
+--R            +--------------+              +----------+
+--R            |             2  +-+      +-+ |   2
+--R           \|- b d e + c d  \|c log(2\|c \|c x  + b x  + 2c x + b)
+--R       + 
+--R                 2 5       2   4            2 3       2 3 2  2
+--R             (A b e  + 3B b d e  - 12B b c d e  + 8B c d e )x
+--R           + 
+--R                  2   4       2 2 3            3 2        2 4         2 2 3
+--R             (2A b d e  + 6B b d e  - 24B b c d e  + 16B c d e)x + A b d e
+--R           + 
+--R                 2 3 2            4        2 5
+--R             3B b d e  - 12B b c d e + 8B c d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                    4                      3          2 2             3
+--R             (2A b e  + (- 4A c - 10B b)d e  + 12B c d e )x - 2A b d e
+--R           + 
+--R                     2 2         3
+--R             - 6B b d e  + 8B c d e
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                 6       2 5  2         2 5        3 4         3 4       4 3
+--R         ((8b d e  - 8c d e )x  + (16b d e  - 16c d e )x + 8b d e  - 8c d e )
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                      3         2 2  2          2 2         3            3
+--R             (4B b d e  - 4B c d e )x  + (8B b d e  - 8B c d e)x + 4B b d e
+--R           + 
+--R                     4
+--R             - 4B c d
+--R        *
+--R                +------------+          +----------+
+--R            +-+ |           2       +-+ |   2
+--R           \|c \|b d e - c d  log(2\|c \|c x  + b x  + 2c x + b)
+--R       + 
+--R                   2 5       2   4            2 3       2 3 2  2
+--R             (- A b e  - 3B b d e  + 12B b c d e  - 8B c d e )x
+--R           + 
+--R                    2   4       2 2 3            3 2        2 4         2 2 3
+--R             (- 2A b d e  - 6B b d e  + 24B b c d e  - 16B c d e)x - A b d e
+--R           + 
+--R                   2 3 2            4        2 5
+--R             - 3B b d e  + 12B b c d e - 8B c d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                   4                     3         2 2            3         2 2
+--R             (A b e  + (- 2A c - 5B b)d e  + 6B c d e )x - A b d e  - 3B b d e
+--R           + 
+--R                   3
+--R             4B c d e
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                 6       2 5  2        2 5       3 4         3 4       4 3
+--R         ((4b d e  - 4c d e )x  + (8b d e  - 8c d e )x + 4b d e  - 4c d e )
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ,
+--R
+--R                 2 5       2   4            2 3       2 3 2  2
+--R             (A b e  + 3B b d e  - 12B b c d e  + 8B c d e )x
+--R           + 
+--R                  2   4       2 2 3            3 2        2 4         2 2 3
+--R             (2A b d e  + 6B b d e  - 24B b c d e  + 16B c d e)x + A b d e
+--R           + 
+--R                 2 3 2            4        2 5
+--R             3B b d e  - 12B b c d e + 8B c d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                       3          2 2  2           2 2          3             3
+--R             (16B b d e  - 16B c d e )x  + (32B b d e  - 32B c d e)x + 16B b d e
+--R           + 
+--R                      4
+--R             - 16B c d
+--R        *
+--R                                        +----------+
+--R            +--------------+            |   2
+--R            |             2  +---+     \|c x  + b x
+--R           \|- b d e + c d  \|- c atan(-------------)
+--R                                            +---+
+--R                                          x\|- c
+--R       + 
+--R                    4                      3          2 2             3
+--R             (2A b e  + (- 4A c - 10B b)d e  + 12B c d e )x - 2A b d e
+--R           + 
+--R                     2 2         3
+--R             - 6B b d e  + 8B c d e
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                 6       2 5  2         2 5        3 4         3 4       4 3
+--R         ((8b d e  - 8c d e )x  + (16b d e  - 16c d e )x + 8b d e  - 8c d e )
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                   2 5       2   4            2 3       2 3 2  2
+--R             (- A b e  - 3B b d e  + 12B b c d e  - 8B c d e )x
+--R           + 
+--R                    2   4       2 2 3            3 2        2 4         2 2 3
+--R             (- 2A b d e  - 6B b d e  + 24B b c d e  - 16B c d e)x - A b d e
+--R           + 
+--R                   2 3 2            4        2 5
+--R             - 3B b d e  + 12B b c d e - 8B c d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                      3         2 2  2           2 2          3            3
+--R             (8B b d e  - 8B c d e )x  + (16B b d e  - 16B c d e)x + 8B b d e
+--R           + 
+--R                     4
+--R             - 8B c d
+--R        *
+--R                                      +----------+
+--R                  +------------+      |   2
+--R            +---+ |           2      \|c x  + b x
+--R           \|- c \|b d e - c d  atan(-------------)
+--R                                          +---+
+--R                                        x\|- c
+--R       + 
+--R                   4                     3         2 2            3         2 2
+--R             (A b e  + (- 2A c - 5B b)d e  + 6B c d e )x - A b d e  - 3B b d e
+--R           + 
+--R                   3
+--R             4B c d e
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                 6       2 5  2        2 5       3 4         3 4       4 3
+--R         ((4b d e  - 4c d e )x  + (8b d e  - 8c d e )x + 4b d e  - 4c d e )
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 340
+
+--S 341 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                              +--------------+
+--R                           2  |             2  +-----------+ +-+ +-+
+--R         (8B b d e - 8B c d )\|- b d e + c d  \|- b e + c d \|c \|d
+--R      *
+--R                   +----------+
+--R               +-+ |   2
+--R         log(2\|c \|c x  + b x  + 2c x + b)
+--R     + 
+--R             2 3       2   2            2        2 3  +-----------+ +-+
+--R         (A b e  + 3B b d e  - 12B b c d e + 8B c d )\|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                  +--------------+
+--R                               2  |             2  +-----------+ +-+ +-+
+--R         (- 16B b d e + 16B c d )\|- b d e + c d  \|- b e + c d \|c \|d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                                                      +--------------+
+--R             2 3       2   2            2        2 3  |             2
+--R         (A b e  + 3B b d e  - 12B b c d e + 8B c d )\|- b d e + c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                         +--------------+
+--R            4       2 3  |             2  +-----------+ +-+
+--R     (8b d e  - 8c d e )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 341
+
+--S 342 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 342
+
+--S 343 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                    +------------+
+--R                           2  +-----------+ +-+ +-+ |           2
+--R         (8B b d e - 8B c d )\|- b e + c d \|c \|d \|b d e - c d
+--R      *
+--R                   +----------+
+--R               +-+ |   2
+--R         log(2\|c \|c x  + b x  + 2c x + b)
+--R     + 
+--R                                                        +------------+
+--R                               2  +-----------+ +-+ +-+ |           2
+--R         (- 16B b d e + 16B c d )\|- b e + c d \|c \|d \|b d e - c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                                                      +------------+
+--R             2 3       2   2            2        2 3  |           2
+--R         (A b e  + 3B b d e  - 12B b c d e + 8B c d )\|b d e - c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                2 3       2   2            2         2 3  +-----------+ +-+
+--R         (- 2A b e  - 6B b d e  + 24B b c d e - 16B c d )\|- b e + c d \|d
+--R      *
+--R               +------------+ +----------+
+--R               |           2  |   2
+--R              \|b d e - c d  \|c x  + b x
+--R         atan(----------------------------)
+--R                      (b e - c d)x
+--R  /
+--R                                           +------------+
+--R            4       2 3  +-----------+ +-+ |           2
+--R     (8b d e  - 8c d e )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 343
+
+--S 344 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 344
+
+)clear all
+
+--S 345 of 1457
+t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^4
+--R 
+--R
+--R                          +----------+
+--R                          |   2
+--R                (B x + A)\|c x  + b x
+--R   (1)  --------------------------------------
+--R         4 4       3 3     2 2 2     3       4
+--R        e x  + 4d e x  + 6d e x  + 4d e x + d
+--R                                                    Type: Expression(Integer)
+--E 345
+
+--S 346 of 1457
+r0:=1/16*b^2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_
+     sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+1/12*(B*_
+     d*(4*c*d-5*b*e)+A*e*(2*c*d-b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*_
+     (d+e*x)^2)+1/24*(B*d*(8*c^2*d^2-14*b*c*d*e+3*b^2*e^2)+A*e*(4*c^2*_
+     d^2-4*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*_
+     (d+e*x))-1/3*(2*B*d+A*e+3*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^3)
+--R 
+--R
+--R   (2)
+--R                  3 4        2        3    3  3
+--R           (- 3A b e  + (6A b c - 3B b )d e )x
+--R         + 
+--R                  3   3         2        3  2 2  2
+--R           (- 9A b d e  + (18A b c - 9B b )d e )x
+--R         + 
+--R                3 2 2         2        3  3          3 3         2        3  4
+--R         (- 9A b d e  + (18A b c - 9B b )d e)x - 3A b d e + (6A b c - 3B b )d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                     2 3                   2    2        2            2
+--R                 6A b e  + (- 8A b c + 6B b )d e  + (8A c  - 28B b c)d e
+--R               + 
+--R                      2 3
+--R                 16B c d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                 2   2                     2  2          2           3
+--R           (16A b d e  + (- 28A b c - 16B b )d e + (24A c  + 4B b c)d )x
+--R         + 
+--R                 2 2                   2  3
+--R           - 6A b d e + (12A b c - 6B b )d
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R             2 2 5          3 4      2 4 3  3
+--R         (48b d e  - 96b c d e  + 48c d e )x
+--R       + 
+--R              2 3 4           4 3       2 5 2  2
+--R         (144b d e  - 288b c d e  + 144c d e )x
+--R       + 
+--R              2 4 3           5 2       2 6         2 5 2          6       2 7
+--R         (144b d e  - 288b c d e  + 144c d e)x + 48b d e  - 96b c d e + 48c d
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 346
+
+--S 347 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                  3 4          2        3    3  3
+--R             (3A b e  + (- 6A b c + 3B b )d e )x
+--R           + 
+--R                  3   3           2        3  2 2  2
+--R             (9A b d e  + (- 18A b c + 9B b )d e )x
+--R           + 
+--R                  3 2 2           2        3  3          3 3
+--R             (9A b d e  + (- 18A b c + 9B b )d e)x + 3A b d e
+--R           + 
+--R                    2        3  4
+--R             (- 6A b c + 3B b )d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                     2 3                   2    2        2            2
+--R                 6A b e  + (- 8A b c + 6B b )d e  + (8A c  - 28B b c)d e
+--R               + 
+--R                      2 3
+--R                 16B c d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                   2   2                     2  2          2           3
+--R             (16A b d e  + (- 28A b c - 16B b )d e + (24A c  + 4B b c)d )x
+--R           + 
+--R                   2 2                   2  3
+--R             - 6A b d e + (12A b c - 6B b )d
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R               2 2 5          3 4      2 4 3  3
+--R           (48b d e  - 96b c d e  + 48c d e )x
+--R         + 
+--R                2 3 4           4 3       2 5 2  2
+--R           (144b d e  - 288b c d e  + 144c d e )x
+--R         + 
+--R              2 4 3           5 2       2 6         2 5 2          6       2 7
+--R         (144b d e  - 288b c d e  + 144c d e)x + 48b d e  - 96b c d e + 48c d
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                    3 4        2        3    3  3
+--R             (- 3A b e  + (6A b c - 3B b )d e )x
+--R           + 
+--R                    3   3         2        3  2 2  2
+--R             (- 9A b d e  + (18A b c - 9B b )d e )x
+--R           + 
+--R                  3 2 2         2        3  3          3 3         2        3  4
+--R           (- 9A b d e  + (18A b c - 9B b )d e)x - 3A b d e + (6A b c - 3B b )d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                       2 3                   2    2        2            2
+--R                   3A b e  + (- 4A b c + 3B b )d e  + (4A c  - 14B b c)d e
+--R                 + 
+--R                       2 3
+--R                   8B c d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                  2   2                    2  2          2           3
+--R             (8A b d e  + (- 14A b c - 8B b )d e + (12A c  + 2B b c)d )x
+--R           + 
+--R                   2 2                  2  3
+--R             - 3A b d e + (6A b c - 3B b )d
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R               2 2 5          3 4      2 4 3  3
+--R           (24b d e  - 48b c d e  + 24c d e )x
+--R         + 
+--R               2 3 4           4 3      2 5 2  2
+--R           (72b d e  - 144b c d e  + 72c d e )x
+--R         + 
+--R               2 4 3           5 2      2 6         2 5 2          6       2 7
+--R           (72b d e  - 144b c d e  + 72c d e)x + 24b d e  - 48b c d e + 24c d
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 347
+
+--S 348 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R             3           2       3    +-----------+ +-+
+--R         (A b e + (- 2A b c + B b )d)\|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                      +--------------+
+--R             3           2       3    |             2
+--R         (A b e + (- 2A b c + B b )d)\|- b d e + c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                     +--------------+
+--R         2 2 2          3       2 4  |             2  +-----------+ +-+
+--R     (16b d e  - 32b c d e + 16c d )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 348
+
+--S 349 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 349
+
+--S 350 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                      +------------+
+--R             3           2       3    |           2
+--R         (A b e + (- 2A b c + B b )d)\|b d e - c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                3         2        3    +-----------+ +-+
+--R         (- 2A b e + (4A b c - 2B b )d)\|- b e + c d \|d
+--R      *
+--R               +------------+ +----------+
+--R               |           2  |   2
+--R              \|b d e - c d  \|c x  + b x
+--R         atan(----------------------------)
+--R                      (b e - c d)x
+--R  /
+--R                                                       +------------+
+--R         2 2 2          3       2 4  +-----------+ +-+ |           2
+--R     (16b d e  - 32b c d e + 16c d )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 350
+
+--S 351 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 351
+
+)clear all
+
+--S 352 of 1457
+t0:=(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^5
+--R 
+--R
+--R                                +----------+
+--R                                |   2
+--R                      (B x + A)\|c x  + b x
+--R   (1)  --------------------------------------------------
+--R         5 5       4 4      2 3 3      3 2 2     4       5
+--R        e x  + 5d e x  + 10d e x  + 10d e x  + 5d e x + d
+--R                                                    Type: Expression(Integer)
+--E 352
+
+--S 353 of 1457
+r0:=-1/128*b^2*(16*A*c^2*d^2-8*b*c*d*(B*d+2*A*e)+b^2*e*(3*B*d+5*A*e))*_
+     atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_
+     c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+1/24*(B*d*(2*c*d-3*b*e)+A*e*(2*c*d-_
+     b*e))*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)^3)+1/96*(B*d*_
+     (8*c^2*d^2-16*b*c*d*e+3*b^2*e^2)+A*e*(8*c^2*d^2-8*b*c*d*e+_
+     5*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+_
+     1/192*(A*e*(16*c^3*d^3-24*b*c^2*d^2*e+38*b^2*c*d*e^2-15*b^3*e^3)+_
+     B*d*(16*c^3*d^3-40*b*c^2*d^2*e+18*b^2*c*d*e^2-9*b^3*e^3))*_
+     sqrt(b*x+c*x^2)/(d^3*e^2*(c*d-b*e)^3*(d+e*x))-1/4*(B*d+A*e+_
+     2*B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x)^4)
+--R 
+--R
+--R   (2)
+--R                   4 6         3        4    5           2 2        3   2 4  4
+--R           (- 15A b e  + (48A b c - 9B b )d e  + (- 48A b c  + 24B b c)d e )x
+--R         + 
+--R                      4   5          3         4  2 4
+--R               - 60A b d e  + (192A b c - 36B b )d e
+--R             + 
+--R                        2 2        3   3 3
+--R               (- 192A b c  + 96B b c)d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      4 2 4          3         4  3 3
+--R               - 90A b d e  + (288A b c - 54B b )d e
+--R             + 
+--R                        2 2         3   4 2
+--R               (- 288A b c  + 144B b c)d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                        4 3 3          3         4  4 2
+--R                 - 60A b d e  + (192A b c - 36B b )d e
+--R               + 
+--R                          2 2        3   5
+--R                 (- 192A b c  + 96B b c)d e
+--R          *
+--R             x
+--R         + 
+--R                  4 4 2         3        4  5            2 2        3   6
+--R           - 15A b d e  + (48A b c - 9B b )d e + (- 48A b c  + 24B b c)d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                    3 5           2         3    4           2        2   2 3
+--R               30A b e  + (- 76A b c + 18B b )d e  + (48A b c  - 36B b c)d e
+--R             + 
+--R                       3          2  3 2        3 4
+--R               (- 32A c  + 80B b c )d e  - 32B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                     3   4            2         3  2 3
+--R               110A b d e  + (- 280A b c + 66B b )d e
+--R             + 
+--R                      2         2   3 2            3           2  4          3 5
+--R             (208A b c  - 184B b c)d e  + (- 128A c  + 336B b c )d e - 128B c d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                     3 2 3            2         3  3 2
+--R               146A b d e  + (- 396A b c - 66B b )d e
+--R             + 
+--R                        2         2   4             3          2  5
+--R               (352A b c  + 188B b c)d e + (- 192A c  - 32B b c )d
+--R          *
+--R             x
+--R         + 
+--R                  3 3 2         2         3  4              2        2   5
+--R           - 30A b d e  + (96A b c - 18B b )d e + (- 96A b c  + 48B b c)d
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R              3 3 7        2   4 6          2 5 5       3 6 4  4
+--R         (384b d e  - 1152b c d e  + 1152b c d e  - 384c d e )x
+--R       + 
+--R               3 4 6        2   5 5          2 6 4        3 7 3  3
+--R         (1536b d e  - 4608b c d e  + 4608b c d e  - 1536c d e )x
+--R       + 
+--R               3 5 5        2   6 4          2 7 3        3 8 2  2
+--R         (2304b d e  - 6912b c d e  + 6912b c d e  - 2304c d e )x
+--R       + 
+--R               3 6 4        2   7 3          2 8 2        3 9          3 7 3
+--R         (1536b d e  - 4608b c d e  + 4608b c d e  - 1536c d e)x + 384b d e
+--R       + 
+--R                2   8 2          2 9        3 10
+--R         - 1152b c d e  + 1152b c d e - 384c d
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 353
+
+--S 354 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                   4 6           3        4    5         2 2        3   2 4  4
+--R             (15A b e  + (- 48A b c + 9B b )d e  + (48A b c  - 24B b c)d e )x
+--R           + 
+--R                      4   5            3         4  2 4
+--R                 60A b d e  + (- 192A b c + 36B b )d e
+--R               + 
+--R                        2 2        3   3 3
+--R                 (192A b c  - 96B b c)d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      4 2 4            3         4  3 3
+--R                 90A b d e  + (- 288A b c + 54B b )d e
+--R               + 
+--R                        2 2         3   4 2
+--R                 (288A b c  - 144B b c)d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4 3 3            3         4  4 2
+--R                   60A b d e  + (- 192A b c + 36B b )d e
+--R                 + 
+--R                          2 2        3   5
+--R                   (192A b c  - 96B b c)d e
+--R            *
+--R               x
+--R           + 
+--R                  4 4 2           3        4  5          2 2        3   6
+--R             15A b d e  + (- 48A b c + 9B b )d e + (48A b c  - 24B b c)d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                      3 5           2         3    4           2        2   2 3
+--R                 30A b e  + (- 76A b c + 18B b )d e  + (48A b c  - 36B b c)d e
+--R               + 
+--R                         3          2  3 2        3 4
+--R                 (- 32A c  + 80B b c )d e  - 32B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                       3   4            2         3  2 3
+--R                 110A b d e  + (- 280A b c + 66B b )d e
+--R               + 
+--R                          2         2   3 2            3           2  4
+--R                 (208A b c  - 184B b c)d e  + (- 128A c  + 336B b c )d e
+--R               + 
+--R                         3 5
+--R                 - 128B c d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                       3 2 3            2         3  3 2
+--R                 146A b d e  + (- 396A b c - 66B b )d e
+--R               + 
+--R                          2         2   4             3          2  5
+--R                 (352A b c  + 188B b c)d e + (- 192A c  - 32B b c )d
+--R            *
+--R               x
+--R           + 
+--R                    3 3 2         2         3  4              2        2   5
+--R             - 30A b d e  + (96A b c - 18B b )d e + (- 96A b c  + 48B b c)d
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                3 3 7        2   4 6          2 5 5       3 6 4  4
+--R           (384b d e  - 1152b c d e  + 1152b c d e  - 384c d e )x
+--R         + 
+--R                 3 4 6        2   5 5          2 6 4        3 7 3  3
+--R           (1536b d e  - 4608b c d e  + 4608b c d e  - 1536c d e )x
+--R         + 
+--R                 3 5 5        2   6 4          2 7 3        3 8 2  2
+--R           (2304b d e  - 6912b c d e  + 6912b c d e  - 2304c d e )x
+--R         + 
+--R                 3 6 4        2   7 3          2 8 2        3 9          3 7 3
+--R           (1536b d e  - 4608b c d e  + 4608b c d e  - 1536c d e)x + 384b d e
+--R         + 
+--R                  2   8 2          2 9        3 10
+--R           - 1152b c d e  + 1152b c d e - 384c d
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                     4 6         3        4    5           2 2        3   2 4  4
+--R             (- 15A b e  + (48A b c - 9B b )d e  + (- 48A b c  + 24B b c)d e )x
+--R           + 
+--R                        4   5          3         4  2 4
+--R                 - 60A b d e  + (192A b c - 36B b )d e
+--R               + 
+--R                          2 2        3   3 3
+--R                 (- 192A b c  + 96B b c)d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        4 2 4          3         4  3 3
+--R                 - 90A b d e  + (288A b c - 54B b )d e
+--R               + 
+--R                          2 2         3   4 2
+--R                 (- 288A b c  + 144B b c)d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4 3 3          3         4  4 2
+--R                 - 60A b d e  + (192A b c - 36B b )d e
+--R               + 
+--R                          2 2        3   5
+--R                 (- 192A b c  + 96B b c)d e
+--R            *
+--R               x
+--R           + 
+--R                    4 4 2         3        4  5            2 2        3   6
+--R             - 15A b d e  + (48A b c - 9B b )d e + (- 48A b c  + 24B b c)d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                      3 5           2        3    4           2        2   2 3
+--R                 15A b e  + (- 38A b c + 9B b )d e  + (24A b c  - 18B b c)d e
+--R               + 
+--R                         3          2  3 2        3 4
+--R                 (- 16A c  + 40B b c )d e  - 16B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      3   4            2         3  2 3
+--R                 55A b d e  + (- 140A b c + 33B b )d e
+--R               + 
+--R                        2        2   3 2           3           2  4         3 5
+--R               (104A b c  - 92B b c)d e  + (- 64A c  + 168B b c )d e - 64B c d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      3 2 3            2         3  3 2
+--R                 73A b d e  + (- 198A b c - 33B b )d e
+--R               + 
+--R                          2        2   4            3          2  5
+--R                 (176A b c  + 94B b c)d e + (- 96A c  - 16B b c )d
+--R            *
+--R               x
+--R           + 
+--R                    3 3 2         2        3  4              2        2   5
+--R             - 15A b d e  + (48A b c - 9B b )d e + (- 48A b c  + 24B b c)d
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                3 3 7       2   4 6         2 5 5       3 6 4  4
+--R           (192b d e  - 576b c d e  + 576b c d e  - 192c d e )x
+--R         + 
+--R                3 4 6        2   5 5          2 6 4       3 7 3  3
+--R           (768b d e  - 2304b c d e  + 2304b c d e  - 768c d e )x
+--R         + 
+--R                 3 5 5        2   6 4          2 7 3        3 8 2  2
+--R           (1152b d e  - 3456b c d e  + 3456b c d e  - 1152c d e )x
+--R         + 
+--R                3 6 4        2   7 3          2 8 2       3 9          3 7 3
+--R           (768b d e  - 2304b c d e  + 2304b c d e  - 768c d e)x + 192b d e
+--R         + 
+--R                 2   8 2         2 9        3 10
+--R           - 576b c d e  + 576b c d e - 192c d
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 354
+
+--S 355 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R              4 2           3        4             2 2       3   2
+--R         (5A b e  + (- 16A b c + 3B b )d e + (16A b c  - 8B b c)d )
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R              4 2           3        4             2 2       3   2
+--R         (5A b e  + (- 16A b c + 3B b )d e + (16A b c  - 8B b c)d )
+--R      *
+--R          +--------------+
+--R          |             2              (b e - 2c d)x - b d
+--R         \|- b d e + c d  atanh(--------------------------------)
+--R                                                    +----------+
+--R                                  +-----------+ +-+ |   2
+--R                                2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                                        +--------------+
+--R            3 3 3       2   4 2         2 5        3 6  |             2
+--R       (128b d e  - 384b c d e  + 384b c d e - 128c d )\|- b d e + c d
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 355
+
+--S 356 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 356
+
+--S 357 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R              4 2           3        4             2 2       3   2
+--R         (5A b e  + (- 16A b c + 3B b )d e + (16A b c  - 8B b c)d )
+--R      *
+--R          +------------+
+--R          |           2              (b e - 2c d)x - b d
+--R         \|b d e - c d  atanh(--------------------------------)
+--R                                                  +----------+
+--R                                +-----------+ +-+ |   2
+--R                              2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                 4 2         3        4               2 2        3   2
+--R         (- 10A b e  + (32A b c - 6B b )d e + (- 32A b c  + 16B b c)d )
+--R      *
+--R                                 +------------+ +----------+
+--R                                 |           2  |   2
+--R          +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|d atan(----------------------------)
+--R                                        (b e - c d)x
+--R  /
+--R            3 3 3       2   4 2         2 5        3 6  +-----------+ +-+
+--R       (128b d e  - 384b c d e  + 384b c d e - 128c d )\|- b e + c d \|d
+--R    *
+--R        +------------+
+--R        |           2
+--R       \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 357
+
+--S 358 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 358
+
+)clear all
+
+--S 359 of 1457
+t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(3/2)
+--R 
+--R
+--R   (1)
+--R            2 5                2             4
+--R       B c e x  + ((A c + B b)e  + 2B c d e)x
+--R     + 
+--R             2                           2  3                           2  2
+--R       (A b e  + (2A c + 2B b)d e + B c d )x  + (2A b d e + (A c + B b)d )x
+--R     + 
+--R            2
+--R       A b d x
+--R  *
+--R      +----------+
+--R      |   2
+--R     \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 359
+
+--S 360 of 1457
+r0:=1/192*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_
+     2*A*e))*x*(b*x+c*x^2)^(3/2)/c^3+1/840*(98*A*c*e*(2*c*d-b*e)+B*(48*_
+     c^2*d^2-146*b*c*d*e+63*b^2*e^2))*(b*x+c*x^2)^(5/2)/c^3+1/7*B*_
+     (d+e*x)^2*(b*x+c*x^2)^(5/2)/c-1/84*e*((5*b*B-14*A*c)*d-(4*B*c*d-_
+     9*b*B*e+14*A*c*e)*x)*(b*x+c*x^2)^(5/2)/c^2+1/1024*b^4*(48*A*c^3*d^2-_
+     9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*_
+     atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)-1/1024*b^3*(48*A*c^3*d^2-_
+     9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*sqrt(b*x+_
+     c*x^2)/c^5+1/1536*b^2*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+_
+     A*e)-24*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^4+1/384*b*_
+     (48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+_
+     2*A*e))*x^2*sqrt(b*x+c*x^2)/c^3
+--R 
+--R
+--R   (2)
+--R                   6          7  2             5 2          6
+--R           (1470A b c - 945B b )e  + (- 5040A b c  + 2940B b c)d e
+--R         + 
+--R                   4 3          5 2  2
+--R           (5040A b c  - 2520B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                   6 2 6             6             5  2           6     5
+--R           15360B c e x  + ((17920A c  + 19200B b c )e  + 35840B c d e)x
+--R         + 
+--R                          5         2 4  2            6             5
+--R               (23296A b c  + 384B b c )e  + (43008A c  + 46592B b c )d e
+--R             + 
+--R                       6 2
+--R               21504B c d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                      2 4         3 3  2              5          2 4
+--R               (672A b c  - 432B b c )e  + (59136A b c  + 1344B b c )d e
+--R             + 
+--R                        6             5  2
+--R               (26880A c  + 29568B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                        3 3         4 2  2           2 4          3 3
+--R               (- 784A b c  + 504B b c )e  + (2688A b c  - 1568B b c )d e
+--R             + 
+--R                          5          2 4  2
+--R               (40320A b c  + 1344B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      4 2         5   2             3 3          4 2
+--R               (980A b c  - 630B b c)e  + (- 3360A b c  + 1960B b c )d e
+--R             + 
+--R                       2 4          3 3  2
+--R               (3360A b c  - 1680B b c )d
+--R          *
+--R             x
+--R         + 
+--R                     5          6  2           4 2          5
+--R           (- 1470A b c + 945B b )e  + (5040A b c  - 2940B b c)d e
+--R         + 
+--R                     3 3          4 2  2
+--R           (- 5040A b c  + 2520B b c )d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R            5 +-+
+--R     107520c \|c
+--R                                                    Type: Expression(Integer)
+--E 360
+
+--S 361 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                     6          7  2             5 2          6
+--R             (1470A b c - 945B b )e  + (- 5040A b c  + 2940B b c)d e
+--R           + 
+--R                     4 3          5 2  2
+--R             (5040A b c  - 2520B b c )d
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                     6 2 6             6             5  2           6     5
+--R             30720B c e x  + ((35840A c  + 38400B b c )e  + 71680B c d e)x
+--R           + 
+--R                            5         2 4  2            6             5
+--R                 (46592A b c  + 768B b c )e  + (86016A c  + 93184B b c )d e
+--R               + 
+--R                         6 2
+--R                 43008B c d
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                         2 4         3 3  2               5          2 4
+--R                 (1344A b c  - 864B b c )e  + (118272A b c  + 2688B b c )d e
+--R               + 
+--R                          6             5  2
+--R                 (53760A c  + 59136B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                           3 3          4 2  2           2 4          3 3
+--R                 (- 1568A b c  + 1008B b c )e  + (5376A b c  - 3136B b c )d e
+--R               + 
+--R                            5          2 4  2
+--R                 (80640A b c  + 2688B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         4 2          5   2             3 3          4 2
+--R                 (1960A b c  - 1260B b c)e  + (- 6720A b c  + 3920B b c )d e
+--R               + 
+--R                         2 4          3 3  2
+--R                 (6720A b c  - 3360B b c )d
+--R            *
+--R               x
+--R           + 
+--R                       5           6  2            4 2          5
+--R             (- 2940A b c + 1890B b )e  + (10080A b c  - 5880B b c)d e
+--R           + 
+--R                        3 3          4 2  2
+--R             (- 10080A b c  + 5040B b c )d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R              5 +-+
+--R       215040c \|c
+--R     ,
+--R
+--R                     6          7  2             5 2          6
+--R             (1470A b c - 945B b )e  + (- 5040A b c  + 2940B b c)d e
+--R           + 
+--R                     4 3          5 2  2
+--R             (5040A b c  - 2520B b c )d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                     6 2 6             6             5  2           6     5
+--R             15360B c e x  + ((17920A c  + 19200B b c )e  + 35840B c d e)x
+--R           + 
+--R                            5         2 4  2            6             5
+--R                 (23296A b c  + 384B b c )e  + (43008A c  + 46592B b c )d e
+--R               + 
+--R                         6 2
+--R                 21504B c d
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                        2 4         3 3  2              5          2 4
+--R                 (672A b c  - 432B b c )e  + (59136A b c  + 1344B b c )d e
+--R               + 
+--R                          6             5  2
+--R                 (26880A c  + 29568B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                          3 3         4 2  2           2 4          3 3
+--R                 (- 784A b c  + 504B b c )e  + (2688A b c  - 1568B b c )d e
+--R               + 
+--R                            5          2 4  2
+--R                 (40320A b c  + 1344B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4 2         5   2             3 3          4 2
+--R                 (980A b c  - 630B b c)e  + (- 3360A b c  + 1960B b c )d e
+--R               + 
+--R                         2 4          3 3  2
+--R                 (3360A b c  - 1680B b c )d
+--R            *
+--R               x
+--R           + 
+--R                       5          6  2           4 2          5
+--R             (- 1470A b c + 945B b )e  + (5040A b c  - 2940B b c)d e
+--R           + 
+--R                       3 3          4 2  2
+--R             (- 5040A b c  + 2520B b c )d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R              5 +---+
+--R       107520c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 361
+
+--S 362 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                 6        7  2           5 2        6
+--R           (14A b c - 9B b )e  + (- 48A b c  + 28B b c)d e
+--R         + 
+--R                 4 3        5 2  2
+--R           (48A b c  - 24B b c )d
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   6         7  2         5 2        6
+--R           (- 28A b c + 18B b )e  + (96A b c  - 56B b c)d e
+--R         + 
+--R                   4 3        5 2  2
+--R           (- 96A b c  + 48B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R  /
+--R          5 +-+
+--R     2048c \|c
+--R                                                    Type: Expression(Integer)
+--E 362
+
+--S 363 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 363
+
+--S 364 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                   6        7  2         5 2        6
+--R           (- 14A b c + 9B b )e  + (48A b c  - 28B b c)d e
+--R         + 
+--R                   4 3        5 2  2
+--R           (- 48A b c  + 24B b c )d
+--R      *
+--R                           +-+
+--R          +---+          x\|c
+--R         \|- c atanh(-------------)
+--R                      +----------+
+--R                      |   2
+--R                     \|c x  + b x
+--R     + 
+--R                 6        7  2           5 2        6
+--R           (14A b c - 9B b )e  + (- 48A b c  + 28B b c)d e
+--R         + 
+--R                 4 3        5 2  2
+--R           (48A b c  - 24B b c )d
+--R      *
+--R                         +----------+
+--R                   +---+ |   2
+--R          +-+     \|- c \|c x  + b x
+--R         \|c atan(-------------------)
+--R                          c x
+--R  /
+--R          5 +---+ +-+
+--R     1024c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 364
+
+--S 365 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 1457
+t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(3/2)
+--R 
+--R
+--R   (1)
+--R             4                          3                          2
+--R     (B c e x  + ((A c + B b)e + B c d)x  + (A b e + (A c + B b)d)x  + A b d x)
+--R  *
+--R      +----------+
+--R      |   2
+--R     \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 366
+
+--S 367 of 1457
+r0:=1/96*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*(b*x+c*x^2)^(3/2)/c^2+_
+     1/60*(2*B*c*d-7*b*B*e+12*A*c*e)*(b*x+c*x^2)^(5/2)/c^2+1/6*B*(d+e*x)*_
+     (b*x+c*x^2)^(5/2)/c+1/512*b^4*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+_
+     A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/512*b^3*_
+     (24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^4+_
+     1/768*b^2*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x*sqrt(b*x+_
+     c*x^2)/c^3+1/192*b*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*x^2*_
+     sqrt(b*x+c*x^2)/c^2
+--R 
+--R
+--R   (2)
+--R                                                                      +-+
+--R                 5          6            4 2         5              x\|c
+--R       ((- 180A b c + 105B b )e + (360A b c  - 180B b c)d)atanh(-------------)
+--R                                                                 +----------+
+--R                                                                 |   2
+--R                                                                \|c x  + b x
+--R     + 
+--R                  5   5            5            4            5   4
+--R           1280B c e x  + ((1536A c  + 1664B b c )e + 1536B c d)x
+--R         + 
+--R                      4        2 3             5            4    3
+--R           ((2112A b c  + 48B b c )e + (1920A c  + 2112B b c )d)x
+--R         + 
+--R                  2 3        3 2               4        2 3    2
+--R           ((96A b c  - 56B b c )e + (2880A b c  + 96B b c )d)x
+--R         + 
+--R                     3 2        4             2 3         3 2
+--R           ((- 120A b c  + 70B b c)e + (240A b c  - 120B b c )d)x
+--R         + 
+--R                  4          5              3 2         4
+--R           (180A b c - 105B b )e + (- 360A b c  + 180B b c)d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R          4 +-+
+--R     7680c \|c
+--R                                                    Type: Expression(Integer)
+--E 367
+
+--S 368 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                   5          6              4 2         5
+--R           ((180A b c - 105B b )e + (- 360A b c  + 180B b c)d)
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                    5   5            5            4            5   4
+--R             2560B c e x  + ((3072A c  + 3328B b c )e + 3072B c d)x
+--R           + 
+--R                        4        2 3             5            4    3
+--R             ((4224A b c  + 96B b c )e + (3840A c  + 4224B b c )d)x
+--R           + 
+--R                     2 3         3 2               4         2 3    2
+--R             ((192A b c  - 112B b c )e + (5760A b c  + 192B b c )d)x
+--R           + 
+--R                       3 2         4             2 3         3 2
+--R             ((- 240A b c  + 140B b c)e + (480A b c  - 240B b c )d)x
+--R           + 
+--R                    4          5              3 2         4
+--R             (360A b c - 210B b )e + (- 720A b c  + 360B b c)d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R             4 +-+
+--R       15360c \|c
+--R     ,
+--R
+--R                     5          6            4 2         5
+--R           ((- 180A b c + 105B b )e + (360A b c  - 180B b c)d)
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                    5   5            5            4            5   4
+--R             1280B c e x  + ((1536A c  + 1664B b c )e + 1536B c d)x
+--R           + 
+--R                        4        2 3             5            4    3
+--R             ((2112A b c  + 48B b c )e + (1920A c  + 2112B b c )d)x
+--R           + 
+--R                    2 3        3 2               4        2 3    2
+--R             ((96A b c  - 56B b c )e + (2880A b c  + 96B b c )d)x
+--R           + 
+--R                       3 2        4             2 3         3 2
+--R             ((- 120A b c  + 70B b c)e + (240A b c  - 120B b c )d)x
+--R           + 
+--R                    4          5              3 2         4
+--R             (180A b c - 105B b )e + (- 360A b c  + 180B b c)d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R            4 +---+
+--R       7680c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 368
+
+--S 369 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                5        6             4 2        5
+--R         ((12A b c - 7B b )e + (- 24A b c  + 12B b c)d)
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                                                  +-+
+--R              5         6             4 2        5              x\|c
+--R       ((24A b c - 14B b )e + (- 48A b c  + 24B b c)d)atanh(-------------)
+--R                                                             +----------+
+--R                                                             |   2
+--R                                                            \|c x  + b x
+--R  /
+--R          4 +-+
+--R     1024c \|c
+--R                                                    Type: Expression(Integer)
+--E 369
+
+--S 370 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 370
+
+--S 371 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                                       +-+
+--R              5        6             4 2        5     +---+          x\|c
+--R       ((12A b c - 7B b )e + (- 24A b c  + 12B b c)d)\|- c atanh(-------------)
+--R                                                                  +----------+
+--R                                                                  |   2
+--R                                                                 \|c x  + b x
+--R     + 
+--R                                                                   +----------+
+--R                                                             +---+ |   2
+--R              5        6           4 2        5     +-+     \|- c \|c x  + b x
+--R     ((- 12A b c + 7B b )e + (24A b c  - 12B b c)d)\|c atan(-------------------)
+--R                                                                    c x
+--R  /
+--R         4 +---+ +-+
+--R     512c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 371
+
+--S 372 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 372
+
+)clear all
+
+--S 373 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(3/2)
+--R 
+--R
+--R                                         +----------+
+--R              3               2          |   2
+--R   (1)  (B c x  + (A c + B b)x  + A b x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 373
+
+--S 374 of 1457
+r0:=-1/8*(b*B-2*A*c)*x*(b*x+c*x^2)^(3/2)/c+1/5*B*(b*x+c*x^2)^(5/2)/c-_
+     3/128*b^4*(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+_
+     3/128*b^3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/c^3-1/64*b^2*(b*B-2*A*c)*x*_
+     sqrt(b*x+c*x^2)/c^2-1/16*b*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c
+--R 
+--R
+--R   (2)
+--R                                     +-+
+--R             4         5           x\|c
+--R       (30A b c - 15B b )atanh(-------------)
+--R                                +----------+
+--R                                |   2
+--R                               \|c x  + b x
+--R     + 
+--R                 4 4          4           3  3            3       2 2  2
+--R           128B c x  + (160A c  + 176B b c )x  + (240A b c  + 8B b c )x
+--R         + 
+--R                 2 2        3           3         4
+--R           (20A b c  - 10B b c)x - 30A b c + 15B b
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R         3 +-+
+--R     640c \|c
+--R                                                    Type: Expression(Integer)
+--E 374
+
+--S 375 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                                  +----------+
+--R               4         5        |   2                     +-+
+--R         (30A b c - 15B b )log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                   4 4          4           3  3            3        2 2  2
+--R             256B c x  + (320A c  + 352B b c )x  + (480A b c  + 16B b c )x
+--R           + 
+--R                   2 2        3           3         4
+--R             (40A b c  - 20B b c)x - 60A b c + 30B b
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R            3 +-+
+--R       1280c \|c
+--R     ,
+--R
+--R                                       +----------+
+--R                                 +---+ |   2
+--R               4         5      \|- c \|c x  + b x
+--R         (30A b c - 15B b )atan(-------------------)
+--R                                        c x
+--R       + 
+--R                   4 4          4           3  3            3       2 2  2
+--R             128B c x  + (160A c  + 176B b c )x  + (240A b c  + 8B b c )x
+--R           + 
+--R                   2 2        3           3         4
+--R             (20A b c  - 10B b c)x - 30A b c + 15B b
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R           3 +---+
+--R       640c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 375
+
+--S 376 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                              +----------+
+--R            4        5        |   2                     +-+
+--R       (6A b c - 3B b )log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                      +-+
+--R               4        5           x\|c
+--R       (- 12A b c + 6B b )atanh(-------------)
+--R                                 +----------+
+--R                                 |   2
+--R                                \|c x  + b x
+--R  /
+--R         3 +-+
+--R     256c \|c
+--R                                                    Type: Expression(Integer)
+--E 376
+
+--S 377 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 377
+
+--S 378 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                           +-+
+--R              4        5  +---+          x\|c
+--R       (- 6A b c + 3B b )\|- c atanh(-------------)
+--R                                      +----------+
+--R                                      |   2
+--R                                     \|c x  + b x
+--R     + 
+--R                                       +----------+
+--R                                 +---+ |   2
+--R            4        5  +-+     \|- c \|c x  + b x
+--R       (6A b c - 3B b )\|c atan(-------------------)
+--R                                        c x
+--R  /
+--R         3 +---+ +-+
+--R     128c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 378
+
+--S 379 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 379
+
+)clear all
+
+--S 380 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)
+--R 
+--R
+--R                                         +----------+
+--R              3               2          |   2
+--R        (B c x  + (A c + B b)x  + A b x)\|c x  + b x
+--R   (1)  ---------------------------------------------
+--R                           e x + d
+--R                                                    Type: Expression(Integer)
+--E 380
+
+--S 381 of 1457
+r0:=-1/24*(8*B*c*d-3*b*B*e-8*A*c*e-6*B*c*e*x)*(b*x+c*x^2)^(3/2)/(c*e^2)-_
+     1/64*(8*A*c*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3)-_
+     B*(128*c^4*d^4-192*b*c^3*d^3*e+48*b^2*c^2*d^2*e^2+8*b^3*c*d*e^3+_
+     3*b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^5)-d^(3/2)*_
+     (B*d-A*e)*(c*d-b*e)^(3/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_
+     sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^5+1/64*(8*A*c*e*(8*c^2*d^2-_
+     10*b*c*d*e+b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+8*b^2*c*d*e^2+_
+     3*b^3*e^3)-2*c*e*(8*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-8*b*c*d*e-_
+     3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^4)
+--R 
+--R
+--R   (2)
+--R                   3        4  4            2 2        3     3
+--R           (- 24A b c + 9B b )e  + (- 144A b c  + 24B b c)d e
+--R         + 
+--R                    3         2 2  2 2            4           3  3          4 4
+--R           (576A b c  + 144B b c )d e  + (- 384A c  - 576B b c )d e + 384B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                  2   2            3           2  2          3 3  +-----------+
+--R         (192A b c d e  + (- 192A c  - 192B b c )d e + 192B c d )\|- b e + c d
+--R      *
+--R          +-+ +-+             (b e - 2c d)x - b d
+--R         \|c \|d atanh(--------------------------------)
+--R                                           +----------+
+--R                         +-----------+ +-+ |   2
+--R                       2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                3 4 3          3          2  4        3   3  2
+--R           48B c e x  + ((64A c  + 72B b c )e  - 64B c d e )x
+--R         + 
+--R                     2       2   4           3           2    3        3 2 2
+--R           ((112A b c  + 6B b c)e  + (- 96A c  - 112B b c )d e  + 96B c d e )x
+--R         + 
+--R                 2        3  4              2        2     3
+--R           (24A b c - 9B b )e  + (- 240A b c  - 24B b c)d e
+--R         + 
+--R                  3           2  2 2         3 3
+--R           (192A c  + 240B b c )d e  - 192B c d e
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R         2 5 +-+
+--R     192c e \|c
+--R                                                    Type: Expression(Integer)
+--E 381
+
+--S 382 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                      2   2          3           2  2          3 3
+--R           (- 384A b c d e  + (384A c  + 384B b c )d e - 384B c d )
+--R        *
+--R            +--------------+
+--R            |             2  +-+
+--R           \|- b d e + c d  \|c
+--R        *
+--R                 +--------------+ +----------+
+--R                 |             2  |   2
+--R               2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(-------------------------------------------------------)
+--R                                       e x + d
+--R       + 
+--R                   3        4  4          2 2        3     3
+--R             (24A b c - 9B b )e  + (144A b c  - 24B b c)d e
+--R           + 
+--R                      3         2 2  2 2          4           3  3          4 4
+--R           (- 576A b c  - 144B b c )d e  + (384A c  + 576B b c )d e - 384B c d
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                  3 4 3           3           2  4         3   3  2
+--R             96B c e x  + ((128A c  + 144B b c )e  - 128B c d e )x
+--R           + 
+--R                          2        2   4            3           2    3
+--R                 (224A b c  + 12B b c)e  + (- 192A c  - 224B b c )d e
+--R               + 
+--R                       3 2 2
+--R                 192B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2         3  4              2        2     3
+--R             (48A b c - 18B b )e  + (- 480A b c  - 48B b c)d e
+--R           + 
+--R                    3           2  2 2         3 3
+--R             (384A c  + 480B b c )d e  - 384B c d e
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R           2 5 +-+
+--R       384c e \|c
+--R     ,
+--R
+--R                   3        4  4          2 2        3     3
+--R             (24A b c - 9B b )e  + (144A b c  - 24B b c)d e
+--R           + 
+--R                      3         2 2  2 2          4           3  3          4 4
+--R           (- 576A b c  - 144B b c )d e  + (384A c  + 576B b c )d e - 384B c d
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                      2   2          3           2  2          3 3  +-+
+--R           (- 768A b c d e  + (768A c  + 768B b c )d e - 768B c d )\|c
+--R        *
+--R                                  +----------+
+--R            +------------+        |   2
+--R            |           2       d\|c x  + b x
+--R           \|b d e - c d  atan(----------------)
+--R                                 +------------+
+--R                                 |           2
+--R                               x\|b d e - c d
+--R       + 
+--R                  3 4 3           3           2  4         3   3  2
+--R             96B c e x  + ((128A c  + 144B b c )e  - 128B c d e )x
+--R           + 
+--R                          2        2   4            3           2    3
+--R                 (224A b c  + 12B b c)e  + (- 192A c  - 224B b c )d e
+--R               + 
+--R                       3 2 2
+--R                 192B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2         3  4              2        2     3
+--R             (48A b c - 18B b )e  + (- 480A b c  - 48B b c)d e
+--R           + 
+--R                    3           2  2 2         3 3
+--R             (384A c  + 480B b c )d e  - 384B c d e
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R           2 5 +-+
+--R       384c e \|c
+--R     ,
+--R
+--R                      2   2          3           2  2          3 3
+--R           (- 192A b c d e  + (192A c  + 192B b c )d e - 192B c d )
+--R        *
+--R            +--------------+
+--R            |             2  +---+
+--R           \|- b d e + c d  \|- c
+--R        *
+--R                 +--------------+ +----------+
+--R                 |             2  |   2
+--R               2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(-------------------------------------------------------)
+--R                                       e x + d
+--R       + 
+--R                     3        4  4            2 2        3     3
+--R             (- 24A b c + 9B b )e  + (- 144A b c  + 24B b c)d e
+--R           + 
+--R                    3         2 2  2 2            4           3  3          4 4
+--R           (576A b c  + 144B b c )d e  + (- 384A c  - 576B b c )d e + 384B c d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                  3 4 3          3          2  4        3   3  2
+--R             48B c e x  + ((64A c  + 72B b c )e  - 64B c d e )x
+--R           + 
+--R                       2       2   4           3           2    3        3 2 2
+--R             ((112A b c  + 6B b c)e  + (- 96A c  - 112B b c )d e  + 96B c d e )x
+--R           + 
+--R                   2        3  4              2        2     3
+--R             (24A b c - 9B b )e  + (- 240A b c  - 24B b c)d e
+--R           + 
+--R                    3           2  2 2         3 3
+--R             (192A c  + 240B b c )d e  - 192B c d e
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R           2 5 +---+
+--R       192c e \|- c
+--R     ,
+--R
+--R                     3        4  4            2 2        3     3
+--R             (- 24A b c + 9B b )e  + (- 144A b c  + 24B b c)d e
+--R           + 
+--R                    3         2 2  2 2            4           3  3          4 4
+--R           (576A b c  + 144B b c )d e  + (- 384A c  - 576B b c )d e + 384B c d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                      2   2          3           2  2          3 3  +---+
+--R           (- 384A b c d e  + (384A c  + 384B b c )d e - 384B c d )\|- c
+--R        *
+--R                                  +----------+
+--R            +------------+        |   2
+--R            |           2       d\|c x  + b x
+--R           \|b d e - c d  atan(----------------)
+--R                                 +------------+
+--R                                 |           2
+--R                               x\|b d e - c d
+--R       + 
+--R                  3 4 3          3          2  4        3   3  2
+--R             48B c e x  + ((64A c  + 72B b c )e  - 64B c d e )x
+--R           + 
+--R                       2       2   4           3           2    3        3 2 2
+--R             ((112A b c  + 6B b c)e  + (- 96A c  - 112B b c )d e  + 96B c d e )x
+--R           + 
+--R                   2        3  4              2        2     3
+--R             (24A b c - 9B b )e  + (- 240A b c  - 24B b c)d e
+--R           + 
+--R                    3           2  2 2         3 3
+--R             (192A c  + 240B b c )d e  - 192B c d e
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R           2 5 +---+
+--R       192c e \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 382
+
+--S 383 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                    2   2          3           2  2          3 3
+--R         (- 128A b c d e  + (128A c  + 128B b c )d e - 128B c d )
+--R      *
+--R          +--------------+
+--R          |             2  +-+
+--R         \|- b d e + c d  \|c
+--R      *
+--R               +--------------+ +----------+
+--R               |             2  |   2
+--R             2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R         log(-------------------------------------------------------)
+--R                                     e x + d
+--R     + 
+--R                3        4  4         2 2       3     3
+--R           (8A b c - 3B b )e  + (48A b c  - 8B b c)d e
+--R         + 
+--R                      3        2 2  2 2          4           3  3          4 4
+--R           (- 192A b c  - 48B b c )d e  + (128A c  + 192B b c )d e - 128B c d
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                 3        4  4         2 2        3     3
+--R           (16A b c - 6B b )e  + (96A b c  - 16B b c)d e
+--R         + 
+--R                      3        2 2  2 2          4           3  3          4 4
+--R           (- 384A b c  - 96B b c )d e  + (256A c  + 384B b c )d e - 256B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                    2   2          3           2  2          3 3  +-----------+
+--R         (- 128A b c d e  + (128A c  + 128B b c )d e - 128B c d )\|- b e + c d
+--R      *
+--R          +-+ +-+             (b e - 2c d)x - b d
+--R         \|c \|d atanh(--------------------------------)
+--R                                           +----------+
+--R                         +-----------+ +-+ |   2
+--R                       2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R         2 5 +-+
+--R     128c e \|c
+--R                                                    Type: Expression(Integer)
+--E 383
+
+--S 384 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 384
+
+--S 385 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                3        4  4         2 2       3     3
+--R           (8A b c - 3B b )e  + (48A b c  - 8B b c)d e
+--R         + 
+--R                      3        2 2  2 2          4           3  3          4 4
+--R           (- 192A b c  - 48B b c )d e  + (128A c  + 192B b c )d e - 128B c d
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                 3        4  4         2 2        3     3
+--R           (16A b c - 6B b )e  + (96A b c  - 16B b c)d e
+--R         + 
+--R                      3        2 2  2 2          4           3  3          4 4
+--R           (- 384A b c  - 96B b c )d e  + (256A c  + 384B b c )d e - 256B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                    2   2          3           2  2          3 3  +-----------+
+--R         (- 128A b c d e  + (128A c  + 128B b c )d e - 128B c d )\|- b e + c d
+--R      *
+--R          +-+ +-+             (b e - 2c d)x - b d
+--R         \|c \|d atanh(--------------------------------)
+--R                                           +----------+
+--R                         +-----------+ +-+ |   2
+--R                       2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                    2   2          3           2  2          3 3  +-+
+--R         (- 256A b c d e  + (256A c  + 256B b c )d e - 256B c d )\|c
+--R      *
+--R                                +----------+
+--R          +------------+        |   2
+--R          |           2       d\|c x  + b x
+--R         \|b d e - c d  atan(----------------)
+--R                               +------------+
+--R                               |           2
+--R                             x\|b d e - c d
+--R  /
+--R         2 5 +-+
+--R     128c e \|c
+--R                                                    Type: Expression(Integer)
+--E 385
+
+--S 386 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 386
+
+)clear all
+
+--S 387 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^2
+--R 
+--R
+--R                                         +----------+
+--R              3               2          |   2
+--R        (B c x  + (A c + B b)x  + A b x)\|c x  + b x
+--R   (1)  ---------------------------------------------
+--R                       2 2             2
+--R                      e x  + 2d e x + d
+--R                                                    Type: Expression(Integer)
+--E 387
+
+--S 388 of 1457
+r0:=1/3*(4*B*d-3*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x))+1/8*(4*b*c*e*_
+     (4*B*d-3*A*e)*(2*c*d-b*e)-(8*B*c*d-b*B*e-6*A*c*e)*(8*c^2*d^2-_
+     4*b*c*d*e-b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^5)+_
+     1/2*(B*d*(8*c*d-5*b*e)-3*A*e*(2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_
+     b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-_
+     b*e)/e^5-1/8*(6*A*c*e*(4*c*d-3*b*e)-B*(32*c^2*d^2-28*b*c*d*e+_
+     b^2*e^2)+2*c*e*(8*B*c*d-b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(c*e^4)
+--R 
+--R
+--R   (2)
+--R                     2        3  4              2        2     3
+--R               (18A b c - 3B b )e  + (- 144A b c  - 36B b c)d e
+--R             + 
+--R                      3           2  2 2         3 3
+--R               (144A c  + 216B b c )d e  - 192B c d e
+--R          *
+--R             x
+--R         + 
+--R                 2        3    3              2        2   2 2
+--R           (18A b c - 3B b )d e  + (- 144A b c  - 36B b c)d e
+--R         + 
+--R                  3           2  3          3 4
+--R           (144A c  + 216B b c )d e - 192B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                       3         2              2        2 2                 2
+--R           (- 36A b c e  + (72A c  + 60B b c)d e  - 96B c d e)x - 36A b c d e
+--R         + 
+--R                 2            2         2 3
+--R           (72A c  + 60B b c)d e - 96B c d
+--R      *
+--R          +-----------+ +-+ +-+             (b e - 2c d)x - b d
+--R         \|- b e + c d \|c \|d atanh(--------------------------------)
+--R                                                         +----------+
+--R                                       +-----------+ +-+ |   2
+--R                                     2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R               2 4 3          2            4        2   3  2
+--R           8B c e x  + ((12A c  + 14B b c)e  - 16B c d e )x
+--R         + 
+--R                           2  4           2              3        2 2 2
+--R           ((30A b c + 3B b )e  + (- 36A c  - 46B b c)d e  + 48B c d e )x
+--R         + 
+--R                          2    3           2            2 2        2 3
+--R           (54A b c + 3B b )d e  + (- 72A c  - 84B b c)d e  + 96B c d e
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R           6           5  +-+
+--R     (24c e x + 24c d e )\|c
+--R                                                    Type: Expression(Integer)
+--E 388
+
+--S 389 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                       3            2               2         2 2
+--R             (72A b c e  + (- 144A c  - 120B b c)d e  + 192B c d e)x
+--R           + 
+--R                        2            2             2          2 3
+--R             72A b c d e  + (- 144A c  - 120B b c)d e + 192B c d
+--R        *
+--R            +--------------+
+--R            |             2  +-+
+--R           \|- b d e + c d  \|c
+--R        *
+--R                 +--------------+ +----------+
+--R                 |             2  |   2
+--R               2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(-------------------------------------------------------)
+--R                                       e x + d
+--R       + 
+--R                       2        3  4              2        2     3
+--R                 (18A b c - 3B b )e  + (- 144A b c  - 36B b c)d e
+--R               + 
+--R                        3           2  2 2         3 3
+--R                 (144A c  + 216B b c )d e  - 192B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2        3    3              2        2   2 2
+--R             (18A b c - 3B b )d e  + (- 144A b c  - 36B b c)d e
+--R           + 
+--R                    3           2  3          3 4
+--R             (144A c  + 216B b c )d e - 192B c d
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                  2 4 3          2            4        2   3  2
+--R             16B c e x  + ((24A c  + 28B b c)e  - 32B c d e )x
+--R           + 
+--R                             2  4           2              3        2 2 2
+--R             ((60A b c + 6B b )e  + (- 72A c  - 92B b c)d e  + 96B c d e )x
+--R           + 
+--R                             2    3            2             2 2         2 3
+--R             (108A b c + 6B b )d e  + (- 144A c  - 168B b c)d e  + 192B c d e
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R             6           5  +-+
+--R       (48c e x + 48c d e )\|c
+--R     ,
+--R
+--R                       2        3  4              2        2     3
+--R                 (18A b c - 3B b )e  + (- 144A b c  - 36B b c)d e
+--R               + 
+--R                        3           2  2 2         3 3
+--R                 (144A c  + 216B b c )d e  - 192B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2        3    3              2        2   2 2
+--R             (18A b c - 3B b )d e  + (- 144A b c  - 36B b c)d e
+--R           + 
+--R                    3           2  3          3 4
+--R             (144A c  + 216B b c )d e - 192B c d
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                        3            2               2         2 2
+--R             (144A b c e  + (- 288A c  - 240B b c)d e  + 384B c d e)x
+--R           + 
+--R                         2            2             2          2 3
+--R             144A b c d e  + (- 288A c  - 240B b c)d e + 384B c d
+--R        *
+--R                                      +----------+
+--R                +------------+        |   2
+--R            +-+ |           2       d\|c x  + b x
+--R           \|c \|b d e - c d  atan(----------------)
+--R                                     +------------+
+--R                                     |           2
+--R                                   x\|b d e - c d
+--R       + 
+--R                  2 4 3          2            4        2   3  2
+--R             16B c e x  + ((24A c  + 28B b c)e  - 32B c d e )x
+--R           + 
+--R                             2  4           2              3        2 2 2
+--R             ((60A b c + 6B b )e  + (- 72A c  - 92B b c)d e  + 96B c d e )x
+--R           + 
+--R                             2    3            2             2 2         2 3
+--R             (108A b c + 6B b )d e  + (- 144A c  - 168B b c)d e  + 192B c d e
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R             6           5  +-+
+--R       (48c e x + 48c d e )\|c
+--R     ,
+--R
+--R                       3           2              2        2 2                 2
+--R             (36A b c e  + (- 72A c  - 60B b c)d e  + 96B c d e)x + 36A b c d e
+--R           + 
+--R                     2            2         2 3
+--R             (- 72A c  - 60B b c)d e + 96B c d
+--R        *
+--R            +--------------+
+--R            |             2  +---+
+--R           \|- b d e + c d  \|- c
+--R        *
+--R                 +--------------+ +----------+
+--R                 |             2  |   2
+--R               2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(-------------------------------------------------------)
+--R                                       e x + d
+--R       + 
+--R                       2        3  4              2        2     3
+--R                 (18A b c - 3B b )e  + (- 144A b c  - 36B b c)d e
+--R               + 
+--R                        3           2  2 2         3 3
+--R                 (144A c  + 216B b c )d e  - 192B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2        3    3              2        2   2 2
+--R             (18A b c - 3B b )d e  + (- 144A b c  - 36B b c)d e
+--R           + 
+--R                    3           2  3          3 4
+--R             (144A c  + 216B b c )d e - 192B c d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                 2 4 3          2            4        2   3  2
+--R             8B c e x  + ((12A c  + 14B b c)e  - 16B c d e )x
+--R           + 
+--R                             2  4           2              3        2 2 2
+--R             ((30A b c + 3B b )e  + (- 36A c  - 46B b c)d e  + 48B c d e )x
+--R           + 
+--R                            2    3           2            2 2        2 3
+--R             (54A b c + 3B b )d e  + (- 72A c  - 84B b c)d e  + 96B c d e
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R             6           5  +---+
+--R       (24c e x + 24c d e )\|- c
+--R     ,
+--R
+--R                       2        3  4              2        2     3
+--R                 (18A b c - 3B b )e  + (- 144A b c  - 36B b c)d e
+--R               + 
+--R                        3           2  2 2         3 3
+--R                 (144A c  + 216B b c )d e  - 192B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2        3    3              2        2   2 2
+--R             (18A b c - 3B b )d e  + (- 144A b c  - 36B b c)d e
+--R           + 
+--R                    3           2  3          3 4
+--R             (144A c  + 216B b c )d e - 192B c d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                       3            2               2         2 2
+--R             (72A b c e  + (- 144A c  - 120B b c)d e  + 192B c d e)x
+--R           + 
+--R                        2            2             2          2 3
+--R             72A b c d e  + (- 144A c  - 120B b c)d e + 192B c d
+--R        *
+--R                                        +----------+
+--R                  +------------+        |   2
+--R            +---+ |           2       d\|c x  + b x
+--R           \|- c \|b d e - c d  atan(----------------)
+--R                                       +------------+
+--R                                       |           2
+--R                                     x\|b d e - c d
+--R       + 
+--R                 2 4 3          2            4        2   3  2
+--R             8B c e x  + ((12A c  + 14B b c)e  - 16B c d e )x
+--R           + 
+--R                             2  4           2              3        2 2 2
+--R             ((30A b c + 3B b )e  + (- 36A c  - 46B b c)d e  + 48B c d e )x
+--R           + 
+--R                            2    3           2            2 2        2 3
+--R             (54A b c + 3B b )d e  + (- 72A c  - 84B b c)d e  + 96B c d e
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R             6           5  +---+
+--R       (24c e x + 24c d e )\|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 389
+
+--S 390 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                                           +--------------+
+--R                   2           2                      2 2  |             2  +-+
+--R         (24A b c e  + (- 48A c  - 40B b c)d e + 64B c d )\|- b d e + c d  \|c
+--R      *
+--R               +--------------+ +----------+
+--R               |             2  |   2
+--R             2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R         log(-------------------------------------------------------)
+--R                                     e x + d
+--R     + 
+--R                2       3  3             2        2     2
+--R           (6A b c - B b )e  + (- 48A b c  - 12B b c)d e
+--R         + 
+--R                 3          2  2         3 3
+--R           (48A c  + 72B b c )d e - 64B c d
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   2        3  3           2        2     2
+--R           (- 12A b c + 2B b )e  + (96A b c  + 24B b c)d e
+--R         + 
+--R                   3           2  2          3 3
+--R           (- 96A c  - 144B b c )d e + 128B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                   2           2                      2 2  +-----------+ +-+ +-+
+--R         (24A b c e  + (- 48A c  - 40B b c)d e + 64B c d )\|- b e + c d \|c \|d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R          5 +-+
+--R     16c e \|c
+--R                                                    Type: Expression(Integer)
+--E 390
+
+--S 391 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 391
+
+--S 392 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                2       3  3             2        2     2
+--R           (6A b c - B b )e  + (- 48A b c  - 12B b c)d e
+--R         + 
+--R                 3          2  2         3 3
+--R           (48A c  + 72B b c )d e - 64B c d
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   2        3  3           2        2     2
+--R           (- 12A b c + 2B b )e  + (96A b c  + 24B b c)d e
+--R         + 
+--R                   3           2  2          3 3
+--R           (- 96A c  - 144B b c )d e + 128B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                   2           2                      2 2  +-----------+ +-+ +-+
+--R         (24A b c e  + (- 48A c  - 40B b c)d e + 64B c d )\|- b e + c d \|c \|d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                                                +------------+
+--R                   2           2                       2 2  +-+ |           2
+--R         (48A b c e  + (- 96A c  - 80B b c)d e + 128B c d )\|c \|b d e - c d
+--R      *
+--R                 +----------+
+--R                 |   2
+--R               d\|c x  + b x
+--R         atan(----------------)
+--R                +------------+
+--R                |           2
+--R              x\|b d e - c d
+--R  /
+--R          5 +-+
+--R     16c e \|c
+--R                                                    Type: Expression(Integer)
+--E 392
+
+--S 393 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 393
+
+)clear all
+
+--S 394 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^3
+--R 
+--R
+--R                                         +----------+
+--R              3               2          |   2
+--R        (B c x  + (A c + B b)x  + A b x)\|c x  + b x
+--R   (1)  ---------------------------------------------
+--R                  3 3       2 2     2       3
+--R                 e x  + 3d e x  + 3d e x + d
+--R                                                    Type: Expression(Integer)
+--E 394
+
+--S 395 of 1457
+r0:=1/2*(2*B*d-A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)-3/4*(4*A*c*e*_
+     (2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+b^2*e^2))*atanh(x*sqrt(c)/_
+     sqrt(b*x+c*x^2))/(e^5*sqrt(c))+3/8*(A*e*(8*c^2*d^2-8*b*c*d*e+_
+     b^2*e^2)-B*d*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2))*atanh(1/2*(b*d+_
+     (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^5*_
+     sqrt(d)*sqrt(c*d-b*e))-3/4*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+_
+     e*(4*B*c*d-b*B*e-2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                           2  4           2              3        2 2 2  2
+--R           ((24A b c + 6B b )e  + (- 48A c  - 72B b c)d e  + 96B c d e )x
+--R         + 
+--R                            2    3           2             2 2         2 3
+--R           ((48A b c + 12B b )d e  + (- 96A c  - 144B b c)d e  + 192B c d e)x
+--R         + 
+--R                          2  2 2           2            3         2 4
+--R           (24A b c + 6B b )d e  + (- 48A c  - 72B b c)d e + 96B c d
+--R      *
+--R                                       +-+
+--R          +-----------+ +-+          x\|c
+--R         \|- b e + c d \|d atanh(-------------)
+--R                                  +----------+
+--R                                  |   2
+--R                                 \|c x  + b x
+--R     + 
+--R                     2 5                   2    4           2            2 3
+--R               - 3A b e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R             + 
+--R                    2 3 2
+--R               48B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                     2   4                   2  2 3           2             3 2
+--R               - 6A b d e  + (48A b c + 30B b )d e  + (- 48A c  - 120B b c)d e
+--R             + 
+--R                    2 4
+--R               96B c d e
+--R          *
+--R             x
+--R         + 
+--R                 2 2 3                   2  3 2           2            4
+--R           - 3A b d e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R         + 
+--R                2 5
+--R           48B c d
+--R      *
+--R          +-+             (b e - 2c d)x - b d
+--R         \|c atanh(--------------------------------)
+--R                                       +----------+
+--R                     +-----------+ +-+ |   2
+--R                   2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                 4 3                   4            3  2
+--R           4B c e x  + ((8A c + 10B b)e  - 16B c d e )x
+--R         + 
+--R                     4                     3          2 2             3
+--R           (- 10A b e  + (36A c + 38B b)d e  - 72B c d e )x - 6A b d e
+--R         + 
+--R                           2 2          3
+--R           (24A c + 24B b)d e  - 48B c d e
+--R      *
+--R                                +----------+
+--R          +-----------+ +-+ +-+ |   2
+--R         \|- b e + c d \|c \|d \|c x  + b x
+--R  /
+--R        7 2        6      2 5  +-----------+ +-+ +-+
+--R     (8e x  + 16d e x + 8d e )\|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 395
+
+--S 396 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                             2  4           2              3        2 2 2  2
+--R             ((12A b c + 3B b )e  + (- 24A c  - 36B b c)d e  + 48B c d e )x
+--R           + 
+--R                             2    3           2            2 2        2 3
+--R             ((24A b c + 6B b )d e  + (- 48A c  - 72B b c)d e  + 96B c d e)x
+--R           + 
+--R                            2  2 2           2            3         2 4
+--R             (12A b c + 3B b )d e  + (- 24A c  - 36B b c)d e + 48B c d
+--R        *
+--R            +--------------+       +----------+
+--R            |             2        |   2                     +-+
+--R           \|- b d e + c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                       2 5                   2    4           2            2 3
+--R                 - 3A b e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R               + 
+--R                      2 3 2
+--R                 48B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                       2   4                   2  2 3
+--R                 - 6A b d e  + (48A b c + 30B b )d e
+--R               + 
+--R                         2             3 2        2 4
+--R                 (- 48A c  - 120B b c)d e  + 96B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2 2 3                   2  3 2           2            4
+--R             - 3A b d e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R           + 
+--R                  2 5
+--R             48B c d
+--R        *
+--R            +-+
+--R           \|c
+--R        *
+--R           log
+--R                                   +----------+
+--R                                2  |   2
+--R                  (2b d e - 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                   4 3                   4            3  2
+--R             4B c e x  + ((8A c + 10B b)e  - 16B c d e )x
+--R           + 
+--R                       4                     3          2 2             3
+--R             (- 10A b e  + (36A c + 38B b)d e  - 72B c d e )x - 6A b d e
+--R           + 
+--R                             2 2          3
+--R             (24A c + 24B b)d e  - 48B c d e
+--R        *
+--R            +--------------+     +----------+
+--R            |             2  +-+ |   2
+--R           \|- b d e + c d  \|c \|c x  + b x
+--R    /
+--R                                 +--------------+
+--R          7 2        6      2 5  |             2  +-+
+--R       (8e x  + 16d e x + 8d e )\|- b d e + c d  \|c
+--R     ,
+--R
+--R                             2  4           2              3        2 2 2  2
+--R             ((12A b c + 3B b )e  + (- 24A c  - 36B b c)d e  + 48B c d e )x
+--R           + 
+--R                             2    3           2            2 2        2 3
+--R             ((24A b c + 6B b )d e  + (- 48A c  - 72B b c)d e  + 96B c d e)x
+--R           + 
+--R                            2  2 2           2            3         2 4
+--R             (12A b c + 3B b )d e  + (- 24A c  - 36B b c)d e + 48B c d
+--R        *
+--R            +------------+       +----------+
+--R            |           2        |   2                     +-+
+--R           \|b d e - c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                       2 5                   2    4           2             2 3
+--R                 - 6A b e  + (48A b c + 30B b )d e  + (- 48A c  - 120B b c)d e
+--R               + 
+--R                      2 3 2
+--R                 96B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2   4                   2  2 3
+--R                 - 12A b d e  + (96A b c + 60B b )d e
+--R               + 
+--R                         2             3 2         2 4
+--R                 (- 96A c  - 240B b c)d e  + 192B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2 2 3                   2  3 2           2             4
+--R             - 6A b d e  + (48A b c + 30B b )d e  + (- 48A c  - 120B b c)d e
+--R           + 
+--R                  2 5
+--R             96B c d
+--R        *
+--R                     +------------+ +----------+
+--R                     |           2  |   2
+--R            +-+     \|b d e - c d  \|c x  + b x
+--R           \|c atan(----------------------------)
+--R                            (b e - c d)x
+--R       + 
+--R                   4 3                   4            3  2
+--R             4B c e x  + ((8A c + 10B b)e  - 16B c d e )x
+--R           + 
+--R                       4                     3          2 2             3
+--R             (- 10A b e  + (36A c + 38B b)d e  - 72B c d e )x - 6A b d e
+--R           + 
+--R                             2 2          3
+--R             (24A c + 24B b)d e  - 48B c d e
+--R        *
+--R                +------------+ +----------+
+--R            +-+ |           2  |   2
+--R           \|c \|b d e - c d  \|c x  + b x
+--R    /
+--R                                     +------------+
+--R          7 2        6      2 5  +-+ |           2
+--R       (8e x  + 16d e x + 8d e )\|c \|b d e - c d
+--R     ,
+--R
+--R                       2 5                   2    4           2            2 3
+--R                 - 3A b e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R               + 
+--R                      2 3 2
+--R                 48B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                       2   4                   2  2 3
+--R                 - 6A b d e  + (48A b c + 30B b )d e
+--R               + 
+--R                         2             3 2        2 4
+--R                 (- 48A c  - 120B b c)d e  + 96B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2 2 3                   2  3 2           2            4
+--R             - 3A b d e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R           + 
+--R                  2 5
+--R             48B c d
+--R        *
+--R            +---+
+--R           \|- c
+--R        *
+--R           log
+--R                                   +----------+
+--R                                2  |   2
+--R                  (2b d e - 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                             2  4           2              3        2 2 2  2
+--R             ((24A b c + 6B b )e  + (- 48A c  - 72B b c)d e  + 96B c d e )x
+--R           + 
+--R                              2    3           2             2 2         2 3
+--R             ((48A b c + 12B b )d e  + (- 96A c  - 144B b c)d e  + 192B c d e)x
+--R           + 
+--R                            2  2 2           2            3         2 4
+--R             (24A b c + 6B b )d e  + (- 48A c  - 72B b c)d e + 96B c d
+--R        *
+--R                                        +----------+
+--R            +--------------+      +---+ |   2
+--R            |             2      \|- c \|c x  + b x
+--R           \|- b d e + c d  atan(-------------------)
+--R                                         c x
+--R       + 
+--R                   4 3                   4            3  2
+--R             4B c e x  + ((8A c + 10B b)e  - 16B c d e )x
+--R           + 
+--R                       4                     3          2 2             3
+--R             (- 10A b e  + (36A c + 38B b)d e  - 72B c d e )x - 6A b d e
+--R           + 
+--R                             2 2          3
+--R             (24A c + 24B b)d e  - 48B c d e
+--R        *
+--R            +--------------+       +----------+
+--R            |             2  +---+ |   2
+--R           \|- b d e + c d  \|- c \|c x  + b x
+--R    /
+--R                                 +--------------+
+--R          7 2        6      2 5  |             2  +---+
+--R       (8e x  + 16d e x + 8d e )\|- b d e + c d  \|- c
+--R     ,
+--R
+--R                       2 5                   2    4           2            2 3
+--R                 - 3A b e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R               + 
+--R                      2 3 2
+--R                 48B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                       2   4                   2  2 3
+--R                 - 6A b d e  + (48A b c + 30B b )d e
+--R               + 
+--R                         2             3 2        2 4
+--R                 (- 48A c  - 120B b c)d e  + 96B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2 2 3                   2  3 2           2            4
+--R             - 3A b d e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R           + 
+--R                  2 5
+--R             48B c d
+--R        *
+--R                       +------------+ +----------+
+--R                       |           2  |   2
+--R            +---+     \|b d e - c d  \|c x  + b x
+--R           \|- c atan(----------------------------)
+--R                              (b e - c d)x
+--R       + 
+--R                             2  4           2              3        2 2 2  2
+--R             ((12A b c + 3B b )e  + (- 24A c  - 36B b c)d e  + 48B c d e )x
+--R           + 
+--R                             2    3           2            2 2        2 3
+--R             ((24A b c + 6B b )d e  + (- 48A c  - 72B b c)d e  + 96B c d e)x
+--R           + 
+--R                            2  2 2           2            3         2 4
+--R             (12A b c + 3B b )d e  + (- 24A c  - 36B b c)d e + 48B c d
+--R        *
+--R                                      +----------+
+--R            +------------+      +---+ |   2
+--R            |           2      \|- c \|c x  + b x
+--R           \|b d e - c d  atan(-------------------)
+--R                                       c x
+--R       + 
+--R                   4 3                  4           3  2
+--R             2B c e x  + ((4A c + 5B b)e  - 8B c d e )x
+--R           + 
+--R                      4                     3          2 2             3
+--R             (- 5A b e  + (18A c + 19B b)d e  - 36B c d e )x - 3A b d e
+--R           + 
+--R                             2 2          3
+--R             (12A c + 12B b)d e  - 24B c d e
+--R        *
+--R                  +------------+ +----------+
+--R            +---+ |           2  |   2
+--R           \|- c \|b d e - c d  \|c x  + b x
+--R    /
+--R                                      +------------+
+--R          7 2       6      2 5  +---+ |           2
+--R       (4e x  + 8d e x + 4d e )\|- c \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 396
+
+--S 397 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                         2  2           2                      2 2
+--R         ((12A b c + 3B b )e  + (- 24A c  - 36B b c)d e + 48B c d )
+--R      *
+--R        +--------------+                         +----------+
+--R        |             2  +-----------+ +-+       |   2                     +-+
+--R       \|- b d e + c d  \|- b e + c d \|d log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   2 3                   2    2           2            2
+--R             - 3A b e  + (24A b c + 15B b )d e  + (- 24A c  - 60B b c)d e
+--R           + 
+--R                  2 3
+--R             48B c d
+--R      *
+--R          +-----------+ +-+ +-+
+--R         \|- b e + c d \|c \|d
+--R      *
+--R         log
+--R                                 +----------+
+--R                              2  |   2
+--R                (2b d e - 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                           2  2         2                      2 2
+--R         ((- 24A b c - 6B b )e  + (48A c  + 72B b c)d e - 96B c d )
+--R      *
+--R          +--------------+                              +-+
+--R          |             2  +-----------+ +-+          x\|c
+--R         \|- b d e + c d  \|- b e + c d \|d atanh(-------------)
+--R                                                   +----------+
+--R                                                   |   2
+--R                                                  \|c x  + b x
+--R     + 
+--R              2 3                     2    2         2            2         2 3
+--R         (3A b e  + (- 24A b c - 15B b )d e  + (24A c  + 60B b c)d e - 48B c d )
+--R      *
+--R          +--------------+
+--R          |             2  +-+             (b e - 2c d)x - b d
+--R         \|- b d e + c d  \|c atanh(--------------------------------)
+--R                                                        +----------+
+--R                                      +-----------+ +-+ |   2
+--R                                    2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R         +--------------+
+--R       5 |             2  +-----------+ +-+ +-+
+--R     8e \|- b d e + c d  \|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 397
+
+--S 398 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 398
+
+--S 399 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                         2  2           2                      2 2
+--R         ((12A b c + 3B b )e  + (- 24A c  - 36B b c)d e + 48B c d )
+--R      *
+--R                            +------------+       +----------+
+--R          +-----------+ +-+ |           2        |   2                     +-+
+--R         \|- b e + c d \|d \|b d e - c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                           2  2         2                      2 2
+--R         ((- 24A b c - 6B b )e  + (48A c  + 72B b c)d e - 96B c d )
+--R      *
+--R                            +------------+            +-+
+--R          +-----------+ +-+ |           2           x\|c
+--R         \|- b e + c d \|d \|b d e - c d  atanh(-------------)
+--R                                                 +----------+
+--R                                                 |   2
+--R                                                \|c x  + b x
+--R     + 
+--R              2 3                     2    2         2            2         2 3
+--R         (3A b e  + (- 24A b c - 15B b )d e  + (24A c  + 60B b c)d e - 48B c d )
+--R      *
+--R              +------------+
+--R          +-+ |           2              (b e - 2c d)x - b d
+--R         \|c \|b d e - c d  atanh(--------------------------------)
+--R                                                      +----------+
+--R                                    +-----------+ +-+ |   2
+--R                                  2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                 2 3                   2    2           2             2
+--R           - 6A b e  + (48A b c + 30B b )d e  + (- 48A c  - 120B b c)d e
+--R         + 
+--R                2 3
+--R           96B c d
+--R      *
+--R                                     +------------+ +----------+
+--R                                     |           2  |   2
+--R          +-----------+ +-+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|c \|d atan(----------------------------)
+--R                                            (b e - c d)x
+--R  /
+--R                               +------------+
+--R       5 +-----------+ +-+ +-+ |           2
+--R     8e \|- b e + c d \|c \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 399
+
+--S 400 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^4
+--R 
+--R
+--R                                         +----------+
+--R              3               2          |   2
+--R        (B c x  + (A c + B b)x  + A b x)\|c x  + b x
+--R   (1)  ---------------------------------------------
+--R             4 4       3 3     2 2 2     3       4
+--R            e x  + 4d e x  + 6d e x  + 4d e x + d
+--R                                                    Type: Expression(Integer)
+--E 401
+
+--S 402 of 1457
+r0:=-1/4*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*(b*x+c*x^2)^(3/2)/(d*e^2*_
+     (c*d-b*e)*(d+e*x)^2)+1/3*(4*B*d-A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/_
+     (e^2*(d+e*x)^3)+1/16*(B*d*(64*c^3*d^3-120*b*c^2*d^2*e+60*b^2*c*d*e^2-_
+     5*b^3*e^3)-A*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3))*_
+     atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_
+     c*x^2)))/(d^(3/2)*e^5*(c*d-b*e)^(3/2))-(8*B*c*d-3*b*B*e-2*A*c*e)*_
+     atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^5-1/8*(A*e*(8*c^2*d^2-_
+     6*b*c*d*e-b^2*e^2)-B*d*(32*c^2*d^2-36*b*c*d*e+5*b^2*e^2)-_
+     2*c*e*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/_
+     (d*e^4*(c*d-b*e)*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                             2    5           2             2 4         2 3 3  3
+--R           ((96A b c + 144B b )d e  + (- 96A c  - 528B b c)d e  + 384B c d e )x
+--R         + 
+--R                                 2  2 4            2              3 3
+--R               (288A b c + 432B b )d e  + (- 288A c  - 1584B b c)d e
+--R             + 
+--R                      2 4 2
+--R               1152B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                                 2  3 3            2              4 2
+--R               (288A b c + 432B b )d e  + (- 288A c  - 1584B b c)d e
+--R             + 
+--R                      2 5
+--R               1152B c d e
+--R          *
+--R             x
+--R         + 
+--R                            2  4 2           2             5          2 6
+--R           (96A b c + 144B b )d e  + (- 96A c  - 528B b c)d e + 384B c d
+--R      *
+--R                                           +-+
+--R          +-----------+ +-+ +-+          x\|c
+--R         \|- b e + c d \|c \|d atanh(-------------)
+--R                                      +----------+
+--R                                      |   2
+--R                                     \|c x  + b x
+--R     + 
+--R                     3 7           2         3    6           2         2   2 5
+--R               - 3A b e  + (- 18A b c - 15B b )d e  + (72A b c  + 180B b c)d e
+--R             + 
+--R                       3           2  3 4         3 4 3
+--R               (- 48A c  - 360B b c )d e  + 192B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                     3   6           2         3  2 5
+--R               - 9A b d e  + (- 54A b c - 45B b )d e
+--R             + 
+--R                        2         2   3 4            3            2  4 3
+--R               (216A b c  + 540B b c)d e  + (- 144A c  - 1080B b c )d e
+--R             + 
+--R                     3 5 2
+--R               576B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                     3 2 5           2         3  3 4
+--R               - 9A b d e  + (- 54A b c - 45B b )d e
+--R             + 
+--R                        2         2   4 3            3            2  5 2
+--R               (216A b c  + 540B b c)d e  + (- 144A c  - 1080B b c )d e
+--R             + 
+--R                     3 6
+--R               576B c d e
+--R          *
+--R             x
+--R         + 
+--R                 3 3 4           2         3  4 3           2         2   5 2
+--R           - 3A b d e  + (- 18A b c - 15B b )d e  + (72A b c  + 180B b c)d e
+--R         + 
+--R                   3           2  6          3 7
+--R           (- 48A c  - 360B b c )d e + 192B c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                       5        2 2 4  3
+--R           (48B b c d e  - 48B c d e )x
+--R         + 
+--R                   2 6                     2    5         2             2 4
+--R               6A b e  + (- 88A b c - 66B b )d e  + (88A c  + 412B b c)d e
+--R             + 
+--R                       2 3 3
+--R               - 352B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      2   5                     2  2 4
+--R               - 16A b d e  + (- 92A b c - 80B b )d e
+--R             + 
+--R                      2             3 3         2 4 2
+--R               (120A c  + 548B b c)d e  - 480B c d e
+--R          *
+--R             x
+--R         + 
+--R                 2 2 4                     2  3 3         2             4 2
+--R           - 6A b d e  + (- 36A b c - 30B b )d e  + (48A c  + 216B b c)d e
+--R         + 
+--R                   2 5
+--R           - 192B c d e
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R                 9        2 8  3          2 8         3 7  2
+--R         (48b d e  - 48c d e )x  + (144b d e  - 144c d e )x
+--R       + 
+--R                3 7         4 6          4 6        5 5
+--R         (144b d e  - 144c d e )x + 48b d e  - 48c d e
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 402
+
+--S 403 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                                   2    5           2             2 4
+--R                   (48A b c + 72B b )d e  + (- 48A c  - 264B b c)d e
+--R                 + 
+--R                         2 3 3
+--R                   192B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                                   2  2 4            2             3 3
+--R                 (144A b c + 216B b )d e  + (- 144A c  - 792B b c)d e
+--R               + 
+--R                       2 4 2
+--R                 576B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                                   2  3 3            2             4 2
+--R                 (144A b c + 216B b )d e  + (- 144A c  - 792B b c)d e
+--R               + 
+--R                       2 5
+--R                 576B c d e
+--R            *
+--R               x
+--R           + 
+--R                             2  4 2           2             5          2 6
+--R             (48A b c + 72B b )d e  + (- 48A c  - 264B b c)d e + 192B c d
+--R        *
+--R            +--------------+              +----------+
+--R            |             2  +-+      +-+ |   2
+--R           \|- b d e + c d  \|c log(2\|c \|c x  + b x  + 2c x + b)
+--R       + 
+--R                     3 7         2         3    6             2         2   2 5
+--R                 3A b e  + (18A b c + 15B b )d e  + (- 72A b c  - 180B b c)d e
+--R               + 
+--R                       3           2  3 4         3 4 3
+--R                 (48A c  + 360B b c )d e  - 192B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                     3   6         2         3  2 5
+--R                 9A b d e  + (54A b c + 45B b )d e
+--R               + 
+--R                            2         2   3 4          3            2  4 3
+--R                 (- 216A b c  - 540B b c)d e  + (144A c  + 1080B b c )d e
+--R               + 
+--R                         3 5 2
+--R                 - 576B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     3 2 5         2         3  3 4
+--R                 9A b d e  + (54A b c + 45B b )d e
+--R               + 
+--R                            2         2   4 3          3            2  5 2
+--R                 (- 216A b c  - 540B b c)d e  + (144A c  + 1080B b c )d e
+--R               + 
+--R                         3 6
+--R                 - 576B c d e
+--R            *
+--R               x
+--R           + 
+--R                 3 3 4         2         3  4 3             2         2   5 2
+--R             3A b d e  + (18A b c + 15B b )d e  + (- 72A b c  - 180B b c)d e
+--R           + 
+--R                   3           2  6          3 7
+--R             (48A c  + 360B b c )d e - 192B c d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                         5        2 2 4  3
+--R             (48B b c d e  - 48B c d e )x
+--R           + 
+--R                     2 6                     2    5         2             2 4
+--R                 6A b e  + (- 88A b c - 66B b )d e  + (88A c  + 412B b c)d e
+--R               + 
+--R                         2 3 3
+--R                 - 352B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2   5                     2  2 4
+--R                 - 16A b d e  + (- 92A b c - 80B b )d e
+--R               + 
+--R                        2             3 3         2 4 2
+--R                 (120A c  + 548B b c)d e  - 480B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2 2 4                     2  3 3         2             4 2
+--R             - 6A b d e  + (- 36A b c - 30B b )d e  + (48A c  + 216B b c)d e
+--R           + 
+--R                     2 5
+--R             - 192B c d e
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                   9        2 8  3          2 8         3 7  2
+--R           (48b d e  - 48c d e )x  + (144b d e  - 144c d e )x
+--R         + 
+--R                  3 7         4 6          4 6        5 5
+--R           (144b d e  - 144c d e )x + 48b d e  - 48c d e
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                              2    5           2             2 4        2 3 3  3
+--R             ((24A b c + 36B b )d e  + (- 24A c  - 132B b c)d e  + 96B c d e )x
+--R           + 
+--R                                    2  2 4           2             3 3
+--R                   (72A b c + 108B b )d e  + (- 72A c  - 396B b c)d e
+--R                 + 
+--R                         2 4 2
+--R                   288B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                               2  3 3           2             4 2         2 5
+--R             ((72A b c + 108B b )d e  + (- 72A c  - 396B b c)d e  + 288B c d e)x
+--R           + 
+--R                             2  4 2           2             5         2 6
+--R             (24A b c + 36B b )d e  + (- 24A c  - 132B b c)d e + 96B c d
+--R        *
+--R                +------------+          +----------+
+--R            +-+ |           2       +-+ |   2
+--R           \|c \|b d e - c d  log(2\|c \|c x  + b x  + 2c x + b)
+--R       + 
+--R                       3 7           2         3    6
+--R                 - 3A b e  + (- 18A b c - 15B b )d e
+--R               + 
+--R                         2         2   2 5           3           2  3 4
+--R                 (72A b c  + 180B b c)d e  + (- 48A c  - 360B b c )d e
+--R               + 
+--R                       3 4 3
+--R                 192B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                       3   6           2         3  2 5
+--R                 - 9A b d e  + (- 54A b c - 45B b )d e
+--R               + 
+--R                          2         2   3 4            3            2  4 3
+--R                 (216A b c  + 540B b c)d e  + (- 144A c  - 1080B b c )d e
+--R               + 
+--R                       3 5 2
+--R                 576B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                       3 2 5           2         3  3 4
+--R                 - 9A b d e  + (- 54A b c - 45B b )d e
+--R               + 
+--R                          2         2   4 3            3            2  5 2
+--R                 (216A b c  + 540B b c)d e  + (- 144A c  - 1080B b c )d e
+--R               + 
+--R                       3 6
+--R                 576B c d e
+--R            *
+--R               x
+--R           + 
+--R                   3 3 4           2         3  4 3           2         2   5 2
+--R             - 3A b d e  + (- 18A b c - 15B b )d e  + (72A b c  + 180B b c)d e
+--R           + 
+--R                     3           2  6          3 7
+--R             (- 48A c  - 360B b c )d e + 192B c d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                         5        2 2 4  3
+--R             (24B b c d e  - 24B c d e )x
+--R           + 
+--R                     2 6                     2    5         2             2 4
+--R                 3A b e  + (- 44A b c - 33B b )d e  + (44A c  + 206B b c)d e
+--R               + 
+--R                         2 3 3
+--R                 - 176B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                       2   5                     2  2 4
+--R                 - 8A b d e  + (- 46A b c - 40B b )d e
+--R               + 
+--R                       2             3 3         2 4 2
+--R                 (60A c  + 274B b c)d e  - 240B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2 2 4                     2  3 3         2             4 2
+--R             - 3A b d e  + (- 18A b c - 15B b )d e  + (24A c  + 108B b c)d e
+--R           + 
+--R                    2 5
+--R             - 96B c d e
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                   9        2 8  3         2 8        3 7  2
+--R           (24b d e  - 24c d e )x  + (72b d e  - 72c d e )x
+--R         + 
+--R                 3 7        4 6          4 6        5 5
+--R           (72b d e  - 72c d e )x + 24b d e  - 24c d e
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ,
+--R
+--R                     3 7         2         3    6             2         2   2 5
+--R                 3A b e  + (18A b c + 15B b )d e  + (- 72A b c  - 180B b c)d e
+--R               + 
+--R                       3           2  3 4         3 4 3
+--R                 (48A c  + 360B b c )d e  - 192B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                     3   6         2         3  2 5
+--R                 9A b d e  + (54A b c + 45B b )d e
+--R               + 
+--R                            2         2   3 4          3            2  4 3
+--R                 (- 216A b c  - 540B b c)d e  + (144A c  + 1080B b c )d e
+--R               + 
+--R                         3 5 2
+--R                 - 576B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     3 2 5         2         3  3 4
+--R                 9A b d e  + (54A b c + 45B b )d e
+--R               + 
+--R                            2         2   4 3          3            2  5 2
+--R                 (- 216A b c  - 540B b c)d e  + (144A c  + 1080B b c )d e
+--R               + 
+--R                         3 6
+--R                 - 576B c d e
+--R            *
+--R               x
+--R           + 
+--R                 3 3 4         2         3  4 3             2         2   5 2
+--R             3A b d e  + (18A b c + 15B b )d e  + (- 72A b c  - 180B b c)d e
+--R           + 
+--R                   3           2  6          3 7
+--R             (48A c  + 360B b c )d e - 192B c d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                                    2    5           2             2 4
+--R                   (96A b c + 144B b )d e  + (- 96A c  - 528B b c)d e
+--R                 + 
+--R                         2 3 3
+--R                   384B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                                   2  2 4            2              3 3
+--R                 (288A b c + 432B b )d e  + (- 288A c  - 1584B b c)d e
+--R               + 
+--R                        2 4 2
+--R                 1152B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                                   2  3 3            2              4 2
+--R                 (288A b c + 432B b )d e  + (- 288A c  - 1584B b c)d e
+--R               + 
+--R                        2 5
+--R                 1152B c d e
+--R            *
+--R               x
+--R           + 
+--R                              2  4 2           2             5          2 6
+--R             (96A b c + 144B b )d e  + (- 96A c  - 528B b c)d e + 384B c d
+--R        *
+--R                                        +----------+
+--R            +--------------+            |   2
+--R            |             2  +---+     \|c x  + b x
+--R           \|- b d e + c d  \|- c atan(-------------)
+--R                                            +---+
+--R                                          x\|- c
+--R       + 
+--R                         5        2 2 4  3
+--R             (48B b c d e  - 48B c d e )x
+--R           + 
+--R                     2 6                     2    5         2             2 4
+--R                 6A b e  + (- 88A b c - 66B b )d e  + (88A c  + 412B b c)d e
+--R               + 
+--R                         2 3 3
+--R                 - 352B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2   5                     2  2 4
+--R                 - 16A b d e  + (- 92A b c - 80B b )d e
+--R               + 
+--R                        2             3 3         2 4 2
+--R                 (120A c  + 548B b c)d e  - 480B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2 2 4                     2  3 3         2             4 2
+--R             - 6A b d e  + (- 36A b c - 30B b )d e  + (48A c  + 216B b c)d e
+--R           + 
+--R                     2 5
+--R             - 192B c d e
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                   9        2 8  3          2 8         3 7  2
+--R           (48b d e  - 48c d e )x  + (144b d e  - 144c d e )x
+--R         + 
+--R                  3 7         4 6          4 6        5 5
+--R           (144b d e  - 144c d e )x + 48b d e  - 48c d e
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                       3 7           2         3    6
+--R                 - 3A b e  + (- 18A b c - 15B b )d e
+--R               + 
+--R                         2         2   2 5           3           2  3 4
+--R                 (72A b c  + 180B b c)d e  + (- 48A c  - 360B b c )d e
+--R               + 
+--R                       3 4 3
+--R                 192B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                       3   6           2         3  2 5
+--R                 - 9A b d e  + (- 54A b c - 45B b )d e
+--R               + 
+--R                          2         2   3 4            3            2  4 3
+--R                 (216A b c  + 540B b c)d e  + (- 144A c  - 1080B b c )d e
+--R               + 
+--R                       3 5 2
+--R                 576B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                       3 2 5           2         3  3 4
+--R                 - 9A b d e  + (- 54A b c - 45B b )d e
+--R               + 
+--R                          2         2   4 3            3            2  5 2
+--R                 (216A b c  + 540B b c)d e  + (- 144A c  - 1080B b c )d e
+--R               + 
+--R                       3 6
+--R                 576B c d e
+--R            *
+--R               x
+--R           + 
+--R                   3 3 4           2         3  4 3           2         2   5 2
+--R             - 3A b d e  + (- 18A b c - 15B b )d e  + (72A b c  + 180B b c)d e
+--R           + 
+--R                     3           2  6          3 7
+--R             (- 48A c  - 360B b c )d e + 192B c d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                                   2    5           2             2 4
+--R                   (48A b c + 72B b )d e  + (- 48A c  - 264B b c)d e
+--R                 + 
+--R                         2 3 3
+--R                   192B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                                   2  2 4            2             3 3
+--R                 (144A b c + 216B b )d e  + (- 144A c  - 792B b c)d e
+--R               + 
+--R                       2 4 2
+--R                 576B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                                   2  3 3            2             4 2
+--R                 (144A b c + 216B b )d e  + (- 144A c  - 792B b c)d e
+--R               + 
+--R                       2 5
+--R                 576B c d e
+--R            *
+--R               x
+--R           + 
+--R                             2  4 2           2             5          2 6
+--R             (48A b c + 72B b )d e  + (- 48A c  - 264B b c)d e + 192B c d
+--R        *
+--R                                      +----------+
+--R                  +------------+      |   2
+--R            +---+ |           2      \|c x  + b x
+--R           \|- c \|b d e - c d  atan(-------------)
+--R                                          +---+
+--R                                        x\|- c
+--R       + 
+--R                         5        2 2 4  3
+--R             (24B b c d e  - 24B c d e )x
+--R           + 
+--R                     2 6                     2    5         2             2 4
+--R                 3A b e  + (- 44A b c - 33B b )d e  + (44A c  + 206B b c)d e
+--R               + 
+--R                         2 3 3
+--R                 - 176B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                       2   5                     2  2 4
+--R                 - 8A b d e  + (- 46A b c - 40B b )d e
+--R               + 
+--R                       2             3 3         2 4 2
+--R                 (60A c  + 274B b c)d e  - 240B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2 2 4                     2  3 3         2             4 2
+--R             - 3A b d e  + (- 18A b c - 15B b )d e  + (24A c  + 108B b c)d e
+--R           + 
+--R                    2 5
+--R             - 96B c d e
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                   9        2 8  3         2 8        3 7  2
+--R           (24b d e  - 24c d e )x  + (72b d e  - 72c d e )x
+--R         + 
+--R                 3 7        4 6          4 6        5 5
+--R           (72b d e  - 72c d e )x + 24b d e  - 24c d e
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 403
+
+--S 404 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                          2    2           2            2         2 3
+--R         ((16A b c + 24B b )d e  + (- 16A c  - 88B b c)d e + 64B c d )
+--R      *
+--R        +--------------+                                +----------+
+--R        |             2  +-----------+ +-+ +-+      +-+ |   2
+--R       \|- b d e + c d  \|- b e + c d \|c \|d log(2\|c \|c x  + b x  + 2c x + b)
+--R     + 
+--R              3 4        2        3    3             2        2   2 2
+--R           A b e  + (6A b c + 5B b )d e  + (- 24A b c  - 60B b c)d e
+--R         + 
+--R                 3           2  3         3 4
+--R           (16A c  + 120B b c )d e - 64B c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                            2    2         2             2          2 3
+--R         ((- 32A b c - 48B b )d e  + (32A c  + 176B b c)d e - 128B c d )
+--R      *
+--R          +--------------+                                  +-+
+--R          |             2  +-----------+ +-+ +-+          x\|c
+--R         \|- b d e + c d  \|- b e + c d \|c \|d atanh(-------------)
+--R                                                       +----------+
+--R                                                       |   2
+--R                                                      \|c x  + b x
+--R     + 
+--R              3 4        2        3    3             2        2   2 2
+--R           A b e  + (6A b c + 5B b )d e  + (- 24A b c  - 60B b c)d e
+--R         + 
+--R                 3           2  3         3 4
+--R           (16A c  + 120B b c )d e - 64B c d
+--R      *
+--R          +--------------+
+--R          |             2              (b e - 2c d)x - b d
+--R         \|- b d e + c d  atanh(--------------------------------)
+--R                                                    +----------+
+--R                                  +-----------+ +-+ |   2
+--R                                2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                           +--------------+
+--R             6        2 5  |             2  +-----------+ +-+
+--R     (16b d e  - 16c d e )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 404
+
+--S 405 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 405
+
+--S 406 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                          2    2           2            2         2 3
+--R         ((16A b c + 24B b )d e  + (- 16A c  - 88B b c)d e + 64B c d )
+--R      *
+--R                              +------------+          +----------+
+--R        +-----------+ +-+ +-+ |           2       +-+ |   2
+--R       \|- b e + c d \|c \|d \|b d e - c d  log(2\|c \|c x  + b x  + 2c x + b)
+--R     + 
+--R                            2    2         2             2          2 3
+--R         ((- 32A b c - 48B b )d e  + (32A c  + 176B b c)d e - 128B c d )
+--R      *
+--R                                +------------+            +-+
+--R          +-----------+ +-+ +-+ |           2           x\|c
+--R         \|- b e + c d \|c \|d \|b d e - c d  atanh(-------------)
+--R                                                     +----------+
+--R                                                     |   2
+--R                                                    \|c x  + b x
+--R     + 
+--R              3 4        2        3    3             2        2   2 2
+--R           A b e  + (6A b c + 5B b )d e  + (- 24A b c  - 60B b c)d e
+--R         + 
+--R                 3           2  3         3 4
+--R           (16A c  + 120B b c )d e - 64B c d
+--R      *
+--R          +------------+
+--R          |           2              (b e - 2c d)x - b d
+--R         \|b d e - c d  atanh(--------------------------------)
+--R                                                  +----------+
+--R                                +-----------+ +-+ |   2
+--R                              2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                 3 4           2         3    3           2         2   2 2
+--R           - 2A b e  + (- 12A b c - 10B b )d e  + (48A b c  + 120B b c)d e
+--R         + 
+--R                   3           2  3          3 4
+--R           (- 32A c  - 240B b c )d e + 128B c d
+--R      *
+--R                                 +------------+ +----------+
+--R                                 |           2  |   2
+--R          +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|d atan(----------------------------)
+--R                                        (b e - c d)x
+--R  /
+--R                                             +------------+
+--R             6        2 5  +-----------+ +-+ |           2
+--R     (16b d e  - 16c d e )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 406
+
+--S 407 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 407
+
+)clear all
+
+--S 408 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^5
+--R 
+--R
+--R                                            +----------+
+--R                 3               2          |   2
+--R           (B c x  + (A c + B b)x  + A b x)\|c x  + b x
+--R   (1)  --------------------------------------------------
+--R         5 5       4 4      2 3 3      3 2 2     4       5
+--R        e x  + 5d e x  + 10d e x  + 10d e x  + 5d e x + d
+--R                                                    Type: Expression(Integer)
+--E 408
+
+--S 409 of 1457
+r0:=1/32*(3*A*b^2*e^3+B*d*(16*c^2*d^2-24*b*c*d*e+5*b^2*e^2))*_
+     (b*x+c*x^2)^(3/2)/(d^2*e^2*(c*d-b*e)^2*(d+e*x)^2)+1/24*(3*A*b*e^2-_
+     B*d*(8*c*d-5*b*e)-6*c*e*(B*d-A*e)*x)*(b*x+c*x^2)^(3/2)/(d*e^2*_
+     (c*d-b*e)*(d+e*x)^3)+1/4*(B*d-A*e)*(b*x+c*x^2)^(5/2)/(d*(c*d-b*e)*_
+     (d+e*x)^4)+2*B*c^(3/2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/e^5+_
+     1/128*(3*A*b^4*e^5-B*d*(128*c^4*d^4-320*b*c^3*d^3*e+240*b^2*c^2*_
+     d^2*e^2-40*b^3*c*d*e^3-5*b^4*e^4))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_
+     (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*e^5*_
+     (c*d-b*e)^(5/2))-1/64*(3*A*b^3*e^4+B*d*(64*c^3*d^3-112*b*c^2*_
+     d^2*e+40*b^2*c*d*e^2+5*b^3*e^3)+2*c*e*(3*A*b^2*e^3+B*d*(16*c^2*_
+     d^2-24*b*c*d*e+5*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d^2*e^4*_
+     (c*d-b*e)^2*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                  2   2 6            2 3 5         3 4 4  4
+--R           (768B b c d e  - 1536B b c d e  + 768B c d e )x
+--R         + 
+--R                   2   3 5            2 4 4          3 5 3  3
+--R           (3072B b c d e  - 6144B b c d e  + 3072B c d e )x
+--R         + 
+--R                   2   4 4            2 5 3          3 6 2  2
+--R           (4608B b c d e  - 9216B b c d e  + 4608B c d e )x
+--R         + 
+--R                   2   5 3            2 6 2          3 7            2   6 2
+--R           (3072B b c d e  - 6144B b c d e  + 3072B c d e)x + 768B b c d e
+--R         + 
+--R                      2 7          3 8
+--R           - 1536B b c d e + 768B c d
+--R      *
+--R                                           +-+
+--R          +-----------+ +-+ +-+          x\|c
+--R         \|- b e + c d \|c \|d atanh(-------------)
+--R                                      +----------+
+--R                                      |   2
+--R                                     \|c x  + b x
+--R     + 
+--R                     4 9        4   8         3   2 7         2 2 3 6
+--R               - 9A b e  - 15B b d e  - 120B b c d e  + 720B b c d e
+--R             + 
+--R                         3 4 5         4 5 4
+--R               - 960B b c d e  + 384B c d e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                      4   8        4 2 7         3   3 6          2 2 4 5
+--R               - 36A b d e  - 60B b d e  - 480B b c d e  + 2880B b c d e
+--R             + 
+--R                          3 5 4          4 6 3
+--R               - 3840B b c d e  + 1536B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      4 2 7        4 3 6         3   4 5          2 2 5 4
+--R               - 54A b d e  - 90B b d e  - 720B b c d e  + 4320B b c d e
+--R             + 
+--R                          3 6 3          4 7 2
+--R               - 5760B b c d e  + 2304B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      4 3 6        4 4 5         3   5 4          2 2 6 3
+--R               - 36A b d e  - 60B b d e  - 480B b c d e  + 2880B b c d e
+--R             + 
+--R                          3 7 2          4 8
+--R               - 3840B b c d e  + 1536B c d e
+--R          *
+--R             x
+--R         + 
+--R                 4 4 5        4 5 4         3   6 3         2 2 7 2
+--R           - 9A b d e  - 15B b d e  - 120B b c d e  + 720B b c d e
+--R         + 
+--R                     3 8          4 9
+--R           - 960B b c d e + 384B c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                    3 8         2         3    7              2         2   2 6
+--R               18A b e  + (12A b c + 30B b )d e  + (- 144A b c  - 764B b c)d e
+--R             + 
+--R                     3            2  3 5         3 4 4
+--R               (96A c  + 1552B b c )d e  - 800B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                    3   7            2          3  2 6
+--R               66A b d e  + (- 264A b c - 146B b )d e
+--R             + 
+--R                        2          2   3 5            2 4 4          3 5 3
+--R               (144A b c  - 1096B b c)d e  + 2960B b c d e  - 1664B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      3 2 6         2          3  3 5         2   4 4
+--R               - 66A b d e  + (12A b c - 110B b )d e  - 860B b c d e
+--R             + 
+--R                        2 5 3          3 6 2
+--R               2368B b c d e  - 1344B c d e
+--R          *
+--R             x
+--R         + 
+--R                3 3 5        3 4 4         2   5 3           2 6 2         3 7
+--R         - 18A b d e  - 30B b d e  - 240B b c d e  + 672B b c d e  - 384B c d e
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R              2 2 11           3 10       2 4 9  4
+--R         (384b d e   - 768b c d e   + 384c d e )x
+--R       + 
+--R               2 3 10            4 9        2 5 8  3
+--R         (1536b d e   - 3072b c d e  + 1536c d e )x
+--R       + 
+--R               2 4 9            5 8        2 6 7  2
+--R         (2304b d e  - 4608b c d e  + 2304c d e )x
+--R       + 
+--R               2 5 8            6 7        2 7 6         2 6 7           7 6
+--R         (1536b d e  - 3072b c d e  + 1536c d e )x + 384b d e  - 768b c d e
+--R       + 
+--R             2 8 5
+--R         384c d e
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 409
+
+--S 410 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                    2   2 6           2 3 5         3 4 4  4
+--R             (384B b c d e  - 768B b c d e  + 384B c d e )x
+--R           + 
+--R                     2   3 5            2 4 4          3 5 3  3
+--R             (1536B b c d e  - 3072B b c d e  + 1536B c d e )x
+--R           + 
+--R                     2   4 4            2 5 3          3 6 2  2
+--R             (2304B b c d e  - 4608B b c d e  + 2304B c d e )x
+--R           + 
+--R                     2   5 3            2 6 2          3 7            2   6 2
+--R             (1536B b c d e  - 3072B b c d e  + 1536B c d e)x + 384B b c d e
+--R           + 
+--R                       2 7          3 8
+--R             - 768B b c d e + 384B c d
+--R        *
+--R            +--------------+              +----------+
+--R            |             2  +-+      +-+ |   2
+--R           \|- b d e + c d  \|c log(2\|c \|c x  + b x  + 2c x + b)
+--R       + 
+--R                     4 9        4   8         3   2 7         2 2 3 6
+--R                 9A b e  + 15B b d e  + 120B b c d e  - 720B b c d e
+--R               + 
+--R                         3 4 5         4 5 4
+--R                 960B b c d e  - 384B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      4   8        4 2 7         3   3 6          2 2 4 5
+--R                 36A b d e  + 60B b d e  + 480B b c d e  - 2880B b c d e
+--R               + 
+--R                          3 5 4          4 6 3
+--R                 3840B b c d e  - 1536B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      4 2 7        4 3 6         3   4 5          2 2 5 4
+--R                 54A b d e  + 90B b d e  + 720B b c d e  - 4320B b c d e
+--R               + 
+--R                          3 6 3          4 7 2
+--R                 5760B b c d e  - 2304B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      4 3 6        4 4 5         3   5 4          2 2 6 3
+--R                 36A b d e  + 60B b d e  + 480B b c d e  - 2880B b c d e
+--R               + 
+--R                          3 7 2          4 8
+--R                 3840B b c d e  - 1536B c d e
+--R            *
+--R               x
+--R           + 
+--R                 4 4 5        4 5 4         3   6 3         2 2 7 2
+--R             9A b d e  + 15B b d e  + 120B b c d e  - 720B b c d e
+--R           + 
+--R                     3 8          4 9
+--R             960B b c d e - 384B c d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                      3 8         2         3    7
+--R                 18A b e  + (12A b c + 30B b )d e
+--R               + 
+--R                            2         2   2 6         3            2  3 5
+--R                 (- 144A b c  - 764B b c)d e  + (96A c  + 1552B b c )d e
+--R               + 
+--R                         3 4 4
+--R                 - 800B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      3   7            2          3  2 6
+--R                 66A b d e  + (- 264A b c - 146B b )d e
+--R               + 
+--R                          2          2   3 5            2 4 4          3 5 3
+--R                 (144A b c  - 1096B b c)d e  + 2960B b c d e  - 1664B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 6         2          3  3 5         2   4 4
+--R                 - 66A b d e  + (12A b c - 110B b )d e  - 860B b c d e
+--R               + 
+--R                          2 5 3          3 6 2
+--R                 2368B b c d e  - 1344B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 5        3 4 4         2   5 3           2 6 2
+--R             - 18A b d e  - 30B b d e  - 240B b c d e  + 672B b c d e
+--R           + 
+--R                     3 7
+--R             - 384B c d e
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                2 2 11           3 10       2 4 9  4
+--R           (384b d e   - 768b c d e   + 384c d e )x
+--R         + 
+--R                 2 3 10            4 9        2 5 8  3
+--R           (1536b d e   - 3072b c d e  + 1536c d e )x
+--R         + 
+--R                 2 4 9            5 8        2 6 7  2
+--R           (2304b d e  - 4608b c d e  + 2304c d e )x
+--R         + 
+--R                 2 5 8            6 7        2 7 6         2 6 7           7 6
+--R           (1536b d e  - 3072b c d e  + 1536c d e )x + 384b d e  - 768b c d e
+--R         + 
+--R               2 8 5
+--R           384c d e
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                    2   2 6           2 3 5         3 4 4  4
+--R             (192B b c d e  - 384B b c d e  + 192B c d e )x
+--R           + 
+--R                    2   3 5            2 4 4         3 5 3  3
+--R             (768B b c d e  - 1536B b c d e  + 768B c d e )x
+--R           + 
+--R                     2   4 4            2 5 3          3 6 2  2
+--R             (1152B b c d e  - 2304B b c d e  + 1152B c d e )x
+--R           + 
+--R                    2   5 3            2 6 2         3 7            2   6 2
+--R             (768B b c d e  - 1536B b c d e  + 768B c d e)x + 192B b c d e
+--R           + 
+--R                       2 7          3 8
+--R             - 384B b c d e + 192B c d
+--R        *
+--R                +------------+          +----------+
+--R            +-+ |           2       +-+ |   2
+--R           \|c \|b d e - c d  log(2\|c \|c x  + b x  + 2c x + b)
+--R       + 
+--R                       4 9        4   8         3   2 7         2 2 3 6
+--R                 - 9A b e  - 15B b d e  - 120B b c d e  + 720B b c d e
+--R               + 
+--R                           3 4 5         4 5 4
+--R                 - 960B b c d e  + 384B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                        4   8        4 2 7         3   3 6          2 2 4 5
+--R                 - 36A b d e  - 60B b d e  - 480B b c d e  + 2880B b c d e
+--R               + 
+--R                            3 5 4          4 6 3
+--R                 - 3840B b c d e  + 1536B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        4 2 7        4 3 6         3   4 5          2 2 5 4
+--R                 - 54A b d e  - 90B b d e  - 720B b c d e  + 4320B b c d e
+--R               + 
+--R                            3 6 3          4 7 2
+--R                 - 5760B b c d e  + 2304B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4 3 6        4 4 5         3   5 4          2 2 6 3
+--R                 - 36A b d e  - 60B b d e  - 480B b c d e  + 2880B b c d e
+--R               + 
+--R                            3 7 2          4 8
+--R                 - 3840B b c d e  + 1536B c d e
+--R            *
+--R               x
+--R           + 
+--R                   4 4 5        4 5 4         3   6 3         2 2 7 2
+--R             - 9A b d e  - 15B b d e  - 120B b c d e  + 720B b c d e
+--R           + 
+--R                       3 8          4 9
+--R             - 960B b c d e + 384B c d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                     3 8        2         3    7             2         2   2 6
+--R                 9A b e  + (6A b c + 15B b )d e  + (- 72A b c  - 382B b c)d e
+--R               + 
+--R                       3           2  3 5         3 4 4
+--R                 (48A c  + 776B b c )d e  - 400B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      3   7            2         3  2 6
+--R                 33A b d e  + (- 132A b c - 73B b )d e
+--R               + 
+--R                         2         2   3 5            2 4 4         3 5 3
+--R                 (72A b c  - 548B b c)d e  + 1480B b c d e  - 832B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 6        2         3  3 5         2   4 4
+--R                 - 33A b d e  + (6A b c - 55B b )d e  - 430B b c d e
+--R               + 
+--R                          2 5 3         3 6 2
+--R                 1184B b c d e  - 672B c d e
+--R            *
+--R               x
+--R           + 
+--R                 3 3 5        3 4 4         2   5 3           2 6 2         3 7
+--R           - 9A b d e  - 15B b d e  - 120B b c d e  + 336B b c d e  - 192B c d e
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                2 2 11           3 10       2 4 9  4
+--R           (192b d e   - 384b c d e   + 192c d e )x
+--R         + 
+--R                2 3 10            4 9       2 5 8  3
+--R           (768b d e   - 1536b c d e  + 768c d e )x
+--R         + 
+--R                 2 4 9            5 8        2 6 7  2
+--R           (1152b d e  - 2304b c d e  + 1152c d e )x
+--R         + 
+--R                2 5 8            6 7       2 7 6         2 6 7           7 6
+--R           (768b d e  - 1536b c d e  + 768c d e )x + 192b d e  - 384b c d e
+--R         + 
+--R               2 8 5
+--R           192c d e
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ,
+--R
+--R                     4 9        4   8         3   2 7         2 2 3 6
+--R                 9A b e  + 15B b d e  + 120B b c d e  - 720B b c d e
+--R               + 
+--R                         3 4 5         4 5 4
+--R                 960B b c d e  - 384B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      4   8        4 2 7         3   3 6          2 2 4 5
+--R                 36A b d e  + 60B b d e  + 480B b c d e  - 2880B b c d e
+--R               + 
+--R                          3 5 4          4 6 3
+--R                 3840B b c d e  - 1536B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      4 2 7        4 3 6         3   4 5          2 2 5 4
+--R                 54A b d e  + 90B b d e  + 720B b c d e  - 4320B b c d e
+--R               + 
+--R                          3 6 3          4 7 2
+--R                 5760B b c d e  - 2304B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      4 3 6        4 4 5         3   5 4          2 2 6 3
+--R                 36A b d e  + 60B b d e  + 480B b c d e  - 2880B b c d e
+--R               + 
+--R                          3 7 2          4 8
+--R                 3840B b c d e  - 1536B c d e
+--R            *
+--R               x
+--R           + 
+--R                 4 4 5        4 5 4         3   6 3         2 2 7 2
+--R             9A b d e  + 15B b d e  + 120B b c d e  - 720B b c d e
+--R           + 
+--R                     3 8          4 9
+--R             960B b c d e - 384B c d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                    2   2 6            2 3 5         3 4 4  4
+--R             (768B b c d e  - 1536B b c d e  + 768B c d e )x
+--R           + 
+--R                     2   3 5            2 4 4          3 5 3  3
+--R             (3072B b c d e  - 6144B b c d e  + 3072B c d e )x
+--R           + 
+--R                     2   4 4            2 5 3          3 6 2  2
+--R             (4608B b c d e  - 9216B b c d e  + 4608B c d e )x
+--R           + 
+--R                     2   5 3            2 6 2          3 7            2   6 2
+--R             (3072B b c d e  - 6144B b c d e  + 3072B c d e)x + 768B b c d e
+--R           + 
+--R                        2 7          3 8
+--R             - 1536B b c d e + 768B c d
+--R        *
+--R                                        +----------+
+--R            +--------------+            |   2
+--R            |             2  +---+     \|c x  + b x
+--R           \|- b d e + c d  \|- c atan(-------------)
+--R                                            +---+
+--R                                          x\|- c
+--R       + 
+--R                      3 8         2         3    7
+--R                 18A b e  + (12A b c + 30B b )d e
+--R               + 
+--R                            2         2   2 6         3            2  3 5
+--R                 (- 144A b c  - 764B b c)d e  + (96A c  + 1552B b c )d e
+--R               + 
+--R                         3 4 4
+--R                 - 800B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      3   7            2          3  2 6
+--R                 66A b d e  + (- 264A b c - 146B b )d e
+--R               + 
+--R                          2          2   3 5            2 4 4          3 5 3
+--R                 (144A b c  - 1096B b c)d e  + 2960B b c d e  - 1664B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 6         2          3  3 5         2   4 4
+--R                 - 66A b d e  + (12A b c - 110B b )d e  - 860B b c d e
+--R               + 
+--R                          2 5 3          3 6 2
+--R                 2368B b c d e  - 1344B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 5        3 4 4         2   5 3           2 6 2
+--R             - 18A b d e  - 30B b d e  - 240B b c d e  + 672B b c d e
+--R           + 
+--R                     3 7
+--R             - 384B c d e
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                2 2 11           3 10       2 4 9  4
+--R           (384b d e   - 768b c d e   + 384c d e )x
+--R         + 
+--R                 2 3 10            4 9        2 5 8  3
+--R           (1536b d e   - 3072b c d e  + 1536c d e )x
+--R         + 
+--R                 2 4 9            5 8        2 6 7  2
+--R           (2304b d e  - 4608b c d e  + 2304c d e )x
+--R         + 
+--R                 2 5 8            6 7        2 7 6         2 6 7           7 6
+--R           (1536b d e  - 3072b c d e  + 1536c d e )x + 384b d e  - 768b c d e
+--R         + 
+--R               2 8 5
+--R           384c d e
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                       4 9        4   8         3   2 7         2 2 3 6
+--R                 - 9A b e  - 15B b d e  - 120B b c d e  + 720B b c d e
+--R               + 
+--R                           3 4 5         4 5 4
+--R                 - 960B b c d e  + 384B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                        4   8        4 2 7         3   3 6          2 2 4 5
+--R                 - 36A b d e  - 60B b d e  - 480B b c d e  + 2880B b c d e
+--R               + 
+--R                            3 5 4          4 6 3
+--R                 - 3840B b c d e  + 1536B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        4 2 7        4 3 6         3   4 5          2 2 5 4
+--R                 - 54A b d e  - 90B b d e  - 720B b c d e  + 4320B b c d e
+--R               + 
+--R                            3 6 3          4 7 2
+--R                 - 5760B b c d e  + 2304B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4 3 6        4 4 5         3   5 4          2 2 6 3
+--R                 - 36A b d e  - 60B b d e  - 480B b c d e  + 2880B b c d e
+--R               + 
+--R                            3 7 2          4 8
+--R                 - 3840B b c d e  + 1536B c d e
+--R            *
+--R               x
+--R           + 
+--R                   4 4 5        4 5 4         3   6 3         2 2 7 2
+--R             - 9A b d e  - 15B b d e  - 120B b c d e  + 720B b c d e
+--R           + 
+--R                       3 8          4 9
+--R             - 960B b c d e + 384B c d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                    2   2 6           2 3 5         3 4 4  4
+--R             (384B b c d e  - 768B b c d e  + 384B c d e )x
+--R           + 
+--R                     2   3 5            2 4 4          3 5 3  3
+--R             (1536B b c d e  - 3072B b c d e  + 1536B c d e )x
+--R           + 
+--R                     2   4 4            2 5 3          3 6 2  2
+--R             (2304B b c d e  - 4608B b c d e  + 2304B c d e )x
+--R           + 
+--R                     2   5 3            2 6 2          3 7            2   6 2
+--R             (1536B b c d e  - 3072B b c d e  + 1536B c d e)x + 384B b c d e
+--R           + 
+--R                       2 7          3 8
+--R             - 768B b c d e + 384B c d
+--R        *
+--R                                      +----------+
+--R                  +------------+      |   2
+--R            +---+ |           2      \|c x  + b x
+--R           \|- c \|b d e - c d  atan(-------------)
+--R                                          +---+
+--R                                        x\|- c
+--R       + 
+--R                     3 8        2         3    7             2         2   2 6
+--R                 9A b e  + (6A b c + 15B b )d e  + (- 72A b c  - 382B b c)d e
+--R               + 
+--R                       3           2  3 5         3 4 4
+--R                 (48A c  + 776B b c )d e  - 400B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      3   7            2         3  2 6
+--R                 33A b d e  + (- 132A b c - 73B b )d e
+--R               + 
+--R                         2         2   3 5            2 4 4         3 5 3
+--R                 (72A b c  - 548B b c)d e  + 1480B b c d e  - 832B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 6        2         3  3 5         2   4 4
+--R                 - 33A b d e  + (6A b c - 55B b )d e  - 430B b c d e
+--R               + 
+--R                          2 5 3         3 6 2
+--R                 1184B b c d e  - 672B c d e
+--R            *
+--R               x
+--R           + 
+--R                 3 3 5        3 4 4         2   5 3           2 6 2         3 7
+--R           - 9A b d e  - 15B b d e  - 120B b c d e  + 336B b c d e  - 192B c d e
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                2 2 11           3 10       2 4 9  4
+--R           (192b d e   - 384b c d e   + 192c d e )x
+--R         + 
+--R                2 3 10            4 9       2 5 8  3
+--R           (768b d e   - 1536b c d e  + 768c d e )x
+--R         + 
+--R                 2 4 9            5 8        2 6 7  2
+--R           (1152b d e  - 2304b c d e  + 1152c d e )x
+--R         + 
+--R                2 5 8            6 7       2 7 6         2 6 7           7 6
+--R           (768b d e  - 1536b c d e  + 768c d e )x + 192b d e  - 384b c d e
+--R         + 
+--R               2 8 5
+--R           192c d e
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 410
+
+--S 411 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                                    +--------------+
+--R                2   2 2           2 3          3 4  |             2
+--R         (128B b c d e  - 256B b c d e + 128B c d )\|- b d e + c d
+--R      *
+--R                                         +----------+
+--R          +-----------+ +-+ +-+      +-+ |   2
+--R         \|- b e + c d \|c \|d log(2\|c \|c x  + b x  + 2c x + b)
+--R     + 
+--R               4 5       4   4        3   2 3         2 2 3 2           3 4
+--R           3A b e  + 5B b d e  + 40B b c d e  - 240B b c d e  + 320B b c d e
+--R         + 
+--R                   4 5
+--R           - 128B c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                                      +--------------+
+--R                  2   2 2           2 3          3 4  |             2
+--R         (- 256B b c d e  + 512B b c d e - 256B c d )\|- b d e + c d
+--R      *
+--R                                           +-+
+--R          +-----------+ +-+ +-+          x\|c
+--R         \|- b e + c d \|c \|d atanh(-------------)
+--R                                      +----------+
+--R                                      |   2
+--R                                     \|c x  + b x
+--R     + 
+--R               4 5       4   4        3   2 3         2 2 3 2           3 4
+--R           3A b e  + 5B b d e  + 40B b c d e  - 240B b c d e  + 320B b c d e
+--R         + 
+--R                   4 5
+--R           - 128B c d
+--R      *
+--R          +--------------+
+--R          |             2              (b e - 2c d)x - b d
+--R         \|- b d e + c d  atanh(--------------------------------)
+--R                                                    +----------+
+--R                                  +-----------+ +-+ |   2
+--R                                2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                           +--------------+
+--R          2 2 7           3 6       2 4 5  |             2  +-----------+ +-+
+--R     (128b d e  - 256b c d e  + 128c d e )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 411
+
+--S 412 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 412
+
+--S 413 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                2   2 2           2 3          3 4  +-----------+ +-+ +-+
+--R         (128B b c d e  - 256B b c d e + 128B c d )\|- b e + c d \|c \|d
+--R      *
+--R          +------------+          +----------+
+--R          |           2       +-+ |   2
+--R         \|b d e - c d  log(2\|c \|c x  + b x  + 2c x + b)
+--R     + 
+--R                  2   2 2           2 3          3 4  +-----------+ +-+ +-+
+--R         (- 256B b c d e  + 512B b c d e - 256B c d )\|- b e + c d \|c \|d
+--R      *
+--R          +------------+            +-+
+--R          |           2           x\|c
+--R         \|b d e - c d  atanh(-------------)
+--R                               +----------+
+--R                               |   2
+--R                              \|c x  + b x
+--R     + 
+--R               4 5       4   4        3   2 3         2 2 3 2           3 4
+--R           3A b e  + 5B b d e  + 40B b c d e  - 240B b c d e  + 320B b c d e
+--R         + 
+--R                   4 5
+--R           - 128B c d
+--R      *
+--R          +------------+
+--R          |           2              (b e - 2c d)x - b d
+--R         \|b d e - c d  atanh(--------------------------------)
+--R                                                  +----------+
+--R                                +-----------+ +-+ |   2
+--R                              2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                 4 5        4   4        3   2 3         2 2 3 2           3 4
+--R           - 6A b e  - 10B b d e  - 80B b c d e  + 480B b c d e  - 640B b c d e
+--R         + 
+--R                 4 5
+--R           256B c d
+--R      *
+--R                                 +------------+ +----------+
+--R                                 |           2  |   2
+--R          +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|d atan(----------------------------)
+--R                                        (b e - c d)x
+--R  /
+--R                                                             +------------+
+--R          2 2 7           3 6       2 4 5  +-----------+ +-+ |           2
+--R     (128b d e  - 256b c d e  + 128c d e )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 413
+
+--S 414 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 414
+
+)clear all
+
+--S 415 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^6
+--R 
+--R
+--R                                                 +----------+
+--R                      3               2          |   2
+--R                (B c x  + (A c + B b)x  + A b x)\|c x  + b x
+--R   (1)  -------------------------------------------------------------
+--R         6 6       5 5      2 4 4      3 3 3      4 2 2     5       6
+--R        e x  + 6d e x  + 15d e x  + 20d e x  + 15d e x  + 6d e x + d
+--R                                                    Type: Expression(Integer)
+--E 415
+
+--S 416 of 1457
+r0:=-1/5*(4*B*d+A*e+5*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^5)-_
+     3/256*b^4*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_
+     (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_
+     1/80*(A*e*(4*c^2*d^2-4*b*c*d*e-b^2*e^2)+B*d*(16*c^2*d^2-26*b*c*d*e+_
+     11*b^2*e^2))*sqrt(b*x+c*x^2)/(d*e^4*(c*d-b*e)*(d+e*x)^3)+1/320*_
+     (A*e*(16*c^3*d^3-24*b*c^2*d^2*e-2*b^2*c*d*e^2+5*b^3*e^3)+B*d*_
+     (64*c^3*d^3-136*b*c^2*d^2*e+72*b^2*c*d*e^2+5*b^3*e^3))*_
+     sqrt(b*x+c*x^2)/(d^2*e^4*(c*d-b*e)^2*(d+e*x)^2)+1/640*(B*d*_
+     (128*c^4*d^4-336*b*c^3*d^3*e+248*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-_
+     15*b^4*e^4)+A*e*(32*c^4*d^4-64*b*c^3*d^3*e+12*b^2*c^2*d^2*e^2+_
+     20*b^3*c*d*e^3-15*b^4*e^4))*sqrt(b*x+c*x^2)/(d^3*e^4*(c*d-b*e)^3*_
+     (d+e*x))-3/40*(B*d*(8*c*d-b*e)+A*e*(2*c*d+b*e)+2*e*(8*B*c*d-_
+     5*b*B*e+2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x)^4)
+--R 
+--R
+--R   (2)
+--R                   5 6         4         5    5  5
+--R           (- 15A b e  + (30A b c - 15B b )d e )x
+--R         + 
+--R                   5   5          4         5  2 4  4
+--R           (- 75A b d e  + (150A b c - 75B b )d e )x
+--R         + 
+--R                    5 2 4          4          5  3 3  3
+--R           (- 150A b d e  + (300A b c - 150B b )d e )x
+--R         + 
+--R                    5 3 3          4          5  4 2  2
+--R           (- 150A b d e  + (300A b c - 150B b )d e )x
+--R         + 
+--R                   5 4 2          4         5  5           5 5
+--R           (- 75A b d e  + (150A b c - 75B b )d e)x - 15A b d e
+--R         + 
+--R                 4         5  6
+--R           (30A b c - 15B b )d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                    4 5           3         4    4           2 2        3   2 3
+--R               30A b e  + (- 40A b c + 30B b )d e  + (- 24A b c  + 20B b c)d e
+--R             + 
+--R                      3         2 2  3 2           4           3  4          4 5
+--R             (128A b c  - 496B b c )d e  + (- 64A c  + 672B b c )d e - 256B c d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                     4   4            3          4  2 3
+--R               140A b d e  + (- 188A b c + 140B b )d e
+--R             + 
+--R                        2 2         3   3 2            3          2 2  4
+--R               (- 184A b c  - 932B b c)d e  + (672A b c  + 1024B b c )d e
+--R             + 
+--R                        4           3  5
+--R               (- 320A c  - 352B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                     4 2 3            3          4  3 2
+--R               256A b d e  + (- 932A b c - 256B b )d e
+--R             + 
+--R                       2 2        3   4               3        2 2  5
+--R               (1336A b c  + 92B b c)d e + (- 480A b c  - 16B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    4 3 2          3          4  4            2 2        3   5
+--R           (- 140A b d e  + (300A b c - 140B b )d e + (- 40A b c  + 20B b c)d )x
+--R         + 
+--R                  4 4          3         4  5
+--R           - 30A b d e + (60A b c - 30B b )d
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R               3 3 8        2   4 7          2 5 6        3 6 5  5
+--R         (1280b d e  - 3840b c d e  + 3840b c d e  - 1280c d e )x
+--R       + 
+--R               3 4 7         2   5 6           2 6 5        3 7 4  4
+--R         (6400b d e  - 19200b c d e  + 19200b c d e  - 6400c d e )x
+--R       + 
+--R                3 5 6         2   6 5           2 7 4         3 8 3  3
+--R         (12800b d e  - 38400b c d e  + 38400b c d e  - 12800c d e )x
+--R       + 
+--R                3 6 5         2   7 4           2 8 3         3 9 2  2
+--R         (12800b d e  - 38400b c d e  + 38400b c d e  - 12800c d e )x
+--R       + 
+--R               3 7 4         2   8 3           2 9 2        3 10           3 8 3
+--R         (6400b d e  - 19200b c d e  + 19200b c d e  - 6400c d  e)x + 1280b d e
+--R       + 
+--R                2   9 2          2 10         3 11
+--R         - 3840b c d e  + 3840b c d  e - 1280c d
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 416
+
+--S 417 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                   5 6           4         5    5  5
+--R             (15A b e  + (- 30A b c + 15B b )d e )x
+--R           + 
+--R                   5   5            4         5  2 4  4
+--R             (75A b d e  + (- 150A b c + 75B b )d e )x
+--R           + 
+--R                    5 2 4            4          5  3 3  3
+--R             (150A b d e  + (- 300A b c + 150B b )d e )x
+--R           + 
+--R                    5 3 3            4          5  4 2  2
+--R             (150A b d e  + (- 300A b c + 150B b )d e )x
+--R           + 
+--R                   5 4 2            4         5  5           5 5
+--R             (75A b d e  + (- 150A b c + 75B b )d e)x + 15A b d e
+--R           + 
+--R                     4         5  6
+--R             (- 30A b c + 15B b )d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                      4 5           3         4    4
+--R                 30A b e  + (- 40A b c + 30B b )d e
+--R               + 
+--R                         2 2        3   2 3            3         2 2  3 2
+--R                 (- 24A b c  + 20B b c)d e  + (128A b c  - 496B b c )d e
+--R               + 
+--R                         4           3  4          4 5
+--R                 (- 64A c  + 672B b c )d e - 256B c d
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                       4   4            3          4  2 3
+--R                 140A b d e  + (- 188A b c + 140B b )d e
+--R               + 
+--R                          2 2         3   3 2            3          2 2  4
+--R                 (- 184A b c  - 932B b c)d e  + (672A b c  + 1024B b c )d e
+--R               + 
+--R                          4           3  5
+--R                 (- 320A c  - 352B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                       4 2 3            3          4  3 2
+--R                 256A b d e  + (- 932A b c - 256B b )d e
+--R               + 
+--R                         2 2        3   4               3        2 2  5
+--R                 (1336A b c  + 92B b c)d e + (- 480A b c  - 16B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         4 3 2          3          4  4
+--R                 - 140A b d e  + (300A b c - 140B b )d e
+--R               + 
+--R                         2 2        3   5
+--R                 (- 40A b c  + 20B b c)d
+--R            *
+--R               x
+--R           + 
+--R                    4 4          3         4  5
+--R             - 30A b d e + (60A b c - 30B b )d
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                 3 3 8        2   4 7          2 5 6        3 6 5  5
+--R           (1280b d e  - 3840b c d e  + 3840b c d e  - 1280c d e )x
+--R         + 
+--R                 3 4 7         2   5 6           2 6 5        3 7 4  4
+--R           (6400b d e  - 19200b c d e  + 19200b c d e  - 6400c d e )x
+--R         + 
+--R                  3 5 6         2   6 5           2 7 4         3 8 3  3
+--R           (12800b d e  - 38400b c d e  + 38400b c d e  - 12800c d e )x
+--R         + 
+--R                  3 6 5         2   7 4           2 8 3         3 9 2  2
+--R           (12800b d e  - 38400b c d e  + 38400b c d e  - 12800c d e )x
+--R         + 
+--R                 3 7 4         2   8 3           2 9 2        3 10
+--R           (6400b d e  - 19200b c d e  + 19200b c d e  - 6400c d  e)x
+--R         + 
+--R                3 8 3        2   9 2          2 10         3 11
+--R           1280b d e  - 3840b c d e  + 3840b c d  e - 1280c d
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                     5 6         4         5    5  5
+--R             (- 15A b e  + (30A b c - 15B b )d e )x
+--R           + 
+--R                     5   5          4         5  2 4  4
+--R             (- 75A b d e  + (150A b c - 75B b )d e )x
+--R           + 
+--R                      5 2 4          4          5  3 3  3
+--R             (- 150A b d e  + (300A b c - 150B b )d e )x
+--R           + 
+--R                      5 3 3          4          5  4 2  2
+--R             (- 150A b d e  + (300A b c - 150B b )d e )x
+--R           + 
+--R                     5 4 2          4         5  5           5 5
+--R             (- 75A b d e  + (150A b c - 75B b )d e)x - 15A b d e
+--R           + 
+--R                   4         5  6
+--R             (30A b c - 15B b )d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                      4 5           3         4    4
+--R                 15A b e  + (- 20A b c + 15B b )d e
+--R               + 
+--R                         2 2        3   2 3           3         2 2  3 2
+--R                 (- 12A b c  + 10B b c)d e  + (64A b c  - 248B b c )d e
+--R               + 
+--R                         4           3  4          4 5
+--R                 (- 32A c  + 336B b c )d e - 128B c d
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      4   4           3         4  2 3
+--R                 70A b d e  + (- 94A b c + 70B b )d e
+--R               + 
+--R                         2 2         3   3 2            3         2 2  4
+--R                 (- 92A b c  - 466B b c)d e  + (336A b c  + 512B b c )d e
+--R               + 
+--R                          4           3  5
+--R                 (- 160A c  - 176B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                       4 2 3            3          4  3 2
+--R                 128A b d e  + (- 466A b c - 128B b )d e
+--R               + 
+--R                        2 2        3   4               3       2 2  5
+--R                 (668A b c  + 46B b c)d e + (- 240A b c  - 8B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     4 3 2          3         4  4            2 2        3   5
+--R             (- 70A b d e  + (150A b c - 70B b )d e + (- 20A b c  + 10B b c)d )x
+--R           + 
+--R                    4 4          3         4  5
+--R             - 15A b d e + (30A b c - 15B b )d
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                3 3 8        2   4 7          2 5 6       3 6 5  5
+--R           (640b d e  - 1920b c d e  + 1920b c d e  - 640c d e )x
+--R         + 
+--R                 3 4 7        2   5 6          2 6 5        3 7 4  4
+--R           (3200b d e  - 9600b c d e  + 9600b c d e  - 3200c d e )x
+--R         + 
+--R                 3 5 6         2   6 5           2 7 4        3 8 3  3
+--R           (6400b d e  - 19200b c d e  + 19200b c d e  - 6400c d e )x
+--R         + 
+--R                 3 6 5         2   7 4           2 8 3        3 9 2  2
+--R           (6400b d e  - 19200b c d e  + 19200b c d e  - 6400c d e )x
+--R         + 
+--R                 3 7 4        2   8 3          2 9 2        3 10          3 8 3
+--R           (3200b d e  - 9600b c d e  + 9600b c d e  - 3200c d  e)x + 640b d e
+--R         + 
+--R                  2   9 2          2 10        3 11
+--R           - 1920b c d e  + 1920b c d  e - 640c d
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 417
+
+--S 418 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R              5           4        5    +-----------+ +-+
+--R         (3A b e + (- 6A b c + 3B b )d)\|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                        +--------------+
+--R              5           4        5    |             2
+--R         (3A b e + (- 6A b c + 3B b )d)\|- b d e + c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                                        +--------------+
+--R            3 3 3       2   4 2         2 5        3 6  |             2
+--R       (256b d e  - 768b c d e  + 768b c d e - 256c d )\|- b d e + c d
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 418
+
+--S 419 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 419
+
+--S 420 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                        +------------+
+--R              5           4        5    |           2
+--R         (3A b e + (- 6A b c + 3B b )d)\|b d e - c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                5          4        5    +-----------+ +-+
+--R         (- 6A b e + (12A b c - 6B b )d)\|- b e + c d \|d
+--R      *
+--R               +------------+ +----------+
+--R               |           2  |   2
+--R              \|b d e - c d  \|c x  + b x
+--R         atan(----------------------------)
+--R                      (b e - c d)x
+--R  /
+--R            3 3 3       2   4 2         2 5        3 6  +-----------+ +-+
+--R       (256b d e  - 768b c d e  + 768b c d e - 256c d )\|- b e + c d \|d
+--R    *
+--R        +------------+
+--R        |           2
+--R       \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 420
+
+--S 421 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 421
+
+)clear all
+
+--S 422 of 1457
+t0:=(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(5/2)
+--R 
+--R
+--R   (1)
+--R          2 2 7        2           2       2     6
+--R       B c e x  + ((A c  + 2B b c)e  + 2B c d e)x
+--R     + 
+--R                     2  2        2                   2 2  5
+--R       ((2A b c + B b )e  + (2A c  + 4B b c)d e + B c d )x
+--R     + 
+--R           2 2                 2           2           2  4
+--R       (A b e  + (4A b c + 2B b )d e + (A c  + 2B b c)d )x
+--R     + 
+--R            2                   2  2  3      2 2 2
+--R       (2A b d e + (2A b c + B b )d )x  + A b d x
+--R  *
+--R      +----------+
+--R      |   2
+--R     \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 422
+
+--S 423 of 1457
+r0:=1/768*b*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_
+     (B*d+2*A*e))*x^2*(b*x+c*x^2)^(3/2)/c^3+1/384*(64*A*c^3*d^2-11*b^3*_
+     B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*(b*x+_
+     c*x^2)^(5/2)/c^3+1/2016*(162*A*c*e*(2*c*d-b*e)+B*(64*c^2*d^2-_
+     226*b*c*d*e+99*b^2*e^2))*(b*x+c*x^2)^(7/2)/c^3+1/9*B*(d+e*x)^2*_
+     (b*x+c*x^2)^(7/2)/c-1/144*e*((7*b*B-18*A*c)*d-(4*B*c*d-11*b*B*e+_
+     18*A*c*e)*x)*(b*x+c*x^2)^(7/2)/c^2-5/32768*b^6*(64*A*c^3*d^2-_
+     11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_
+     atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)+5/32768*b^5*(64*A*c^3*_
+     d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*_
+     sqrt(b*x+c*x^2)/c^6-5/49152*b^4*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*_
+     c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*x*sqrt(b*x+c*x^2)/c^5+_
+     1/12288*b^3*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-_
+     32*b*c^2*d*(B*d+2*A*e))*x^2*sqrt(b*x+c*x^2)/c^4+1/2048*b^2*_
+     (64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*_
+     (B*d+2*A*e))*x^3*sqrt(b*x+c*x^2)/c^3
+--R 
+--R
+--R   (2)
+--R                     8           9  2            7 2           8
+--R           (- 5670A b c + 3465B b )e  + (20160A b c  - 11340B b c)d e
+--R         + 
+--R                      6 3           7 2  2
+--R           (- 20160A b c  + 10080B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                    8 2 8              8              7  2            8     7
+--R           229376B c e x  + ((258048A c  + 530432B b c )e  + 516096B c d e)x
+--R         + 
+--R                           7            2 6  2             8               7
+--R               (608256A b c  + 316416B b c )e  + (589824A c  + 1216512B b c )d e
+--R             + 
+--R                        8 2
+--R               294912B c d
+--R          *
+--R              6
+--R             x
+--R         + 
+--R                         2 6          3 5  2                7            2 6
+--R               (373248A b c  + 1280B b c )e  + (1425408A b c  + 746496B b c )d e
+--R             + 
+--R                         8              7  2
+--R               (344064A c  + 712704B b c )d
+--R          *
+--R              5
+--R             x
+--R         + 
+--R                       3 5          4 4  2             2 6          3 5
+--R               (2304A b c  - 1408B b c )e  + (909312A b c  + 4608B b c )d e
+--R             + 
+--R                           7            2 6  2
+--R               (860160A b c  + 454656B b c )d
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                         4 4          5 3  2           3 5          4 4
+--R               (- 2592A b c  + 1584B b c )e  + (9216A b c  - 5184B b c )d e
+--R             + 
+--R                         2 6          3 5  2
+--R               (580608A b c  + 4608B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                       5 3          6 2  2              4 4          5 3
+--R               (3024A b c  - 1848B b c )e  + (- 10752A b c  + 6048B b c )d e
+--R             + 
+--R                        3 5          4 4  2
+--R               (10752A b c  - 5376B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                         6 2          7   2            5 3          6 2
+--R               (- 3780A b c  + 2310B b c)e  + (13440A b c  - 7560B b c )d e
+--R             + 
+--R                          4 4          5 3  2
+--R               (- 13440A b c  + 6720B b c )d
+--R          *
+--R             x
+--R         + 
+--R                   7           8  2              6 2           7
+--R           (5670A b c - 3465B b )e  + (- 20160A b c  + 11340B b c)d e
+--R         + 
+--R                    5 3           6 2  2
+--R           (20160A b c  - 10080B b c )d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R             6 +-+
+--R     2064384c \|c
+--R                                                    Type: Expression(Integer)
+--E 423
+
+--S 424 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                       8           9  2            7 2           8
+--R             (- 5670A b c + 3465B b )e  + (20160A b c  - 11340B b c)d e
+--R           + 
+--R                        6 3           7 2  2
+--R             (- 20160A b c  + 10080B b c )d
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                      8 2 8
+--R             458752B c e x
+--R           + 
+--R                        8               7  2             8     7
+--R             ((516096A c  + 1060864B b c )e  + 1032192B c d e)x
+--R           + 
+--R                              7            2 6  2
+--R                 (1216512A b c  + 632832B b c )e
+--R               + 
+--R                            8               7                8 2
+--R                 (1179648A c  + 2433024B b c )d e + 589824B c d
+--R            *
+--R                6
+--R               x
+--R           + 
+--R                           2 6          3 5  2
+--R                 (746496A b c  + 2560B b c )e
+--R               + 
+--R                              7             2 6
+--R                 (2850816A b c  + 1492992B b c )d e
+--R               + 
+--R                           8               7  2
+--R                 (688128A c  + 1425408B b c )d
+--R            *
+--R                5
+--R               x
+--R           + 
+--R                         3 5          4 4  2              2 6          3 5
+--R                 (4608A b c  - 2816B b c )e  + (1818624A b c  + 9216B b c )d e
+--R               + 
+--R                              7            2 6  2
+--R                 (1720320A b c  + 909312B b c )d
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                           4 4          5 3  2            3 5           4 4
+--R                 (- 5184A b c  + 3168B b c )e  + (18432A b c  - 10368B b c )d e
+--R               + 
+--R                            2 6          3 5  2
+--R                 (1161216A b c  + 9216B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         5 3          6 2  2              4 4           5 3
+--R                 (6048A b c  - 3696B b c )e  + (- 21504A b c  + 12096B b c )d e
+--R               + 
+--R                          3 5           4 4  2
+--R                 (21504A b c  - 10752B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                           6 2          7   2            5 3           6 2
+--R                 (- 7560A b c  + 4620B b c)e  + (26880A b c  - 15120B b c )d e
+--R               + 
+--R                            4 4           5 3  2
+--R                 (- 26880A b c  + 13440B b c )d
+--R            *
+--R               x
+--R           + 
+--R                      7           8  2              6 2           7
+--R             (11340A b c - 6930B b )e  + (- 40320A b c  + 22680B b c)d e
+--R           + 
+--R                      5 3           6 2  2
+--R             (40320A b c  - 20160B b c )d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R               6 +-+
+--R       4128768c \|c
+--R     ,
+--R
+--R                       8           9  2            7 2           8
+--R             (- 5670A b c + 3465B b )e  + (20160A b c  - 11340B b c)d e
+--R           + 
+--R                        6 3           7 2  2
+--R             (- 20160A b c  + 10080B b c )d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                      8 2 8              8              7  2            8     7
+--R             229376B c e x  + ((258048A c  + 530432B b c )e  + 516096B c d e)x
+--R           + 
+--R                             7            2 6  2
+--R                 (608256A b c  + 316416B b c )e
+--R               + 
+--R                           8               7                8 2
+--R                 (589824A c  + 1216512B b c )d e + 294912B c d
+--R            *
+--R                6
+--R               x
+--R           + 
+--R                           2 6          3 5  2
+--R                 (373248A b c  + 1280B b c )e
+--R               + 
+--R                            7            2 6                 8              7  2
+--R               (1425408A b c  + 746496B b c )d e + (344064A c  + 712704B b c )d
+--R            *
+--R                5
+--R               x
+--R           + 
+--R                         3 5          4 4  2             2 6          3 5
+--R                 (2304A b c  - 1408B b c )e  + (909312A b c  + 4608B b c )d e
+--R               + 
+--R                             7            2 6  2
+--R                 (860160A b c  + 454656B b c )d
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                           4 4          5 3  2           3 5          4 4
+--R                 (- 2592A b c  + 1584B b c )e  + (9216A b c  - 5184B b c )d e
+--R               + 
+--R                           2 6          3 5  2
+--R                 (580608A b c  + 4608B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         5 3          6 2  2              4 4          5 3
+--R                 (3024A b c  - 1848B b c )e  + (- 10752A b c  + 6048B b c )d e
+--R               + 
+--R                          3 5          4 4  2
+--R                 (10752A b c  - 5376B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                           6 2          7   2            5 3          6 2
+--R                 (- 3780A b c  + 2310B b c)e  + (13440A b c  - 7560B b c )d e
+--R               + 
+--R                            4 4          5 3  2
+--R                 (- 13440A b c  + 6720B b c )d
+--R            *
+--R               x
+--R           + 
+--R                     7           8  2              6 2           7
+--R             (5670A b c - 3465B b )e  + (- 20160A b c  + 11340B b c)d e
+--R           + 
+--R                      5 3           6 2  2
+--R             (20160A b c  - 10080B b c )d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R               6 +---+
+--R       2064384c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 424
+
+--S 425 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                   8         9  2          7 2         8
+--R           (- 90A b c + 55B b )e  + (320A b c  - 180B b c)d e
+--R         + 
+--R                    6 3         7 2  2
+--R           (- 320A b c  + 160B b c )d
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                  8          9  2            7 2         8
+--R           (180A b c - 110B b )e  + (- 640A b c  + 360B b c)d e
+--R         + 
+--R                  6 3         7 2  2
+--R           (640A b c  - 320B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R  /
+--R           6 +-+
+--R     65536c \|c
+--R                                                    Type: Expression(Integer)
+--E 425
+
+--S 426 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 426
+
+--S 427 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                 8         9  2            7 2         8
+--R           (90A b c - 55B b )e  + (- 320A b c  + 180B b c)d e
+--R         + 
+--R                  6 3         7 2  2
+--R           (320A b c  - 160B b c )d
+--R      *
+--R                           +-+
+--R          +---+          x\|c
+--R         \|- c atanh(-------------)
+--R                      +----------+
+--R                      |   2
+--R                     \|c x  + b x
+--R     + 
+--R                   8         9  2          7 2         8
+--R           (- 90A b c + 55B b )e  + (320A b c  - 180B b c)d e
+--R         + 
+--R                    6 3         7 2  2
+--R           (- 320A b c  + 160B b c )d
+--R      *
+--R                         +----------+
+--R                   +---+ |   2
+--R          +-+     \|- c \|c x  + b x
+--R         \|c atan(-------------------)
+--R                          c x
+--R  /
+--R           6 +---+ +-+
+--R     32768c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 427
+
+--S 428 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 428
+
+)clear all
+
+--S 429 of 1457
+t0:=(A+B*x)*(d+e*x)*(b*x+c*x^2)^(5/2)
+--R 
+--R
+--R   (1)
+--R          2   6        2                 2   5
+--R       B c e x  + ((A c  + 2B b c)e + B c d)x
+--R     + 
+--R                     2         2             4       2                 2    3
+--R       ((2A b c + B b )e + (A c  + 2B b c)d)x  + (A b e + (2A b c + B b )d)x
+--R     + 
+--R          2   2
+--R       A b d x
+--R  *
+--R      +----------+
+--R      |   2
+--R     \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 429
+
+--S 430 of 1457
+r0:=1/384*b*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*_
+     (b*x+c*x^2)^(3/2)/c^2+1/192*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*_
+     x*(b*x+c*x^2)^(5/2)/c^2+1/112*(2*B*c*d-9*b*B*e+16*A*c*e)*_
+     (b*x+c*x^2)^(7/2)/c^2+1/8*B*(d+e*x)*(b*x+c*x^2)^(7/2)/c-_
+     5/16384*b^6*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*atanh(x*_
+     sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+5/16384*b^5*(32*A*c^2*d+9*b^2*B*e-_
+     16*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/c^5-5/24576*b^4*(32*A*c^2*d+_
+     9*b^2*B*e-16*b*c*(B*d+A*e))*x*sqrt(b*x+c*x^2)/c^4+1/6144*b^3*_
+     (32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^2*sqrt(b*x+c*x^2)/c^3+_
+     1/1024*b^2*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*x^3*_
+     sqrt(b*x+c*x^2)/c^2
+--R 
+--R
+--R   (2)
+--R                  7          8               6 2          7
+--R         ((1680A b c - 945B b )e + (- 3360A b c  + 1680B b c)d)
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                   7   7             7              6             7   6
+--R           43008B c e x  + ((49152A c  + 101376B b c )e + 49152B c d)x
+--R         + 
+--R                        6           2 5              7              6    5
+--R           ((118784A b c  + 62208B b c )e + (57344A c  + 118784B b c )d)x
+--R         + 
+--R                     2 5         3 4                 6           2 5    4
+--R           ((75776A b c  + 384B b c )e + (143360A b c  + 75776B b c )d)x
+--R         + 
+--R                   3 4         4 3              2 5         3 4    3
+--R           ((768A b c  - 432B b c )e + (96768A b c  + 768B b c )d)x
+--R         + 
+--R                     4 3         5 2             3 4         4 3    2
+--R           ((- 896A b c  + 504B b c )e + (1792A b c  - 896B b c )d)x
+--R         + 
+--R                    5 2         6                4 3          5 2
+--R           ((1120A b c  - 630B b c)e + (- 2240A b c  + 1120B b c )d)x
+--R         + 
+--R                     6          7             5 2          6
+--R           (- 1680A b c + 945B b )e + (3360A b c  - 1680B b c)d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R            5 +-+
+--R     344064c \|c
+--R                                                    Type: Expression(Integer)
+--E 430
+
+--S 431 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                    7          8               6 2          7
+--R           ((1680A b c - 945B b )e + (- 3360A b c  + 1680B b c)d)
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                     7   7             7              6             7   6
+--R             86016B c e x  + ((98304A c  + 202752B b c )e + 98304B c d)x
+--R           + 
+--R                          6            2 5               7              6    5
+--R             ((237568A b c  + 124416B b c )e + (114688A c  + 237568B b c )d)x
+--R           + 
+--R                        2 5         3 4                 6            2 5    4
+--R             ((151552A b c  + 768B b c )e + (286720A b c  + 151552B b c )d)x
+--R           + 
+--R                      3 4         4 3               2 5          3 4    3
+--R             ((1536A b c  - 864B b c )e + (193536A b c  + 1536B b c )d)x
+--R           + 
+--R                        4 3          5 2             3 4          4 3    2
+--R             ((- 1792A b c  + 1008B b c )e + (3584A b c  - 1792B b c )d)x
+--R           + 
+--R                      5 2          6                4 3          5 2
+--R             ((2240A b c  - 1260B b c)e + (- 4480A b c  + 2240B b c )d)x
+--R           + 
+--R                       6           7             5 2          6
+--R             (- 3360A b c + 1890B b )e + (6720A b c  - 3360B b c)d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R              5 +-+
+--R       688128c \|c
+--R     ,
+--R
+--R                    7          8               6 2          7
+--R           ((1680A b c - 945B b )e + (- 3360A b c  + 1680B b c)d)
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                     7   7             7              6             7   6
+--R             43008B c e x  + ((49152A c  + 101376B b c )e + 49152B c d)x
+--R           + 
+--R                          6           2 5              7              6    5
+--R             ((118784A b c  + 62208B b c )e + (57344A c  + 118784B b c )d)x
+--R           + 
+--R                       2 5         3 4                 6           2 5    4
+--R             ((75776A b c  + 384B b c )e + (143360A b c  + 75776B b c )d)x
+--R           + 
+--R                     3 4         4 3              2 5         3 4    3
+--R             ((768A b c  - 432B b c )e + (96768A b c  + 768B b c )d)x
+--R           + 
+--R                       4 3         5 2             3 4         4 3    2
+--R             ((- 896A b c  + 504B b c )e + (1792A b c  - 896B b c )d)x
+--R           + 
+--R                      5 2         6                4 3          5 2
+--R             ((1120A b c  - 630B b c)e + (- 2240A b c  + 1120B b c )d)x
+--R           + 
+--R                       6          7             5 2          6
+--R             (- 1680A b c + 945B b )e + (3360A b c  - 1680B b c)d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R              5 +---+
+--R       344064c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 431
+
+--S 432 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                7         8              6 2        7
+--R         ((80A b c - 45B b )e + (- 160A b c  + 80B b c)d)
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                                                     +-+
+--R                 7         8            6 2         7              x\|c
+--R       ((- 160A b c + 90B b )e + (320A b c  - 160B b c)d)atanh(-------------)
+--R                                                                +----------+
+--R                                                                |   2
+--R                                                               \|c x  + b x
+--R  /
+--R           5 +-+
+--R     32768c \|c
+--R                                                    Type: Expression(Integer)
+--E 432
+
+--S 433 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 433
+
+--S 434 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                  7         8            6 2        7     +---+
+--R         ((- 80A b c + 45B b )e + (160A b c  - 80B b c)d)\|- c
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                7         8              6 2        7     +-+
+--R         ((80A b c - 45B b )e + (- 160A b c  + 80B b c)d)\|c
+--R      *
+--R                     +----------+
+--R               +---+ |   2
+--R              \|- c \|c x  + b x
+--R         atan(-------------------)
+--R                      c x
+--R  /
+--R           5 +---+ +-+
+--R     16384c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 434
+
+--S 435 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(5/2)
+--R 
+--R
+--R                                                                  +----------+
+--R            2 5       2           4                2  3      2 2  |   2
+--R   (1)  (B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 436
+
+--S 437 of 1457
+r0:=-1/24*b*(b*B-2*A*c)*x^2*(b*x+c*x^2)^(3/2)/c-1/12*(b*B-2*A*c)*x*_
+     (b*x+c*x^2)^(5/2)/c+1/7*B*(b*x+c*x^2)^(7/2)/c+5/1024*b^6*(b*B-_
+     2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-5/1024*b^5*(b*B-_
+     2*A*c)*sqrt(b*x+c*x^2)/c^4+5/1536*b^4*(b*B-2*A*c)*x*sqrt(b*x+_
+     c*x^2)/c^3-1/384*b^3*(b*B-2*A*c)*x^2*sqrt(b*x+c*x^2)/c^2-1/64*b^2*_
+     (b*B-2*A*c)*x^3*sqrt(b*x+c*x^2)/c
+--R 
+--R
+--R   (2)
+--R                                         +-+
+--R                6          7           x\|c
+--R       (- 210A b c + 105B b )atanh(-------------)
+--R                                    +----------+
+--R                                    |   2
+--R                                   \|c x  + b x
+--R     + 
+--R                  6 6           6            5  5             5          2 4  4
+--R           3072B c x  + (3584A c  + 7424B b c )x  + (8960A b c  + 4736B b c )x
+--R         + 
+--R                   2 4        3 3  3          3 3        4 2  2
+--R           (6048A b c  + 48B b c )x  + (112A b c  - 56B b c )x
+--R         + 
+--R                    4 2        5            5          6
+--R           (- 140A b c  + 70B b c)x + 210A b c - 105B b
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R           4 +-+
+--R     21504c \|c
+--R                                                    Type: Expression(Integer)
+--E 437
+
+--S 438 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                                      +----------+
+--R                6          7          |   2                     +-+
+--R         (210A b c - 105B b )log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                    6 6           6             5  5
+--R             6144B c x  + (7168A c  + 14848B b c )x
+--R           + 
+--R                        5          2 4  4            2 4        3 3  3
+--R             (17920A b c  + 9472B b c )x  + (12096A b c  + 96B b c )x
+--R           + 
+--R                    3 3         4 2  2            4 2         5            5
+--R             (224A b c  - 112B b c )x  + (- 280A b c  + 140B b c)x + 420A b c
+--R           + 
+--R                     6
+--R             - 210B b
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R             4 +-+
+--R       43008c \|c
+--R     ,
+--R
+--R                                           +----------+
+--R                                     +---+ |   2
+--R                  6          7      \|- c \|c x  + b x
+--R         (- 210A b c + 105B b )atan(-------------------)
+--R                                            c x
+--R       + 
+--R                    6 6           6            5  5
+--R             3072B c x  + (3584A c  + 7424B b c )x
+--R           + 
+--R                       5          2 4  4           2 4        3 3  3
+--R             (8960A b c  + 4736B b c )x  + (6048A b c  + 48B b c )x
+--R           + 
+--R                    3 3        4 2  2            4 2        5            5
+--R             (112A b c  - 56B b c )x  + (- 140A b c  + 70B b c)x + 210A b c
+--R           + 
+--R                     6
+--R             - 105B b
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R             4 +---+
+--R       21504c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 438
+
+--S 439 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                 +----------+
+--R             6        7          |   2                     +-+
+--R       (10A b c - 5B b )log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                     +-+
+--R             6         7           x\|c
+--R       (20A b c - 10B b )atanh(-------------)
+--R                                +----------+
+--R                                |   2
+--R                               \|c x  + b x
+--R  /
+--R          4 +-+
+--R     2048c \|c
+--R                                                    Type: Expression(Integer)
+--E 439
+
+--S 440 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 440
+
+--S 441 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                          +-+
+--R             6        7  +---+          x\|c
+--R       (10A b c - 5B b )\|- c atanh(-------------)
+--R                                     +----------+
+--R                                     |   2
+--R                                    \|c x  + b x
+--R     + 
+--R                                          +----------+
+--R                                    +---+ |   2
+--R               6        7  +-+     \|- c \|c x  + b x
+--R       (- 10A b c + 5B b )\|c atan(-------------------)
+--R                                           c x
+--R  /
+--R          4 +---+ +-+
+--R     1024c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 441
+
+--S 442 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 442
+
+)clear all
+
+--S 443 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)
+--R 
+--R
+--R                                                                  +----------+
+--R            2 5       2           4                2  3      2 2  |   2
+--R        (B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x )\|c x  + b x
+--R   (1)  ----------------------------------------------------------------------
+--R                                        e x + d
+--R                                                    Type: Expression(Integer)
+--E 443
+
+--S 444 of 1457
+r0:=1/192*(4*A*c*e*(16*c^2*d^2-22*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-_
+     88*b*c^2*d^2*e+12*b^2*c*d*e^2+5*b^3*e^3)-2*c*e*(12*A*c*e*(2*c*d-_
+     b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/_
+     (c^2*e^4)-1/60*(12*B*c*d-5*b*B*e-12*A*c*e-10*B*c*e*x)*(b*x+_
+     c*x^2)^(5/2)/(c*e^2)-1/512*(4*A*c*e*(256*c^5*d^5-640*b*c^4*d^4*e+_
+     480*b^2*c^3*d^3*e^2-80*b^3*c^2*d^2*e^3-10*b^4*c*d*e^4-3*b^5*e^5)-_
+     B*(1024*c^6*d^6-2560*b*c^5*d^5*e+1920*b^2*c^4*d^4*e^2-320*b^3*_
+     c^3*d^3*e^3-40*b^4*c^2*d^2*e^4-12*b^5*c*d*e^5-5*b^6*e^6))*_
+     atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(7/2)*e^7)-d^(5/2)*(B*d-A*e)*_
+     (c*d-b*e)^(5/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_
+     sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7+1/1536*(3*(4*A*c*e*(128*c^4*d^4-_
+     288*b*c^3*d^3*e+176*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-3*b^4*e^4)-_
+     B*(512*c^5*d^5-1152*b*c^4*d^4*e+704*b^2*c^3*d^3*e^2-40*b^3*c^2*_
+     d^2*e^3-12*b^4*c*d*e^4-5*b^5*e^5))-2*c*e*(8*b*c*d*e*(2*c*d-b*e)*_
+     (12*B*c*d-5*b*B*e-12*A*c*e)+(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2)*_
+     (12*A*c*e*(2*c*d-b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2)))*x)*_
+     sqrt(b*x+c*x^2)/(c^3*e^6)
+--R 
+--R
+--R   (2)
+--R                  5         6  6          4 2         5     5
+--R           (180A b c - 75B b )e  + (600A b c  - 180B b c)d e
+--R         + 
+--R                   3 3         4 2  2 4              2 4          3 3  3 3
+--R           (4800A b c  - 600B b c )d e  + (- 28800A b c  - 4800B b c )d e
+--R         + 
+--R                      5           2 4  4 2              6             5  5
+--R           (38400A b c  + 28800B b c )d e  + (- 15360A c  - 38400B b c )d e
+--R         + 
+--R                   6 6
+--R           15360B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                    2 3 2 3              4          2 3  3 2
+--R           - 7680A b c d e  + (15360A b c  + 7680B b c )d e
+--R         + 
+--R                     5             4  4           5 5
+--R           (- 7680A c  - 15360B b c )d e + 7680B c d
+--R      *
+--R          +-----------+ +-+ +-+             (b e - 2c d)x - b d
+--R         \|- b e + c d \|c \|d atanh(--------------------------------)
+--R                                                         +----------+
+--R                                       +-----------+ +-+ |   2
+--R                                     2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  5 6 5            5            4  6          5   5  4
+--R           1280B c e x  + ((1536A c  + 3200B b c )e  - 1536B c d e )x
+--R         + 
+--R                         4          2 3  6             5            4    5
+--R               (4032A b c  + 2160B b c )e  + (- 1920A c  - 4032B b c )d e
+--R             + 
+--R                      5 2 4
+--R               1920B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                       2 3        3 2  6               4          2 3    5
+--R               (2976A b c  + 40B b c )e  + (- 5440A b c  - 2976B b c )d e
+--R             + 
+--R                       5            4  2 4          5 3 3
+--R               (2560A c  + 5440B b c )d e  - 2560B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      3 2        4   6             2 3         3 2    5
+--R               (120A b c  - 50B b c)e  + (- 4720A b c  - 120B b c )d e
+--R             + 
+--R                         4          2 3  2 4             5            4  3 3
+--R               (8320A b c  + 4720B b c )d e  + (- 3840A c  - 8320B b c )d e
+--R             + 
+--R                      5 4 2
+--R               3840B c d e
+--R          *
+--R             x
+--R         + 
+--R                    4         5  6            3 2         4     5
+--R           (- 180A b c + 75B b )e  + (- 600A b c  + 180B b c)d e
+--R         + 
+--R                    2 3         3 2  2 4                4           2 3  3 3
+--R           (10560A b c  + 600B b c )d e  + (- 17280A b c  - 10560B b c )d e
+--R         + 
+--R                   5             4  4 2          5 5
+--R           (7680A c  + 17280B b c )d e  - 7680B c d e
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R          3 7 +-+
+--R     7680c e \|c
+--R                                                    Type: Expression(Integer)
+--E 444
+
+--S 445 of 1457
+--a0:=integrate(t0,x)
+--E 445
+
+--S 446 of 1457
+--m0:=a0-r0
+--E 446
+
+--S 447 of 1457
+--d0:=D(m0,x)
+--E 447
+
+)clear all
+
+--S 448 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^2
+--R 
+--R
+--R                                                                  +----------+
+--R            2 5       2           4                2  3      2 2  |   2
+--R        (B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x )\|c x  + b x
+--R   (1)  ----------------------------------------------------------------------
+--R                                   2 2             2
+--R                                  e x  + 2d e x + d
+--R                                                    Type: Expression(Integer)
+--E 448
+
+--S 449 of 1457
+r0:=-1/48*(10*A*c*e*(8*c*d-7*b*e)-B*(96*c^2*d^2-92*b*c*d*e+3*b^2*e^2)+_
+     6*c*e*(12*B*c*d-b*B*e-10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(c*e^4)+_
+     1/5*(6*B*d-5*A*e+B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x))+_
+     1/128*(10*A*c*e*(128*c^4*d^4-256*b*c^3*d^3*e+144*b^2*c^2*d^2*e^2-_
+     16*b^3*c*d*e^3-b^4*e^4)-B*(1536*c^5*d^5-3200*b*c^4*d^4*e+_
+     1920*b^2*c^3*d^3*e^2-240*b^3*c^2*d^2*e^3-20*b^4*c*d*e^4-3*b^5*e^5))*_
+     atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^7)+1/2*d^(3/2)*_
+     (c*d-b*e)^(3/2)*(B*d*(12*c*d-7*b*e)-5*A*e*(2*c*d-b*e))*atanh(1/2*_
+     (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7-_
+     1/128*(10*A*c*e*(64*c^3*d^3-112*b*c^2*d^2*e+48*b^2*c*d*e^2-b^3*e^3)-_
+     B*(768*c^4*d^4-1408*b*c^3*d^3*e+656*b^2*c^2*d^2*e^2-20*b^3*c*d*e^3-_
+     3*b^4*e^4)-2*c*e*(8*b*c*e*(6*B*d-5*A*e)*(2*c*d-b*e)-(12*B*c*d-b*B*e-_
+     10*A*c*e)*(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^6)
+--R 
+--R
+--R   (2)
+--R                        4         5  6             3 2         4     5
+--R               (- 150A b c + 45B b )e  + (- 2400A b c  + 300B b c)d e
+--R             + 
+--R                        2 3          3 2  2 4
+--R               (21600A b c  + 3600B b c )d e
+--R             + 
+--R                            4           2 3  3 3            5             4  4 2
+--R               (- 38400A b c  - 28800B b c )d e  + (19200A c  + 48000B b c )d e
+--R             + 
+--R                         5 5
+--R               - 23040B c d e
+--R          *
+--R             x
+--R         + 
+--R                    4         5    5             3 2         4   2 4
+--R           (- 150A b c + 45B b )d e  + (- 2400A b c  + 300B b c)d e
+--R         + 
+--R                    2 3          3 2  3 3                4           2 3  4 2
+--R           (21600A b c  + 3600B b c )d e  + (- 38400A b c  - 28800B b c )d e
+--R         + 
+--R                    5             4  5            5 6
+--R           (19200A c  + 48000B b c )d e - 23040B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                      2 2   4                3          2 2  2 3
+--R               4800A b c d e  + (- 14400A b c  - 6720B b c )d e
+--R             + 
+--R                       4             3  3 2           4 4
+--R               (9600A c  + 18240B b c )d e  - 11520B c d e
+--R          *
+--R             x
+--R         + 
+--R                  2 2 2 3                3          2 2  3 2
+--R           4800A b c d e  + (- 14400A b c  - 6720B b c )d e
+--R         + 
+--R                   4             3  4            4 5
+--R           (9600A c  + 18240B b c )d e - 11520B c d
+--R      *
+--R          +-----------+ +-+ +-+             (b e - 2c d)x - b d
+--R         \|- b e + c d \|c \|d atanh(--------------------------------)
+--R                                                         +----------+
+--R                                       +-----------+ +-+ |   2
+--R                                     2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                 4 6 5           4            3  6         4   5  4
+--R           384B c e x  + ((480A c  + 1008B b c )e  - 576B c d e )x
+--R         + 
+--R                         3         2 2  6            4            3    5
+--R               (1360A b c  + 744B b c )e  + (- 800A c  - 1712B b c )d e
+--R             + 
+--R                     4 2 4
+--R               960B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                       2 2        3   6               3          2 2    5
+--R               (1180A b c  + 30B b c)e  + (- 2800A b c  - 1616B b c )d e
+--R             + 
+--R                       4            3  2 4          4 3 3
+--R               (1600A c  + 3520B b c )d e  - 1920B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      3         4  6             2 2         3     5
+--R               (150A b c - 45B b )e  + (- 4100A b c  - 270B b c)d e
+--R             + 
+--R                         3          2 2  2 4             4             3  3 3
+--R               (8800A b c  + 5560B b c )d e  + (- 4800A c  - 11040B b c )d e
+--R             + 
+--R                      4 4 2
+--R               5760B c d e
+--R          *
+--R             x
+--R         + 
+--R                  3         4    5             2 2         3   2 4
+--R           (150A b c - 45B b )d e  + (- 7200A b c  - 300B b c)d e
+--R         + 
+--R                      3          2 2  3 3             4             3  4 2
+--R           (16800A b c  + 9840B b c )d e  + (- 9600A c  - 21120B b c )d e
+--R         + 
+--R                   4 5
+--R           11520B c d e
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R           2 8         2   7  +-+
+--R     (1920c e x + 1920c d e )\|c
+--R                                                    Type: Expression(Integer)
+--E 449
+
+--S 450 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                        4         5  6           3 2         4     5
+--R                 (150A b c - 45B b )e  + (2400A b c  - 300B b c)d e
+--R               + 
+--R                            2 3          3 2  2 4
+--R                 (- 21600A b c  - 3600B b c )d e
+--R               + 
+--R                            4           2 3  3 3
+--R                 (38400A b c  + 28800B b c )d e
+--R               + 
+--R                            5             4  4 2           5 5
+--R                 (- 19200A c  - 48000B b c )d e  + 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                    4         5    5           3 2         4   2 4
+--R             (150A b c - 45B b )d e  + (2400A b c  - 300B b c)d e
+--R           + 
+--R                        2 3          3 2  3 3              4           2 3  4 2
+--R             (- 21600A b c  - 3600B b c )d e  + (38400A b c  + 28800B b c )d e
+--R           + 
+--R                        5             4  5            5 6
+--R             (- 19200A c  - 48000B b c )d e + 23040B c d
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                        2 2   4                3           2 2  2 3
+--R                 9600A b c d e  + (- 28800A b c  - 13440B b c )d e
+--R               + 
+--R                          4             3  3 2           4 4
+--R                 (19200A c  + 36480B b c )d e  - 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2 2 2 3                3           2 2  3 2
+--R             9600A b c d e  + (- 28800A b c  - 13440B b c )d e
+--R           + 
+--R                      4             3  4            4 5
+--R             (19200A c  + 36480B b c )d e - 23040B c d
+--R        *
+--R            +--------------+
+--R            |             2  +-+
+--R           \|- b d e + c d  \|c
+--R        *
+--R                   +--------------+ +----------+
+--R                   |             2  |   2
+--R               - 2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(---------------------------------------------------------)
+--R                                        e x + d
+--R       + 
+--R                   4 6 5           4            3  6          4   5  4
+--R             768B c e x  + ((960A c  + 2016B b c )e  - 1152B c d e )x
+--R           + 
+--R                           3          2 2  6             4            3    5
+--R                 (2720A b c  + 1488B b c )e  + (- 1600A c  - 3424B b c )d e
+--R               + 
+--R                        4 2 4
+--R                 1920B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         2 2        3   6               3          2 2    5
+--R                 (2360A b c  + 60B b c)e  + (- 5600A b c  - 3232B b c )d e
+--R               + 
+--R                         4            3  2 4          4 3 3
+--R                 (3200A c  + 7040B b c )d e  - 3840B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3         4  6             2 2         3     5
+--R                 (300A b c - 90B b )e  + (- 8200A b c  - 540B b c)d e
+--R               + 
+--R                            3           2 2  2 4
+--R                 (17600A b c  + 11120B b c )d e
+--R               + 
+--R                           4             3  3 3           4 4 2
+--R                 (- 9600A c  - 22080B b c )d e  + 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3         4    5              2 2         3   2 4
+--R             (300A b c - 90B b )d e  + (- 14400A b c  - 600B b c)d e
+--R           + 
+--R                        3           2 2  3 3              4             3  4 2
+--R             (33600A b c  + 19680B b c )d e  + (- 19200A c  - 42240B b c )d e
+--R           + 
+--R                     4 5
+--R             23040B c d e
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R             2 8         2   7  +-+
+--R       (3840c e x + 3840c d e )\|c
+--R     ,
+--R
+--R                        4         5  6           3 2         4     5
+--R                 (150A b c - 45B b )e  + (2400A b c  - 300B b c)d e
+--R               + 
+--R                            2 3          3 2  2 4
+--R                 (- 21600A b c  - 3600B b c )d e
+--R               + 
+--R                            4           2 3  3 3
+--R                 (38400A b c  + 28800B b c )d e
+--R               + 
+--R                            5             4  4 2           5 5
+--R                 (- 19200A c  - 48000B b c )d e  + 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                    4         5    5           3 2         4   2 4
+--R             (150A b c - 45B b )d e  + (2400A b c  - 300B b c)d e
+--R           + 
+--R                        2 3          3 2  3 3              4           2 3  4 2
+--R             (- 21600A b c  - 3600B b c )d e  + (38400A b c  + 28800B b c )d e
+--R           + 
+--R                        5             4  5            5 6
+--R             (- 19200A c  - 48000B b c )d e + 23040B c d
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                           2 2   4              3           2 2  2 3
+--R                 - 19200A b c d e  + (57600A b c  + 26880B b c )d e
+--R               + 
+--R                            4             3  3 2           4 4
+--R                 (- 38400A c  - 72960B b c )d e  + 46080B c d e
+--R            *
+--R               x
+--R           + 
+--R                       2 2 2 3              3           2 2  3 2
+--R             - 19200A b c d e  + (57600A b c  + 26880B b c )d e
+--R           + 
+--R                        4             3  4            4 5
+--R             (- 38400A c  - 72960B b c )d e + 46080B c d
+--R        *
+--R                                      +----------+
+--R                +------------+        |   2
+--R            +-+ |           2       d\|c x  + b x
+--R           \|c \|b d e - c d  atan(----------------)
+--R                                     +------------+
+--R                                     |           2
+--R                                   x\|b d e - c d
+--R       + 
+--R                   4 6 5           4            3  6          4   5  4
+--R             768B c e x  + ((960A c  + 2016B b c )e  - 1152B c d e )x
+--R           + 
+--R                           3          2 2  6             4            3    5
+--R                 (2720A b c  + 1488B b c )e  + (- 1600A c  - 3424B b c )d e
+--R               + 
+--R                        4 2 4
+--R                 1920B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         2 2        3   6               3          2 2    5
+--R                 (2360A b c  + 60B b c)e  + (- 5600A b c  - 3232B b c )d e
+--R               + 
+--R                         4            3  2 4          4 3 3
+--R                 (3200A c  + 7040B b c )d e  - 3840B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3         4  6             2 2         3     5
+--R                 (300A b c - 90B b )e  + (- 8200A b c  - 540B b c)d e
+--R               + 
+--R                            3           2 2  2 4
+--R                 (17600A b c  + 11120B b c )d e
+--R               + 
+--R                           4             3  3 3           4 4 2
+--R                 (- 9600A c  - 22080B b c )d e  + 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3         4    5              2 2         3   2 4
+--R             (300A b c - 90B b )d e  + (- 14400A b c  - 600B b c)d e
+--R           + 
+--R                        3           2 2  3 3              4             3  4 2
+--R             (33600A b c  + 19680B b c )d e  + (- 19200A c  - 42240B b c )d e
+--R           + 
+--R                     4 5
+--R             23040B c d e
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R             2 8         2   7  +-+
+--R       (3840c e x + 3840c d e )\|c
+--R     ,
+--R
+--R                        2 2   4                3          2 2  2 3
+--R                 4800A b c d e  + (- 14400A b c  - 6720B b c )d e
+--R               + 
+--R                         4             3  3 2           4 4
+--R                 (9600A c  + 18240B b c )d e  - 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2 2 2 3                3          2 2  3 2
+--R             4800A b c d e  + (- 14400A b c  - 6720B b c )d e
+--R           + 
+--R                     4             3  4            4 5
+--R             (9600A c  + 18240B b c )d e - 11520B c d
+--R        *
+--R            +--------------+
+--R            |             2  +---+
+--R           \|- b d e + c d  \|- c
+--R        *
+--R                   +--------------+ +----------+
+--R                   |             2  |   2
+--R               - 2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(---------------------------------------------------------)
+--R                                        e x + d
+--R       + 
+--R                          4         5  6             3 2         4     5
+--R                 (- 150A b c + 45B b )e  + (- 2400A b c  + 300B b c)d e
+--R               + 
+--R                          2 3          3 2  2 4
+--R                 (21600A b c  + 3600B b c )d e
+--R               + 
+--R                              4           2 3  3 3
+--R                 (- 38400A b c  - 28800B b c )d e
+--R               + 
+--R                          5             4  4 2           5 5
+--R                 (19200A c  + 48000B b c )d e  - 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                      4         5    5             3 2         4   2 4
+--R             (- 150A b c + 45B b )d e  + (- 2400A b c  + 300B b c)d e
+--R           + 
+--R                      2 3          3 2  3 3                4           2 3  4 2
+--R             (21600A b c  + 3600B b c )d e  + (- 38400A b c  - 28800B b c )d e
+--R           + 
+--R                      5             4  5            5 6
+--R             (19200A c  + 48000B b c )d e - 23040B c d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                   4 6 5           4            3  6         4   5  4
+--R             384B c e x  + ((480A c  + 1008B b c )e  - 576B c d e )x
+--R           + 
+--R                           3         2 2  6            4            3    5
+--R                 (1360A b c  + 744B b c )e  + (- 800A c  - 1712B b c )d e
+--R               + 
+--R                       4 2 4
+--R                 960B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         2 2        3   6               3          2 2    5
+--R                 (1180A b c  + 30B b c)e  + (- 2800A b c  - 1616B b c )d e
+--R               + 
+--R                         4            3  2 4          4 3 3
+--R                 (1600A c  + 3520B b c )d e  - 1920B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3         4  6             2 2         3     5
+--R                 (150A b c - 45B b )e  + (- 4100A b c  - 270B b c)d e
+--R               + 
+--R                           3          2 2  2 4             4             3  3 3
+--R                 (8800A b c  + 5560B b c )d e  + (- 4800A c  - 11040B b c )d e
+--R               + 
+--R                        4 4 2
+--R                 5760B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3         4    5             2 2         3   2 4
+--R             (150A b c - 45B b )d e  + (- 7200A b c  - 300B b c)d e
+--R           + 
+--R                        3          2 2  3 3             4             3  4 2
+--R             (16800A b c  + 9840B b c )d e  + (- 9600A c  - 21120B b c )d e
+--R           + 
+--R                     4 5
+--R             11520B c d e
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R             2 8         2   7  +---+
+--R       (1920c e x + 1920c d e )\|- c
+--R     ,
+--R
+--R                          4         5  6             3 2         4     5
+--R                 (- 150A b c + 45B b )e  + (- 2400A b c  + 300B b c)d e
+--R               + 
+--R                          2 3          3 2  2 4
+--R                 (21600A b c  + 3600B b c )d e
+--R               + 
+--R                              4           2 3  3 3
+--R                 (- 38400A b c  - 28800B b c )d e
+--R               + 
+--R                          5             4  4 2           5 5
+--R                 (19200A c  + 48000B b c )d e  - 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                      4         5    5             3 2         4   2 4
+--R             (- 150A b c + 45B b )d e  + (- 2400A b c  + 300B b c)d e
+--R           + 
+--R                      2 3          3 2  3 3                4           2 3  4 2
+--R             (21600A b c  + 3600B b c )d e  + (- 38400A b c  - 28800B b c )d e
+--R           + 
+--R                      5             4  5            5 6
+--R             (19200A c  + 48000B b c )d e - 23040B c d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                          2 2   4              3           2 2  2 3
+--R                 - 9600A b c d e  + (28800A b c  + 13440B b c )d e
+--R               + 
+--R                            4             3  3 2           4 4
+--R                 (- 19200A c  - 36480B b c )d e  + 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                      2 2 2 3              3           2 2  3 2
+--R             - 9600A b c d e  + (28800A b c  + 13440B b c )d e
+--R           + 
+--R                        4             3  4            4 5
+--R             (- 19200A c  - 36480B b c )d e + 23040B c d
+--R        *
+--R                                        +----------+
+--R                  +------------+        |   2
+--R            +---+ |           2       d\|c x  + b x
+--R           \|- c \|b d e - c d  atan(----------------)
+--R                                       +------------+
+--R                                       |           2
+--R                                     x\|b d e - c d
+--R       + 
+--R                   4 6 5           4            3  6         4   5  4
+--R             384B c e x  + ((480A c  + 1008B b c )e  - 576B c d e )x
+--R           + 
+--R                           3         2 2  6            4            3    5
+--R                 (1360A b c  + 744B b c )e  + (- 800A c  - 1712B b c )d e
+--R               + 
+--R                       4 2 4
+--R                 960B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         2 2        3   6               3          2 2    5
+--R                 (1180A b c  + 30B b c)e  + (- 2800A b c  - 1616B b c )d e
+--R               + 
+--R                         4            3  2 4          4 3 3
+--R                 (1600A c  + 3520B b c )d e  - 1920B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3         4  6             2 2         3     5
+--R                 (150A b c - 45B b )e  + (- 4100A b c  - 270B b c)d e
+--R               + 
+--R                           3          2 2  2 4             4             3  3 3
+--R                 (8800A b c  + 5560B b c )d e  + (- 4800A c  - 11040B b c )d e
+--R               + 
+--R                        4 4 2
+--R                 5760B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3         4    5             2 2         3   2 4
+--R             (150A b c - 45B b )d e  + (- 7200A b c  - 300B b c)d e
+--R           + 
+--R                        3          2 2  3 3             4             3  4 2
+--R             (16800A b c  + 9840B b c )d e  + (- 9600A c  - 21120B b c )d e
+--R           + 
+--R                     4 5
+--R             11520B c d e
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R             2 8         2   7  +---+
+--R       (1920c e x + 1920c d e )\|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 450
+
+--S 451 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                 4        5  5          3 2        4     4
+--R           (10A b c - 3B b )e  + (160A b c  - 20B b c)d e
+--R         + 
+--R                     2 3         3 2  2 3             4          2 3  3 2
+--R           (- 1440A b c  - 240B b c )d e  + (2560A b c  + 1920B b c )d e
+--R         + 
+--R                     5            4  4           5 5
+--R           (- 1280A c  - 3200B b c )d e + 1536B c d
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                 2 2   3               3         2 2  2 2
+--R           640A b c d e  + (- 1920A b c  - 896B b c )d e
+--R         + 
+--R                   4            3  3           4 4
+--R           (1280A c  + 2432B b c )d e - 1536B c d
+--R      *
+--R          +--------------+
+--R          |             2  +-+
+--R         \|- b d e + c d  \|c
+--R      *
+--R                 +--------------+ +----------+
+--R                 |             2  |   2
+--R             - 2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R         log(---------------------------------------------------------)
+--R                                      e x + d
+--R     + 
+--R                 4        5  5          3 2        4     4
+--R           (20A b c - 6B b )e  + (320A b c  - 40B b c)d e
+--R         + 
+--R                     2 3         3 2  2 3             4          2 3  3 2
+--R           (- 2880A b c  - 480B b c )d e  + (5120A b c  + 3840B b c )d e
+--R         + 
+--R                     5            4  4           5 5
+--R           (- 2560A c  - 6400B b c )d e + 3072B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                   2 2   3             3         2 2  2 2
+--R           - 640A b c d e  + (1920A b c  + 896B b c )d e
+--R         + 
+--R                     4            3  3           4 4
+--R           (- 1280A c  - 2432B b c )d e + 1536B c d
+--R      *
+--R          +-----------+ +-+ +-+             (b e - 2c d)x - b d
+--R         \|- b e + c d \|c \|d atanh(--------------------------------)
+--R                                                         +----------+
+--R                                       +-----------+ +-+ |   2
+--R                                     2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R         2 7 +-+
+--R     256c e \|c
+--R                                                    Type: Expression(Integer)
+--E 451
+
+--S 452 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 452
+
+--S 453 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                 4        5  5          3 2        4     4
+--R           (10A b c - 3B b )e  + (160A b c  - 20B b c)d e
+--R         + 
+--R                     2 3         3 2  2 3             4          2 3  3 2
+--R           (- 1440A b c  - 240B b c )d e  + (2560A b c  + 1920B b c )d e
+--R         + 
+--R                     5            4  4           5 5
+--R           (- 1280A c  - 3200B b c )d e + 1536B c d
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                 4        5  5          3 2        4     4
+--R           (20A b c - 6B b )e  + (320A b c  - 40B b c)d e
+--R         + 
+--R                     2 3         3 2  2 3             4          2 3  3 2
+--R           (- 2880A b c  - 480B b c )d e  + (5120A b c  + 3840B b c )d e
+--R         + 
+--R                     5            4  4           5 5
+--R           (- 2560A c  - 6400B b c )d e + 3072B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                   2 2   3             3         2 2  2 2
+--R           - 640A b c d e  + (1920A b c  + 896B b c )d e
+--R         + 
+--R                     4            3  3           4 4
+--R           (- 1280A c  - 2432B b c )d e + 1536B c d
+--R      *
+--R          +-----------+ +-+ +-+             (b e - 2c d)x - b d
+--R         \|- b e + c d \|c \|d atanh(--------------------------------)
+--R                                                         +----------+
+--R                                       +-----------+ +-+ |   2
+--R                                     2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                    2 2   3             3          2 2  2 2
+--R           - 1280A b c d e  + (3840A b c  + 1792B b c )d e
+--R         + 
+--R                     4            3  3           4 4
+--R           (- 2560A c  - 4864B b c )d e + 3072B c d
+--R      *
+--R                                    +----------+
+--R              +------------+        |   2
+--R          +-+ |           2       d\|c x  + b x
+--R         \|c \|b d e - c d  atan(----------------)
+--R                                   +------------+
+--R                                   |           2
+--R                                 x\|b d e - c d
+--R  /
+--R         2 7 +-+
+--R     256c e \|c
+--R                                                    Type: Expression(Integer)
+--E 453
+
+--S 454 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 454
+
+)clear all
+
+--S 455 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^3
+--R 
+--R
+--R                                                                  +----------+
+--R            2 5       2           4                2  3      2 2  |   2
+--R        (B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x )\|c x  + b x
+--R   (1)  ----------------------------------------------------------------------
+--R                              3 3       2 2     2       3
+--R                             e x  + 3d e x  + 3d e x + d
+--R                                                    Type: Expression(Integer)
+--E 455
+
+--S 456 of 1457
+r0:=-5/24*(B*d*(24*c*d-13*b*e)-2*A*e*(8*c*d-3*b*e)+e*(6*B*c*d-b*B*e-_
+     4*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/4*(3*B*d-2*A*e+B*e*x)*_
+     (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)-5/64*(8*A*c*e*(32*c^3*d^3-48*b*c^2*_
+     d^2*e+18*b^2*c*d*e^2-b^3*e^3)-B*(384*c^4*d^4-640*b*c^3*d^3*e+288*b^2*_
+     c^2*d^2*e^2-24*b^3*c*d*e^3-b^4*e^4))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_
+     (c^(3/2)*e^7)+5/8*(A*e*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)-B*d*(24*c^2*_
+     d^2-28*b*c*d*e+7*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_
+     sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^7+5/64*_
+     (8*A*c*e*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2)-B*(192*c^3*d^3-272*b*c^2*_
+     d^2*e+88*b^2*c*d*e^2-b^3*e^3)-2*c*e*(16*A*c*e*(2*c*d-b*e)-B*(48*c^2*_
+     d^2-32*b*c*d*e+b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c*e^6)
+--R 
+--R
+--R   (2)
+--R                      3         4  6             2 2         3     5
+--R               (120A b c - 15B b )e  + (- 2160A b c  - 360B b c)d e
+--R             + 
+--R                         3          2 2  2 4             4            3  3 3
+--R               (5760A b c  + 4320B b c )d e  + (- 3840A c  - 9600B b c )d e
+--R             + 
+--R                      4 4 2
+--R               5760B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      3         4    5             2 2         3   2 4
+--R               (240A b c - 30B b )d e  + (- 4320A b c  - 720B b c)d e
+--R             + 
+--R                          3          2 2  3 3             4             3  4 2
+--R               (11520A b c  + 8640B b c )d e  + (- 7680A c  - 19200B b c )d e
+--R             + 
+--R                       4 5
+--R               11520B c d e
+--R          *
+--R             x
+--R         + 
+--R                  3         4  2 4             2 2         3   3 3
+--R           (120A b c - 15B b )d e  + (- 2160A b c  - 360B b c)d e
+--R         + 
+--R                     3          2 2  4 2             4            3  5
+--R           (5760A b c  + 4320B b c )d e  + (- 3840A c  - 9600B b c )d e
+--R         + 
+--R                  4 6
+--R           5760B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                       2   5             2         2     4
+--R               - 360A b c e  + (1920A b c  + 840B b c)d e
+--R             + 
+--R                         3            2  2 3          3 3 2
+--R               (- 1920A c  - 3360B b c )d e  + 2880B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                       2     4             2          2   2 3
+--R               - 720A b c d e  + (3840A b c  + 1680B b c)d e
+--R             + 
+--R                         3            2  3 2          3 4
+--R               (- 3840A c  - 6720B b c )d e  + 5760B c d e
+--R          *
+--R             x
+--R         + 
+--R                   2   2 3             2         2   3 2
+--R           - 360A b c d e  + (1920A b c  + 840B b c)d e
+--R         + 
+--R                     3            2  4           3 5
+--R           (- 1920A c  - 3360B b c )d e + 2880B c d
+--R      *
+--R          +-----------+ +-+ +-+             (b e - 2c d)x - b d
+--R         \|- b e + c d \|c \|d atanh(--------------------------------)
+--R                                                         +----------+
+--R                                       +-----------+ +-+ |   2
+--R                                     2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                3 6 5          3           2  6        3   5  4
+--R           48B c e x  + ((64A c  + 136B b c )e  - 96B c d e )x
+--R         + 
+--R                        2         2   6            3           2    5
+--R               (208A b c  + 118B b c)e  + (- 160A c  - 352B b c )d e
+--R             + 
+--R                     3 2 4
+--R               240B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      2         3  6              2         2     5
+--R               (264A b c + 15B b )e  + (- 880A b c  - 556B b c)d e
+--R             + 
+--R                      3            2  2 4         3 3 3
+--R               (640A c  + 1480B b c )d e  - 960B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      2         3    5               2          2   2 4
+--R               (960A b c + 30B b )d e  + (- 3680A b c  - 2090B b c)d e
+--R             + 
+--R                       3            2  3 3          3 4 2
+--R               (2880A c  + 6240B b c )d e  - 4320B c d e
+--R          *
+--R             x
+--R         + 
+--R                  2         3  2 4               2          2   3 3
+--R           (600A b c + 15B b )d e  + (- 2400A b c  - 1320B b c)d e
+--R         + 
+--R                   3            2  4 2          3 5
+--R           (1920A c  + 4080B b c )d e  - 2880B c d e
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R            9 2           8          2 7  +-+
+--R     (192c e x  + 384c d e x + 192c d e )\|c
+--R                                                    Type: Expression(Integer)
+--E 456
+
+--S 457 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                          3         4  6           2 2         3     5
+--R                 (- 120A b c + 15B b )e  + (2160A b c  + 360B b c)d e
+--R               + 
+--R                             3          2 2  2 4           4            3  3 3
+--R                 (- 5760A b c  - 4320B b c )d e  + (3840A c  + 9600B b c )d e
+--R               + 
+--R                          4 4 2
+--R                 - 5760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                          3         4    5           2 2         3   2 4
+--R                 (- 240A b c + 30B b )d e  + (4320A b c  + 720B b c)d e
+--R               + 
+--R                              3          2 2  3 3           4             3  4 2
+--R                 (- 11520A b c  - 8640B b c )d e  + (7680A c  + 19200B b c )d e
+--R               + 
+--R                           4 5
+--R                 - 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                      3         4  2 4           2 2         3   3 3
+--R             (- 120A b c + 15B b )d e  + (2160A b c  + 360B b c)d e
+--R           + 
+--R                         3          2 2  4 2           4            3  5
+--R             (- 5760A b c  - 4320B b c )d e  + (3840A c  + 9600B b c )d e
+--R           + 
+--R                      4 6
+--R             - 5760B c d
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                         2   5             2          2     4
+--R                 - 720A b c e  + (3840A b c  + 1680B b c)d e
+--R               + 
+--R                           3            2  2 3          3 3 2
+--R                 (- 3840A c  - 6720B b c )d e  + 5760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                          2     4             2          2   2 3
+--R                 - 1440A b c d e  + (7680A b c  + 3360B b c)d e
+--R               + 
+--R                           3             2  3 2           3 4
+--R                 (- 7680A c  - 13440B b c )d e  + 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                     2   2 3             2          2   3 2
+--R             - 720A b c d e  + (3840A b c  + 1680B b c)d e
+--R           + 
+--R                       3            2  4           3 5
+--R             (- 3840A c  - 6720B b c )d e + 5760B c d
+--R        *
+--R            +--------------+
+--R            |             2  +-+
+--R           \|- b d e + c d  \|c
+--R        *
+--R                   +--------------+ +----------+
+--R                   |             2  |   2
+--R               - 2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(---------------------------------------------------------)
+--R                                        e x + d
+--R       + 
+--R                  3 6 5           3           2  6         3   5  4
+--R             96B c e x  + ((128A c  + 272B b c )e  - 192B c d e )x
+--R           + 
+--R                          2         2   6            3           2    5
+--R                 (416A b c  + 236B b c)e  + (- 320A c  - 704B b c )d e
+--R               + 
+--R                       3 2 4
+--R                 480B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2         3  6               2          2     5
+--R                 (528A b c + 30B b )e  + (- 1760A b c  - 1112B b c)d e
+--R               + 
+--R                         3            2  2 4          3 3 3
+--R                 (1280A c  + 2960B b c )d e  - 1920B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         2         3    5               2          2   2 4
+--R                 (1920A b c + 60B b )d e  + (- 7360A b c  - 4180B b c)d e
+--R               + 
+--R                         3             2  3 3          3 4 2
+--R                 (5760A c  + 12480B b c )d e  - 8640B c d e
+--R            *
+--R               x
+--R           + 
+--R                     2         3  2 4               2          2   3 3
+--R             (1200A b c + 30B b )d e  + (- 4800A b c  - 2640B b c)d e
+--R           + 
+--R                     3            2  4 2          3 5
+--R             (3840A c  + 8160B b c )d e  - 5760B c d e
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R              9 2           8          2 7  +-+
+--R       (384c e x  + 768c d e x + 384c d e )\|c
+--R     ,
+--R
+--R                          3         4  6           2 2         3     5
+--R                 (- 120A b c + 15B b )e  + (2160A b c  + 360B b c)d e
+--R               + 
+--R                             3          2 2  2 4           4            3  3 3
+--R                 (- 5760A b c  - 4320B b c )d e  + (3840A c  + 9600B b c )d e
+--R               + 
+--R                          4 4 2
+--R                 - 5760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                          3         4    5           2 2         3   2 4
+--R                 (- 240A b c + 30B b )d e  + (4320A b c  + 720B b c)d e
+--R               + 
+--R                              3          2 2  3 3           4             3  4 2
+--R                 (- 11520A b c  - 8640B b c )d e  + (7680A c  + 19200B b c )d e
+--R               + 
+--R                           4 5
+--R                 - 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                      3         4  2 4           2 2         3   3 3
+--R             (- 120A b c + 15B b )d e  + (2160A b c  + 360B b c)d e
+--R           + 
+--R                         3          2 2  4 2           4            3  5
+--R             (- 5760A b c  - 4320B b c )d e  + (3840A c  + 9600B b c )d e
+--R           + 
+--R                      4 6
+--R             - 5760B c d
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                        2   5               2          2     4
+--R                 1440A b c e  + (- 7680A b c  - 3360B b c)d e
+--R               + 
+--R                         3             2  2 3           3 3 2
+--R                 (7680A c  + 13440B b c )d e  - 11520B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2     4                2          2   2 3
+--R                 2880A b c d e  + (- 15360A b c  - 6720B b c)d e
+--R               + 
+--R                          3             2  3 2           3 4
+--R                 (15360A c  + 26880B b c )d e  - 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2   2 3               2          2   3 2
+--R             1440A b c d e  + (- 7680A b c  - 3360B b c)d e
+--R           + 
+--R                     3             2  4            3 5
+--R             (7680A c  + 13440B b c )d e - 11520B c d
+--R        *
+--R                                      +----------+
+--R                +------------+        |   2
+--R            +-+ |           2       d\|c x  + b x
+--R           \|c \|b d e - c d  atan(----------------)
+--R                                     +------------+
+--R                                     |           2
+--R                                   x\|b d e - c d
+--R       + 
+--R                  3 6 5           3           2  6         3   5  4
+--R             96B c e x  + ((128A c  + 272B b c )e  - 192B c d e )x
+--R           + 
+--R                          2         2   6            3           2    5
+--R                 (416A b c  + 236B b c)e  + (- 320A c  - 704B b c )d e
+--R               + 
+--R                       3 2 4
+--R                 480B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2         3  6               2          2     5
+--R                 (528A b c + 30B b )e  + (- 1760A b c  - 1112B b c)d e
+--R               + 
+--R                         3            2  2 4          3 3 3
+--R                 (1280A c  + 2960B b c )d e  - 1920B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         2         3    5               2          2   2 4
+--R                 (1920A b c + 60B b )d e  + (- 7360A b c  - 4180B b c)d e
+--R               + 
+--R                         3             2  3 3          3 4 2
+--R                 (5760A c  + 12480B b c )d e  - 8640B c d e
+--R            *
+--R               x
+--R           + 
+--R                     2         3  2 4               2          2   3 3
+--R             (1200A b c + 30B b )d e  + (- 4800A b c  - 2640B b c)d e
+--R           + 
+--R                     3            2  4 2          3 5
+--R             (3840A c  + 8160B b c )d e  - 5760B c d e
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R              9 2           8          2 7  +-+
+--R       (384c e x  + 768c d e x + 384c d e )\|c
+--R     ,
+--R
+--R                         2   5             2         2     4
+--R                 - 360A b c e  + (1920A b c  + 840B b c)d e
+--R               + 
+--R                           3            2  2 3          3 3 2
+--R                 (- 1920A c  - 3360B b c )d e  + 2880B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         2     4             2          2   2 3
+--R                 - 720A b c d e  + (3840A b c  + 1680B b c)d e
+--R               + 
+--R                           3            2  3 2          3 4
+--R                 (- 3840A c  - 6720B b c )d e  + 5760B c d e
+--R            *
+--R               x
+--R           + 
+--R                     2   2 3             2         2   3 2
+--R             - 360A b c d e  + (1920A b c  + 840B b c)d e
+--R           + 
+--R                       3            2  4           3 5
+--R             (- 1920A c  - 3360B b c )d e + 2880B c d
+--R        *
+--R            +--------------+
+--R            |             2  +---+
+--R           \|- b d e + c d  \|- c
+--R        *
+--R                   +--------------+ +----------+
+--R                   |             2  |   2
+--R               - 2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R           log(---------------------------------------------------------)
+--R                                        e x + d
+--R       + 
+--R                        3         4  6             2 2         3     5
+--R                 (120A b c - 15B b )e  + (- 2160A b c  - 360B b c)d e
+--R               + 
+--R                           3          2 2  2 4             4            3  3 3
+--R                 (5760A b c  + 4320B b c )d e  + (- 3840A c  - 9600B b c )d e
+--R               + 
+--R                        4 4 2
+--R                 5760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3         4    5             2 2         3   2 4
+--R                 (240A b c - 30B b )d e  + (- 4320A b c  - 720B b c)d e
+--R               + 
+--R                            3          2 2  3 3             4             3  4 2
+--R                 (11520A b c  + 8640B b c )d e  + (- 7680A c  - 19200B b c )d e
+--R               + 
+--R                         4 5
+--R                 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3         4  2 4             2 2         3   3 3
+--R             (120A b c - 15B b )d e  + (- 2160A b c  - 360B b c)d e
+--R           + 
+--R                       3          2 2  4 2             4            3  5
+--R             (5760A b c  + 4320B b c )d e  + (- 3840A c  - 9600B b c )d e
+--R           + 
+--R                    4 6
+--R             5760B c d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                  3 6 5          3           2  6        3   5  4
+--R             48B c e x  + ((64A c  + 136B b c )e  - 96B c d e )x
+--R           + 
+--R                          2         2   6            3           2    5
+--R                 (208A b c  + 118B b c)e  + (- 160A c  - 352B b c )d e
+--R               + 
+--R                       3 2 4
+--R                 240B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2         3  6              2         2     5
+--R                 (264A b c + 15B b )e  + (- 880A b c  - 556B b c)d e
+--R               + 
+--R                        3            2  2 4         3 3 3
+--R                 (640A c  + 1480B b c )d e  - 960B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2         3    5               2          2   2 4
+--R                 (960A b c + 30B b )d e  + (- 3680A b c  - 2090B b c)d e
+--R               + 
+--R                         3            2  3 3          3 4 2
+--R                 (2880A c  + 6240B b c )d e  - 4320B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2         3  2 4               2          2   3 3
+--R             (600A b c + 15B b )d e  + (- 2400A b c  - 1320B b c)d e
+--R           + 
+--R                     3            2  4 2          3 5
+--R             (1920A c  + 4080B b c )d e  - 2880B c d e
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R              9 2           8          2 7  +---+
+--R       (192c e x  + 384c d e x + 192c d e )\|- c
+--R     ,
+--R
+--R                        3         4  6             2 2         3     5
+--R                 (120A b c - 15B b )e  + (- 2160A b c  - 360B b c)d e
+--R               + 
+--R                           3          2 2  2 4             4            3  3 3
+--R                 (5760A b c  + 4320B b c )d e  + (- 3840A c  - 9600B b c )d e
+--R               + 
+--R                        4 4 2
+--R                 5760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3         4    5             2 2         3   2 4
+--R                 (240A b c - 30B b )d e  + (- 4320A b c  - 720B b c)d e
+--R               + 
+--R                            3          2 2  3 3             4             3  4 2
+--R                 (11520A b c  + 8640B b c )d e  + (- 7680A c  - 19200B b c )d e
+--R               + 
+--R                         4 5
+--R                 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3         4  2 4             2 2         3   3 3
+--R             (120A b c - 15B b )d e  + (- 2160A b c  - 360B b c)d e
+--R           + 
+--R                       3          2 2  4 2             4            3  5
+--R             (5760A b c  + 4320B b c )d e  + (- 3840A c  - 9600B b c )d e
+--R           + 
+--R                    4 6
+--R             5760B c d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                       2   5               2          2     4
+--R                 720A b c e  + (- 3840A b c  - 1680B b c)d e
+--R               + 
+--R                         3            2  2 3          3 3 2
+--R                 (3840A c  + 6720B b c )d e  - 5760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2     4               2          2   2 3
+--R                 1440A b c d e  + (- 7680A b c  - 3360B b c)d e
+--R               + 
+--R                         3             2  3 2           3 4
+--R                 (7680A c  + 13440B b c )d e  - 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2   2 3               2          2   3 2
+--R             720A b c d e  + (- 3840A b c  - 1680B b c)d e
+--R           + 
+--R                     3            2  4           3 5
+--R             (3840A c  + 6720B b c )d e - 5760B c d
+--R        *
+--R                                        +----------+
+--R                  +------------+        |   2
+--R            +---+ |           2       d\|c x  + b x
+--R           \|- c \|b d e - c d  atan(----------------)
+--R                                       +------------+
+--R                                       |           2
+--R                                     x\|b d e - c d
+--R       + 
+--R                  3 6 5          3           2  6        3   5  4
+--R             48B c e x  + ((64A c  + 136B b c )e  - 96B c d e )x
+--R           + 
+--R                          2         2   6            3           2    5
+--R                 (208A b c  + 118B b c)e  + (- 160A c  - 352B b c )d e
+--R               + 
+--R                       3 2 4
+--R                 240B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2         3  6              2         2     5
+--R                 (264A b c + 15B b )e  + (- 880A b c  - 556B b c)d e
+--R               + 
+--R                        3            2  2 4         3 3 3
+--R                 (640A c  + 1480B b c )d e  - 960B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2         3    5               2          2   2 4
+--R                 (960A b c + 30B b )d e  + (- 3680A b c  - 2090B b c)d e
+--R               + 
+--R                         3            2  3 3          3 4 2
+--R                 (2880A c  + 6240B b c )d e  - 4320B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2         3  2 4               2          2   3 3
+--R             (600A b c + 15B b )d e  + (- 2400A b c  - 1320B b c)d e
+--R           + 
+--R                     3            2  4 2          3 5
+--R             (1920A c  + 4080B b c )d e  - 2880B c d e
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R              9 2           8          2 7  +---+
+--R       (192c e x  + 384c d e x + 192c d e )\|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 457
+
+--S 458 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                   3        4  4          2 2         3     3
+--R           (- 40A b c + 5B b )e  + (720A b c  + 120B b c)d e
+--R         + 
+--R                       3          2 2  2 2           4            3  3
+--R           (- 1920A b c  - 1440B b c )d e  + (1280A c  + 3200B b c )d e
+--R         + 
+--R                    4 4
+--R           - 1920B c d
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   2   3             2         2     2
+--R           - 240A b c e  + (1280A b c  + 560B b c)d e
+--R         + 
+--R                     3            2  2           3 3
+--R           (- 1280A c  - 2240B b c )d e + 1920B c d
+--R      *
+--R          +--------------+
+--R          |             2  +-+
+--R         \|- b d e + c d  \|c
+--R      *
+--R                 +--------------+ +----------+
+--R                 |             2  |   2
+--R             - 2\|- b d e + c d  \|c x  + b x  + (- b e + 2c d)x + b d
+--R         log(---------------------------------------------------------)
+--R                                      e x + d
+--R     + 
+--R                   3         4  4           2 2         3     3
+--R           (- 80A b c + 10B b )e  + (1440A b c  + 240B b c)d e
+--R         + 
+--R                       3          2 2  2 2           4            3  3
+--R           (- 3840A b c  - 2880B b c )d e  + (2560A c  + 6400B b c )d e
+--R         + 
+--R                    4 4
+--R           - 3840B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                 2   3               2         2     2
+--R           240A b c e  + (- 1280A b c  - 560B b c)d e
+--R         + 
+--R                   3            2  2           3 3
+--R           (1280A c  + 2240B b c )d e - 1920B c d
+--R      *
+--R          +-----------+ +-+ +-+             (b e - 2c d)x - b d
+--R         \|- b e + c d \|c \|d atanh(--------------------------------)
+--R                                                         +----------+
+--R                                       +-----------+ +-+ |   2
+--R                                     2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R           7 +-+
+--R     128c e \|c
+--R                                                    Type: Expression(Integer)
+--E 458
+
+--S 459 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 459
+
+--S 460 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                   3        4  4          2 2         3     3
+--R           (- 40A b c + 5B b )e  + (720A b c  + 120B b c)d e
+--R         + 
+--R                       3          2 2  2 2           4            3  3
+--R           (- 1920A b c  - 1440B b c )d e  + (1280A c  + 3200B b c )d e
+--R         + 
+--R                    4 4
+--R           - 1920B c d
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   3         4  4           2 2         3     3
+--R           (- 80A b c + 10B b )e  + (1440A b c  + 240B b c)d e
+--R         + 
+--R                       3          2 2  2 2           4            3  3
+--R           (- 3840A b c  - 2880B b c )d e  + (2560A c  + 6400B b c )d e
+--R         + 
+--R                    4 4
+--R           - 3840B c d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                 2   3               2         2     2
+--R           240A b c e  + (- 1280A b c  - 560B b c)d e
+--R         + 
+--R                   3            2  2           3 3
+--R           (1280A c  + 2240B b c )d e - 1920B c d
+--R      *
+--R          +-----------+ +-+ +-+             (b e - 2c d)x - b d
+--R         \|- b e + c d \|c \|d atanh(--------------------------------)
+--R                                                         +----------+
+--R                                       +-----------+ +-+ |   2
+--R                                     2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                 2   3               2          2     2
+--R           480A b c e  + (- 2560A b c  - 1120B b c)d e
+--R         + 
+--R                   3            2  2           3 3
+--R           (2560A c  + 4480B b c )d e - 3840B c d
+--R      *
+--R                                    +----------+
+--R              +------------+        |   2
+--R          +-+ |           2       d\|c x  + b x
+--R         \|c \|b d e - c d  atan(----------------)
+--R                                   +------------+
+--R                                   |           2
+--R                                 x\|b d e - c d
+--R  /
+--R           7 +-+
+--R     128c e \|c
+--R                                                    Type: Expression(Integer)
+--E 460
+
+--S 461 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 461
+
+)clear all
+
+--S 462 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^4
+--R 
+--R
+--R                                                                  +----------+
+--R            2 5       2           4                2  3      2 2  |   2
+--R        (B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x )\|c x  + b x
+--R   (1)  ----------------------------------------------------------------------
+--R                         4 4       3 3     2 2 2     3       4
+--R                        e x  + 4d e x  + 6d e x  + 4d e x + d
+--R                                                    Type: Expression(Integer)
+--E 462
+
+--S 463 of 1457
+r0:=-5/12*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+e*(4*B*c*d-b*B*e-2*A*c*e)*x)*_
+     (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(2*B*d-A*e+B*e*x)*_
+     (b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)+5/8*(2*A*c*e*(16*c^2*d^2-_
+     16*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+24*b^2*c*d*e^2-_
+     b^3*e^3))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^7*sqrt(c))+5/16*(B*d*_
+     (64*c^3*d^3-112*b*c^2*d^2*e+56*b^2*c*d*e^2-7*b^3*e^3)-A*e*(32*c^3*d^3-_
+     48*b*c^2*d^2*e+18*b^2*c*d*e^2-b^3*e^3))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_
+     (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^7*sqrt(d)*sqrt(c*d-b*e))-_
+     5/8*(A*e*(16*c^2*d^2-12*b*c*d*e+b^2*e^2)-2*B*d*(16*c^2*d^2-_
+     16*b*c*d*e+3*b^2*e^2)+e*(4*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+_
+     b^2*e^2))*x)*sqrt(b*x+c*x^2)/(e^6*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                      2         3  6              2         2     5
+--R               (180A b c + 30B b )e  + (- 960A b c  - 720B b c)d e
+--R             + 
+--R                      3            2  2 4          3 3 3
+--R               (960A c  + 2400B b c )d e  - 1920B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      2         3    5               2          2   2 4
+--R               (540A b c + 90B b )d e  + (- 2880A b c  - 2160B b c)d e
+--R             + 
+--R                       3            2  3 3          3 4 2
+--R               (2880A c  + 7200B b c )d e  - 5760B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      2         3  2 4               2          2   3 3
+--R               (540A b c + 90B b )d e  + (- 2880A b c  - 2160B b c)d e
+--R             + 
+--R                       3            2  4 2          3 5
+--R               (2880A c  + 7200B b c )d e  - 5760B c d e
+--R          *
+--R             x
+--R         + 
+--R                  2         3  3 3              2         2   4 2
+--R           (180A b c + 30B b )d e  + (- 960A b c  - 720B b c)d e
+--R         + 
+--R                  3            2  5           3 6
+--R           (960A c  + 2400B b c )d e - 1920B c d
+--R      *
+--R                                       +-+
+--R          +-----------+ +-+          x\|c
+--R         \|- b e + c d \|d atanh(-------------)
+--R                                  +----------+
+--R                                  |   2
+--R                                 \|c x  + b x
+--R     + 
+--R                      3 7          2          3    6
+--R               - 15A b e  + (270A b c + 105B b )d e
+--R             + 
+--R                          2         2   2 5          3            2  3 4
+--R               (- 720A b c  - 840B b c)d e  + (480A c  + 1680B b c )d e
+--R             + 
+--R                       3 4 3
+--R               - 960B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      3   6          2          3  2 5
+--R               - 45A b d e  + (810A b c + 315B b )d e
+--R             + 
+--R                           2          2   3 4           3            2  4 3
+--R               (- 2160A b c  - 2520B b c)d e  + (1440A c  + 5040B b c )d e
+--R             + 
+--R                        3 5 2
+--R               - 2880B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      3 2 5          2          3  3 4
+--R               - 45A b d e  + (810A b c + 315B b )d e
+--R             + 
+--R                           2          2   4 3           3            2  5 2
+--R               (- 2160A b c  - 2520B b c)d e  + (1440A c  + 5040B b c )d e
+--R             + 
+--R                        3 6
+--R               - 2880B c d e
+--R          *
+--R             x
+--R         + 
+--R                  3 3 4          2          3  4 3
+--R           - 15A b d e  + (270A b c + 105B b )d e
+--R         + 
+--R                      2         2   5 2          3            2  6          3 7
+--R           (- 720A b c  - 840B b c)d e  + (480A c  + 1680B b c )d e - 960B c d
+--R      *
+--R          +-+             (b e - 2c d)x - b d
+--R         \|c atanh(--------------------------------)
+--R                                       +----------+
+--R                     +-----------+ +-+ |   2
+--R                   2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                2 6 5          2            6        2   5  4
+--R           16B c e x  + ((24A c  + 52B b c)e  - 48B c d e )x
+--R         + 
+--R                             2  6            2               5         2 2 4  3
+--R           ((108A b c + 66B b )e  + (- 120A c  - 276B b c)d e  + 240B c d e )x
+--R         + 
+--R                      2 6                     2    5
+--R               - 66A b e  + (700A b c + 372B b )d e
+--R             + 
+--R                        2              2 4          2 3 3
+--R               (- 880A c  - 1840B b c)d e  + 1760B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      2   5                     2  2 4
+--R               - 80A b d e  + (920A b c + 470B b )d e
+--R             + 
+--R                         2              3 3          2 4 2
+--R               (- 1200A c  - 2440B b c)d e  + 2400B c d e
+--R          *
+--R             x
+--R         + 
+--R                  2 2 4                     2  3 3            2             4 2
+--R           - 30A b d e  + (360A b c + 180B b )d e  + (- 480A c  - 960B b c)d e
+--R         + 
+--R                 2 5
+--R           960B c d e
+--R      *
+--R                                +----------+
+--R          +-----------+ +-+ +-+ |   2
+--R         \|- b e + c d \|c \|d \|c x  + b x
+--R  /
+--R         10 3         9 2       2 8       3 7  +-----------+ +-+ +-+
+--R     (48e  x  + 144d e x  + 144d e x + 48d e )\|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 463
+
+--S 464 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                       2         3  6              2         2     5
+--R                 (90A b c + 15B b )e  + (- 480A b c  - 360B b c)d e
+--R               + 
+--R                        3            2  2 4         3 3 3
+--R                 (480A c  + 1200B b c )d e  - 960B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2         3    5               2          2   2 4
+--R                 (270A b c + 45B b )d e  + (- 1440A b c  - 1080B b c)d e
+--R               + 
+--R                         3            2  3 3          3 4 2
+--R                 (1440A c  + 3600B b c )d e  - 2880B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2         3  2 4               2          2   3 3
+--R                 (270A b c + 45B b )d e  + (- 1440A b c  - 1080B b c)d e
+--R               + 
+--R                         3            2  4 2          3 5
+--R                 (1440A c  + 3600B b c )d e  - 2880B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2         3  3 3              2         2   4 2
+--R             (90A b c + 15B b )d e  + (- 480A b c  - 360B b c)d e
+--R           + 
+--R                    3            2  5          3 6
+--R             (480A c  + 1200B b c )d e - 960B c d
+--R        *
+--R            +--------------+       +----------+
+--R            |             2        |   2                     +-+
+--R           \|- b d e + c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                        3 7          2          3    6
+--R                 - 15A b e  + (270A b c + 105B b )d e
+--R               + 
+--R                            2         2   2 5          3            2  3 4
+--R                 (- 720A b c  - 840B b c)d e  + (480A c  + 1680B b c )d e
+--R               + 
+--R                         3 4 3
+--R                 - 960B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        3   6          2          3  2 5
+--R                 - 45A b d e  + (810A b c + 315B b )d e
+--R               + 
+--R                             2          2   3 4           3            2  4 3
+--R                 (- 2160A b c  - 2520B b c)d e  + (1440A c  + 5040B b c )d e
+--R               + 
+--R                          3 5 2
+--R                 - 2880B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 5          2          3  3 4
+--R                 - 45A b d e  + (810A b c + 315B b )d e
+--R               + 
+--R                             2          2   4 3           3            2  5 2
+--R                 (- 2160A b c  - 2520B b c)d e  + (1440A c  + 5040B b c )d e
+--R               + 
+--R                          3 6
+--R                 - 2880B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 4          2          3  4 3
+--R             - 15A b d e  + (270A b c + 105B b )d e
+--R           + 
+--R                      2         2   5 2          3            2  6          3 7
+--R           (- 720A b c  - 840B b c)d e  + (480A c  + 1680B b c )d e - 960B c d
+--R        *
+--R            +-+
+--R           \|c
+--R        *
+--R           log
+--R                                   +----------+
+--R                                2  |   2
+--R                  (2b d e - 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                  2 6 5          2            6        2   5  4
+--R             16B c e x  + ((24A c  + 52B b c)e  - 48B c d e )x
+--R           + 
+--R                                    2  6            2               5
+--R                   (108A b c + 66B b )e  + (- 120A c  - 276B b c)d e
+--R                 + 
+--R                         2 2 4
+--R                   240B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2 6                     2    5
+--R                 - 66A b e  + (700A b c + 372B b )d e
+--R               + 
+--R                          2              2 4          2 3 3
+--R                 (- 880A c  - 1840B b c)d e  + 1760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2   5                     2  2 4
+--R                 - 80A b d e  + (920A b c + 470B b )d e
+--R               + 
+--R                           2              3 3          2 4 2
+--R                 (- 1200A c  - 2440B b c)d e  + 2400B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2 2 4                     2  3 3
+--R             - 30A b d e  + (360A b c + 180B b )d e
+--R           + 
+--R                      2             4 2         2 5
+--R             (- 480A c  - 960B b c)d e  + 960B c d e
+--R        *
+--R            +--------------+     +----------+
+--R            |             2  +-+ |   2
+--R           \|- b d e + c d  \|c \|c x  + b x
+--R    /
+--R                                                 +--------------+
+--R           10 3         9 2       2 8       3 7  |             2  +-+
+--R       (48e  x  + 144d e x  + 144d e x + 48d e )\|- b d e + c d  \|c
+--R     ,
+--R
+--R                       2         3  6              2         2     5
+--R                 (90A b c + 15B b )e  + (- 480A b c  - 360B b c)d e
+--R               + 
+--R                        3            2  2 4         3 3 3
+--R                 (480A c  + 1200B b c )d e  - 960B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2         3    5               2          2   2 4
+--R                 (270A b c + 45B b )d e  + (- 1440A b c  - 1080B b c)d e
+--R               + 
+--R                         3            2  3 3          3 4 2
+--R                 (1440A c  + 3600B b c )d e  - 2880B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2         3  2 4               2          2   3 3
+--R                 (270A b c + 45B b )d e  + (- 1440A b c  - 1080B b c)d e
+--R               + 
+--R                         3            2  4 2          3 5
+--R                 (1440A c  + 3600B b c )d e  - 2880B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2         3  3 3              2         2   4 2
+--R             (90A b c + 15B b )d e  + (- 480A b c  - 360B b c)d e
+--R           + 
+--R                    3            2  5          3 6
+--R             (480A c  + 1200B b c )d e - 960B c d
+--R        *
+--R            +------------+       +----------+
+--R            |           2        |   2                     +-+
+--R           \|b d e - c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                        3 7          2          3    6
+--R                 - 30A b e  + (540A b c + 210B b )d e
+--R               + 
+--R                             2          2   2 5          3            2  3 4
+--R                 (- 1440A b c  - 1680B b c)d e  + (960A c  + 3360B b c )d e
+--R               + 
+--R                          3 4 3
+--R                 - 1920B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        3   6           2          3  2 5
+--R                 - 90A b d e  + (1620A b c + 630B b )d e
+--R               + 
+--R                             2          2   3 4           3             2  4 3
+--R                 (- 4320A b c  - 5040B b c)d e  + (2880A c  + 10080B b c )d e
+--R               + 
+--R                          3 5 2
+--R                 - 5760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 5           2          3  3 4
+--R                 - 90A b d e  + (1620A b c + 630B b )d e
+--R               + 
+--R                             2          2   4 3           3             2  5 2
+--R                 (- 4320A b c  - 5040B b c)d e  + (2880A c  + 10080B b c )d e
+--R               + 
+--R                          3 6
+--R                 - 5760B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 4          2          3  4 3
+--R             - 30A b d e  + (540A b c + 210B b )d e
+--R           + 
+--R                         2          2   5 2          3            2  6
+--R             (- 1440A b c  - 1680B b c)d e  + (960A c  + 3360B b c )d e
+--R           + 
+--R                      3 7
+--R             - 1920B c d
+--R        *
+--R                     +------------+ +----------+
+--R                     |           2  |   2
+--R            +-+     \|b d e - c d  \|c x  + b x
+--R           \|c atan(----------------------------)
+--R                            (b e - c d)x
+--R       + 
+--R                  2 6 5          2            6        2   5  4
+--R             16B c e x  + ((24A c  + 52B b c)e  - 48B c d e )x
+--R           + 
+--R                                    2  6            2               5
+--R                   (108A b c + 66B b )e  + (- 120A c  - 276B b c)d e
+--R                 + 
+--R                         2 2 4
+--R                   240B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2 6                     2    5
+--R                 - 66A b e  + (700A b c + 372B b )d e
+--R               + 
+--R                          2              2 4          2 3 3
+--R                 (- 880A c  - 1840B b c)d e  + 1760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2   5                     2  2 4
+--R                 - 80A b d e  + (920A b c + 470B b )d e
+--R               + 
+--R                           2              3 3          2 4 2
+--R                 (- 1200A c  - 2440B b c)d e  + 2400B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2 2 4                     2  3 3
+--R             - 30A b d e  + (360A b c + 180B b )d e
+--R           + 
+--R                      2             4 2         2 5
+--R             (- 480A c  - 960B b c)d e  + 960B c d e
+--R        *
+--R                +------------+ +----------+
+--R            +-+ |           2  |   2
+--R           \|c \|b d e - c d  \|c x  + b x
+--R    /
+--R                                                     +------------+
+--R           10 3         9 2       2 8       3 7  +-+ |           2
+--R       (48e  x  + 144d e x  + 144d e x + 48d e )\|c \|b d e - c d
+--R     ,
+--R
+--R                        3 7          2          3    6
+--R                 - 15A b e  + (270A b c + 105B b )d e
+--R               + 
+--R                            2         2   2 5          3            2  3 4
+--R                 (- 720A b c  - 840B b c)d e  + (480A c  + 1680B b c )d e
+--R               + 
+--R                         3 4 3
+--R                 - 960B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        3   6          2          3  2 5
+--R                 - 45A b d e  + (810A b c + 315B b )d e
+--R               + 
+--R                             2          2   3 4           3            2  4 3
+--R                 (- 2160A b c  - 2520B b c)d e  + (1440A c  + 5040B b c )d e
+--R               + 
+--R                          3 5 2
+--R                 - 2880B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 5          2          3  3 4
+--R                 - 45A b d e  + (810A b c + 315B b )d e
+--R               + 
+--R                             2          2   4 3           3            2  5 2
+--R                 (- 2160A b c  - 2520B b c)d e  + (1440A c  + 5040B b c )d e
+--R               + 
+--R                          3 6
+--R                 - 2880B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 4          2          3  4 3
+--R             - 15A b d e  + (270A b c + 105B b )d e
+--R           + 
+--R                      2         2   5 2          3            2  6          3 7
+--R           (- 720A b c  - 840B b c)d e  + (480A c  + 1680B b c )d e - 960B c d
+--R        *
+--R            +---+
+--R           \|- c
+--R        *
+--R           log
+--R                                   +----------+
+--R                                2  |   2
+--R                  (2b d e - 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                        2         3  6              2         2     5
+--R                 (180A b c + 30B b )e  + (- 960A b c  - 720B b c)d e
+--R               + 
+--R                        3            2  2 4          3 3 3
+--R                 (960A c  + 2400B b c )d e  - 1920B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2         3    5               2          2   2 4
+--R                 (540A b c + 90B b )d e  + (- 2880A b c  - 2160B b c)d e
+--R               + 
+--R                         3            2  3 3          3 4 2
+--R                 (2880A c  + 7200B b c )d e  - 5760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2         3  2 4               2          2   3 3
+--R                 (540A b c + 90B b )d e  + (- 2880A b c  - 2160B b c)d e
+--R               + 
+--R                         3            2  4 2          3 5
+--R                 (2880A c  + 7200B b c )d e  - 5760B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2         3  3 3              2         2   4 2
+--R             (180A b c + 30B b )d e  + (- 960A b c  - 720B b c)d e
+--R           + 
+--R                    3            2  5           3 6
+--R             (960A c  + 2400B b c )d e - 1920B c d
+--R        *
+--R                                        +----------+
+--R            +--------------+      +---+ |   2
+--R            |             2      \|- c \|c x  + b x
+--R           \|- b d e + c d  atan(-------------------)
+--R                                         c x
+--R       + 
+--R                  2 6 5          2            6        2   5  4
+--R             16B c e x  + ((24A c  + 52B b c)e  - 48B c d e )x
+--R           + 
+--R                                    2  6            2               5
+--R                   (108A b c + 66B b )e  + (- 120A c  - 276B b c)d e
+--R                 + 
+--R                         2 2 4
+--R                   240B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2 6                     2    5
+--R                 - 66A b e  + (700A b c + 372B b )d e
+--R               + 
+--R                          2              2 4          2 3 3
+--R                 (- 880A c  - 1840B b c)d e  + 1760B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2   5                     2  2 4
+--R                 - 80A b d e  + (920A b c + 470B b )d e
+--R               + 
+--R                           2              3 3          2 4 2
+--R                 (- 1200A c  - 2440B b c)d e  + 2400B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2 2 4                     2  3 3
+--R             - 30A b d e  + (360A b c + 180B b )d e
+--R           + 
+--R                      2             4 2         2 5
+--R             (- 480A c  - 960B b c)d e  + 960B c d e
+--R        *
+--R            +--------------+       +----------+
+--R            |             2  +---+ |   2
+--R           \|- b d e + c d  \|- c \|c x  + b x
+--R    /
+--R                                                 +--------------+
+--R           10 3         9 2       2 8       3 7  |             2  +---+
+--R       (48e  x  + 144d e x  + 144d e x + 48d e )\|- b d e + c d  \|- c
+--R     ,
+--R
+--R                        3 7          2          3    6
+--R                 - 15A b e  + (270A b c + 105B b )d e
+--R               + 
+--R                            2         2   2 5          3            2  3 4
+--R                 (- 720A b c  - 840B b c)d e  + (480A c  + 1680B b c )d e
+--R               + 
+--R                         3 4 3
+--R                 - 960B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        3   6          2          3  2 5
+--R                 - 45A b d e  + (810A b c + 315B b )d e
+--R               + 
+--R                             2          2   3 4           3            2  4 3
+--R                 (- 2160A b c  - 2520B b c)d e  + (1440A c  + 5040B b c )d e
+--R               + 
+--R                          3 5 2
+--R                 - 2880B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 5          2          3  3 4
+--R                 - 45A b d e  + (810A b c + 315B b )d e
+--R               + 
+--R                             2          2   4 3           3            2  5 2
+--R                 (- 2160A b c  - 2520B b c)d e  + (1440A c  + 5040B b c )d e
+--R               + 
+--R                          3 6
+--R                 - 2880B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 4          2          3  4 3
+--R             - 15A b d e  + (270A b c + 105B b )d e
+--R           + 
+--R                      2         2   5 2          3            2  6          3 7
+--R           (- 720A b c  - 840B b c)d e  + (480A c  + 1680B b c )d e - 960B c d
+--R        *
+--R                       +------------+ +----------+
+--R                       |           2  |   2
+--R            +---+     \|b d e - c d  \|c x  + b x
+--R           \|- c atan(----------------------------)
+--R                              (b e - c d)x
+--R       + 
+--R                       2         3  6              2         2     5
+--R                 (90A b c + 15B b )e  + (- 480A b c  - 360B b c)d e
+--R               + 
+--R                        3            2  2 4         3 3 3
+--R                 (480A c  + 1200B b c )d e  - 960B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        2         3    5               2          2   2 4
+--R                 (270A b c + 45B b )d e  + (- 1440A b c  - 1080B b c)d e
+--R               + 
+--R                         3            2  3 3          3 4 2
+--R                 (1440A c  + 3600B b c )d e  - 2880B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2         3  2 4               2          2   3 3
+--R                 (270A b c + 45B b )d e  + (- 1440A b c  - 1080B b c)d e
+--R               + 
+--R                         3            2  4 2          3 5
+--R                 (1440A c  + 3600B b c )d e  - 2880B c d e
+--R            *
+--R               x
+--R           + 
+--R                   2         3  3 3              2         2   4 2
+--R             (90A b c + 15B b )d e  + (- 480A b c  - 360B b c)d e
+--R           + 
+--R                    3            2  5          3 6
+--R             (480A c  + 1200B b c )d e - 960B c d
+--R        *
+--R                                      +----------+
+--R            +------------+      +---+ |   2
+--R            |           2      \|- c \|c x  + b x
+--R           \|b d e - c d  atan(-------------------)
+--R                                       c x
+--R       + 
+--R                 2 6 5          2            6        2   5  4
+--R             8B c e x  + ((12A c  + 26B b c)e  - 24B c d e )x
+--R           + 
+--R                              2  6           2               5         2 2 4  3
+--R             ((54A b c + 33B b )e  + (- 60A c  - 138B b c)d e  + 120B c d e )x
+--R           + 
+--R                        2 6                     2    5
+--R                 - 33A b e  + (350A b c + 186B b )d e
+--R               + 
+--R                          2             2 4         2 3 3
+--R                 (- 440A c  - 920B b c)d e  + 880B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        2   5                     2  2 4
+--R                 - 40A b d e  + (460A b c + 235B b )d e
+--R               + 
+--R                          2              3 3          2 4 2
+--R                 (- 600A c  - 1220B b c)d e  + 1200B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2 2 4                    2  3 3            2             4 2
+--R             - 15A b d e  + (180A b c + 90B b )d e  + (- 240A c  - 480B b c)d e
+--R           + 
+--R                   2 5
+--R             480B c d e
+--R        *
+--R                  +------------+ +----------+
+--R            +---+ |           2  |   2
+--R           \|- c \|b d e - c d  \|c x  + b x
+--R    /
+--R                                                     +------------+
+--R           10 3        9 2      2 8       3 7  +---+ |           2
+--R       (24e  x  + 72d e x  + 72d e x + 24d e )\|- c \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 464
+
+--S 465 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                 2        3  3              2         2     2
+--R           (30A b c + 5B b )e  + (- 160A b c  - 120B b c)d e
+--R         + 
+--R                  3           2  2          3 3
+--R           (160A c  + 400B b c )d e - 320B c d
+--R      *
+--R        +--------------+                         +----------+
+--R        |             2  +-----------+ +-+       |   2                     +-+
+--R       \|- b d e + c d  \|- b e + c d \|d log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                 3 4         2         3    3              2         2   2 2
+--R           - 5A b e  + (90A b c + 35B b )d e  + (- 240A b c  - 280B b c)d e
+--R         + 
+--R                  3           2  3          3 4
+--R           (160A c  + 560B b c )d e - 320B c d
+--R      *
+--R          +-----------+ +-+ +-+
+--R         \|- b e + c d \|c \|d
+--R      *
+--R         log
+--R                                 +----------+
+--R                              2  |   2
+--R                (2b d e - 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                   2         3  3            2         2     2
+--R           (- 60A b c - 10B b )e  + (320A b c  + 240B b c)d e
+--R         + 
+--R                    3           2  2          3 3
+--R           (- 320A c  - 800B b c )d e + 640B c d
+--R      *
+--R          +--------------+                              +-+
+--R          |             2  +-----------+ +-+          x\|c
+--R         \|- b d e + c d  \|- b e + c d \|d atanh(-------------)
+--R                                                   +----------+
+--R                                                   |   2
+--R                                                  \|c x  + b x
+--R     + 
+--R               3 4           2         3    3            2         2   2 2
+--R           5A b e  + (- 90A b c - 35B b )d e  + (240A b c  + 280B b c)d e
+--R         + 
+--R                    3           2  3          3 4
+--R           (- 160A c  - 560B b c )d e + 320B c d
+--R      *
+--R          +--------------+
+--R          |             2  +-+             (b e - 2c d)x - b d
+--R         \|- b d e + c d  \|c atanh(--------------------------------)
+--R                                                        +----------+
+--R                                      +-----------+ +-+ |   2
+--R                                    2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R          +--------------+
+--R        7 |             2  +-----------+ +-+ +-+
+--R     16e \|- b d e + c d  \|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 465
+
+--S 466 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 466
+
+--S 467 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                 2        3  3              2         2     2
+--R           (30A b c + 5B b )e  + (- 160A b c  - 120B b c)d e
+--R         + 
+--R                  3           2  2          3 3
+--R           (160A c  + 400B b c )d e - 320B c d
+--R      *
+--R                            +------------+       +----------+
+--R          +-----------+ +-+ |           2        |   2                     +-+
+--R         \|- b e + c d \|d \|b d e - c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   2         3  3            2         2     2
+--R           (- 60A b c - 10B b )e  + (320A b c  + 240B b c)d e
+--R         + 
+--R                    3           2  2          3 3
+--R           (- 320A c  - 800B b c )d e + 640B c d
+--R      *
+--R                            +------------+            +-+
+--R          +-----------+ +-+ |           2           x\|c
+--R         \|- b e + c d \|d \|b d e - c d  atanh(-------------)
+--R                                                 +----------+
+--R                                                 |   2
+--R                                                \|c x  + b x
+--R     + 
+--R               3 4           2         3    3            2         2   2 2
+--R           5A b e  + (- 90A b c - 35B b )d e  + (240A b c  + 280B b c)d e
+--R         + 
+--R                    3           2  3          3 4
+--R           (- 160A c  - 560B b c )d e + 320B c d
+--R      *
+--R              +------------+
+--R          +-+ |           2              (b e - 2c d)x - b d
+--R         \|c \|b d e - c d  atanh(--------------------------------)
+--R                                                      +----------+
+--R                                    +-----------+ +-+ |   2
+--R                                  2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  3 4          2         3    3              2         2   2 2
+--R           - 10A b e  + (180A b c + 70B b )d e  + (- 480A b c  - 560B b c)d e
+--R         + 
+--R                  3            2  3          3 4
+--R           (320A c  + 1120B b c )d e - 640B c d
+--R      *
+--R                                     +------------+ +----------+
+--R                                     |           2  |   2
+--R          +-----------+ +-+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|c \|d atan(----------------------------)
+--R                                            (b e - c d)x
+--R  /
+--R                                +------------+
+--R        7 +-----------+ +-+ +-+ |           2
+--R     16e \|- b e + c d \|c \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 467
+
+--S 468 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 468
+
+)clear all
+
+--S 469 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^5
+--R 
+--R
+--R                                                                  +----------+
+--R            2 5       2           4                2  3      2 2  |   2
+--R        (B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x )\|c x  + b x
+--R   (1)  ----------------------------------------------------------------------
+--R                   5 5       4 4      2 3 3      3 2 2     4       5
+--R                  e x  + 5d e x  + 10d e x  + 10d e x  + 5d e x + d
+--R                                                    Type: Expression(Integer)
+--E 469
+
+--S 470 of 1457
+r0:=-5/32*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*d^2-64*b*c*d*e+_
+     17*b^2*e^2))*(b*x+c*x^2)^(3/2)/(d*e^4*(c*d-b*e)*(d+e*x)^2)-5/24*_
+     (B*d*(24*c*d-11*b*e)-A*e*(8*c*d-b*e)+6*e*(3*B*c*d-b*B*e-A*c*e)*x)*_
+     (b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^3)+1/4*(3*B*d-A*e+2*B*e*x)*(b*x+_
+     c*x^2)^(5/2)/(e^2*(d+e*x)^4)+5/128*(A*e*(128*c^4*d^4-256*b*c^3*d^3*e+_
+     144*b^2*c^2*d^2*e^2-16*b^3*c*d*e^3-b^4*e^4)-B*d*(384*c^4*d^4-_
+     896*b*c^3*d^3*e+672*b^2*c^2*d^2*e^2-168*b^3*c*d*e^3+7*b^4*e^4))*_
+     atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_
+     c*x^2)))/(d^(3/2)*e^7*(c*d-b*e)^(3/2))-5/4*(4*A*c*e*(2*c*d-b*e)-_
+     B*(24*c^2*d^2-20*b*c*d*e+3*b^2*e^2))*atanh(x*sqrt(c)/sqrt(b*x+_
+     c*x^2))*sqrt(c)/e^7-5/64*(B*d*(192*c^3*d^3-304*b*c^2*d^2*e+120*_
+     b^2*c*d*e^2-7*b^3*e^3)-A*e*(64*c^3*d^3-80*b*c^2*d^2*e+16*b^2*c*d*_
+     e^2+b^3*e^3)-2*c*e*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*_
+     d^2-64*b*c*d*e+17*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d*e^6*(c*d-b*e)*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                       2           3    7               2           2   2 6
+--R               (1920A b c + 1440B b )d e  + (- 5760A b c  - 11040B b c)d e
+--R             + 
+--R                       3             2  3 5           3 4 4
+--R               (3840A c  + 21120B b c )d e  - 11520B c d e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                       2           3  2 6                2           2   3 5
+--R               (7680A b c + 5760B b )d e  + (- 23040A b c  - 44160B b c)d e
+--R             + 
+--R                        3             2  4 4           3 5 3
+--R               (15360A c  + 84480B b c )d e  - 46080B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                        2           3  3 5                2           2   4 4
+--R               (11520A b c + 8640B b )d e  + (- 34560A b c  - 66240B b c)d e
+--R             + 
+--R                        3              2  5 3           3 6 2
+--R               (23040A c  + 126720B b c )d e  - 69120B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                       2           3  4 4                2           2   5 3
+--R               (7680A b c + 5760B b )d e  + (- 23040A b c  - 44160B b c)d e
+--R             + 
+--R                        3             2  6 2           3 7
+--R               (15360A c  + 84480B b c )d e  - 46080B c d e
+--R          *
+--R             x
+--R         + 
+--R                   2           3  5 3               2           2   6 2
+--R           (1920A b c + 1440B b )d e  + (- 5760A b c  - 11040B b c)d e
+--R         + 
+--R                   3             2  7            3 8
+--R           (3840A c  + 21120B b c )d e - 11520B c d
+--R      *
+--R                                           +-+
+--R          +-----------+ +-+ +-+          x\|c
+--R         \|- b e + c d \|c \|d atanh(-------------)
+--R                                      +----------+
+--R                                      |   2
+--R                                     \|c x  + b x
+--R     + 
+--R                      4 9            3          4    8
+--R               - 15A b e  + (- 240A b c - 105B b )d e
+--R             + 
+--R                       2 2          3   2 7               3           2 2  3 6
+--R               (2160A b c  + 2520B b c)d e  + (- 3840A b c  - 10080B b c )d e
+--R             + 
+--R                       4             3  4 5          4 5 4
+--R               (1920A c  + 13440B b c )d e  - 5760B c d e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                      4   8            3          4  2 7
+--R               - 60A b d e  + (- 960A b c - 420B b )d e
+--R             + 
+--R                       2 2           3   3 6                3           2 2  4 5
+--R               (8640A b c  + 10080B b c)d e  + (- 15360A b c  - 40320B b c )d e
+--R             + 
+--R                       4             3  5 4           4 6 3
+--R               (7680A c  + 53760B b c )d e  - 23040B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      4 2 7             3          4  3 6
+--R               - 90A b d e  + (- 1440A b c - 630B b )d e
+--R             + 
+--R                        2 2           3   4 5
+--R               (12960A b c  + 15120B b c)d e
+--R             + 
+--R                            3           2 2  5 4            4             3  6 3
+--R               (- 23040A b c  - 60480B b c )d e  + (11520A c  + 80640B b c )d e
+--R             + 
+--R                         4 7 2
+--R               - 34560B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      4 3 6            3          4  4 5
+--R               - 60A b d e  + (- 960A b c - 420B b )d e
+--R             + 
+--R                       2 2           3   5 4                3           2 2  6 3
+--R               (8640A b c  + 10080B b c)d e  + (- 15360A b c  - 40320B b c )d e
+--R             + 
+--R                       4             3  7 2           4 8
+--R               (7680A c  + 53760B b c )d e  - 23040B c d e
+--R          *
+--R             x
+--R         + 
+--R                  4 4 5            3          4  5 4
+--R           - 15A b d e  + (- 240A b c - 105B b )d e
+--R         + 
+--R                   2 2          3   6 3               3           2 2  7 2
+--R           (2160A b c  + 2520B b c)d e  + (- 3840A b c  - 10080B b c )d e
+--R         + 
+--R                   4             3  8           4 9
+--R           (1920A c  + 13440B b c )d e - 5760B c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                    2   7         3 2 6  5
+--R           (192B b c d e  - 192B c d e )x
+--R         + 
+--R                        2         2     7            3            2  2 6
+--R               (384A b c  + 864B b c)d e  + (- 384A c  - 2016B b c )d e
+--R             + 
+--R                      3 3 5
+--R               1152B c d e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                    3 8             2          3    7
+--R               30A b e  + (- 1292A b c - 558B b )d e
+--R             + 
+--R                         2          2   2 6             3             2  3 5
+--R               (5232A b c  + 8284B b c)d e  + (- 4000A c  - 19696B b c )d e
+--R             + 
+--R                       3 4 4
+--R               12000B c d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                       3   7             2           3  2 6
+--R               - 146A b d e  + (- 2264A b c - 1022B b )d e
+--R             + 
+--R                          2           2   3 5             3             2  4 4
+--R               (10640A b c  + 16392B b c)d e  + (- 8320A c  - 40240B b c )d e
+--R             + 
+--R                       3 5 3
+--R               24960B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                       3 2 6             2          3  3 5
+--R               - 110A b d e  + (- 1740A b c - 770B b )d e
+--R             + 
+--R                         2           2   4 4             3             2  5 3
+--R               (8480A b c  + 12860B b c)d e  + (- 6720A c  - 32160B b c )d e
+--R             + 
+--R                       3 6 2
+--R               20160B c d e
+--R          *
+--R             x
+--R         + 
+--R                  3 3 5            2          3  4 4
+--R           - 30A b d e  + (- 480A b c - 210B b )d e
+--R         + 
+--R                     2          2   5 3             3            2  6 2
+--R           (2400A b c  + 3600B b c)d e  + (- 1920A c  - 9120B b c )d e
+--R         + 
+--R                  3 7
+--R           5760B c d e
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R                  12         2 11  4           2 11          3 10  3
+--R         (384b d e   - 384c d e  )x  + (1536b d e   - 1536c d e  )x
+--R       + 
+--R                 3 10          4 9  2           4 9          5 8           5 8
+--R         (2304b d e   - 2304c d e )x  + (1536b d e  - 1536c d e )x + 384b d e
+--R       + 
+--R                 6 7
+--R         - 384c d e
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 470
+
+--S 471 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                        2          3    7               2          2   2 6
+--R                 (960A b c + 720B b )d e  + (- 2880A b c  - 5520B b c)d e
+--R               + 
+--R                         3             2  3 5          3 4 4
+--R                 (1920A c  + 10560B b c )d e  - 5760B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                         2           3  2 6                2           2   3 5
+--R                 (3840A b c + 2880B b )d e  + (- 11520A b c  - 22080B b c)d e
+--R               + 
+--R                         3             2  4 4           3 5 3
+--R                 (7680A c  + 42240B b c )d e  - 23040B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         2           3  3 5                2           2   4 4
+--R                 (5760A b c + 4320B b )d e  + (- 17280A b c  - 33120B b c)d e
+--R               + 
+--R                          3             2  5 3           3 6 2
+--R                 (11520A c  + 63360B b c )d e  - 34560B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         2           3  4 4                2           2   5 3
+--R                 (3840A b c + 2880B b )d e  + (- 11520A b c  - 22080B b c)d e
+--R               + 
+--R                         3             2  6 2           3 7
+--R                 (7680A c  + 42240B b c )d e  - 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2          3  5 3               2          2   6 2
+--R             (960A b c + 720B b )d e  + (- 2880A b c  - 5520B b c)d e
+--R           + 
+--R                     3             2  7           3 8
+--R             (1920A c  + 10560B b c )d e - 5760B c d
+--R        *
+--R            +--------------+              +----------+
+--R            |             2  +-+      +-+ |   2
+--R           \|- b d e + c d  \|c log(2\|c \|c x  + b x  + 2c x + b)
+--R       + 
+--R                      4 9          3          4    8
+--R                 15A b e  + (240A b c + 105B b )d e
+--R               + 
+--R                           2 2          3   2 7             3           2 2  3 6
+--R                 (- 2160A b c  - 2520B b c)d e  + (3840A b c  + 10080B b c )d e
+--R               + 
+--R                           4             3  4 5          4 5 4
+--R                 (- 1920A c  - 13440B b c )d e  + 5760B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      4   8          3          4  2 7
+--R                 60A b d e  + (960A b c + 420B b )d e
+--R               + 
+--R                           2 2           3   3 6
+--R                 (- 8640A b c  - 10080B b c)d e
+--R               + 
+--R                            3           2 2  4 5
+--R                 (15360A b c  + 40320B b c )d e
+--R               + 
+--R                           4             3  5 4           4 6 3
+--R                 (- 7680A c  - 53760B b c )d e  + 23040B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      4 2 7           3          4  3 6
+--R                 90A b d e  + (1440A b c + 630B b )d e
+--R               + 
+--R                            2 2           3   4 5
+--R                 (- 12960A b c  - 15120B b c)d e
+--R               + 
+--R                            3           2 2  5 4
+--R                 (23040A b c  + 60480B b c )d e
+--R               + 
+--R                            4             3  6 3           4 7 2
+--R                 (- 11520A c  - 80640B b c )d e  + 34560B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      4 3 6          3          4  4 5
+--R                 60A b d e  + (960A b c + 420B b )d e
+--R               + 
+--R                           2 2           3   5 4
+--R                 (- 8640A b c  - 10080B b c)d e
+--R               + 
+--R                            3           2 2  6 3
+--R                 (15360A b c  + 40320B b c )d e
+--R               + 
+--R                           4             3  7 2           4 8
+--R                 (- 7680A c  - 53760B b c )d e  + 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                  4 4 5          3          4  5 4
+--R             15A b d e  + (240A b c + 105B b )d e
+--R           + 
+--R                       2 2          3   6 3             3           2 2  7 2
+--R             (- 2160A b c  - 2520B b c)d e  + (3840A b c  + 10080B b c )d e
+--R           + 
+--R                       4             3  8           4 9
+--R             (- 1920A c  - 13440B b c )d e + 5760B c d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                      2   7         3 2 6  5
+--R             (192B b c d e  - 192B c d e )x
+--R           + 
+--R                          2         2     7            3            2  2 6
+--R                 (384A b c  + 864B b c)d e  + (- 384A c  - 2016B b c )d e
+--R               + 
+--R                        3 3 5
+--R                 1152B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      3 8             2          3    7
+--R                 30A b e  + (- 1292A b c - 558B b )d e
+--R               + 
+--R                           2          2   2 6             3             2  3 5
+--R                 (5232A b c  + 8284B b c)d e  + (- 4000A c  - 19696B b c )d e
+--R               + 
+--R                         3 4 4
+--R                 12000B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         3   7             2           3  2 6
+--R                 - 146A b d e  + (- 2264A b c - 1022B b )d e
+--R               + 
+--R                            2           2   3 5             3             2  4 4
+--R                 (10640A b c  + 16392B b c)d e  + (- 8320A c  - 40240B b c )d e
+--R               + 
+--R                         3 5 3
+--R                 24960B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         3 2 6             2          3  3 5
+--R                 - 110A b d e  + (- 1740A b c - 770B b )d e
+--R               + 
+--R                           2           2   4 4             3             2  5 3
+--R                 (8480A b c  + 12860B b c)d e  + (- 6720A c  - 32160B b c )d e
+--R               + 
+--R                         3 6 2
+--R                 20160B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 5            2          3  4 4
+--R             - 30A b d e  + (- 480A b c - 210B b )d e
+--R           + 
+--R                       2          2   5 3             3            2  6 2
+--R             (2400A b c  + 3600B b c)d e  + (- 1920A c  - 9120B b c )d e
+--R           + 
+--R                    3 7
+--R             5760B c d e
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                    12         2 11  4           2 11          3 10  3
+--R           (384b d e   - 384c d e  )x  + (1536b d e   - 1536c d e  )x
+--R         + 
+--R                   3 10          4 9  2           4 9          5 8           5 8
+--R           (2304b d e   - 2304c d e )x  + (1536b d e  - 1536c d e )x + 384b d e
+--R         + 
+--R                   6 7
+--R           - 384c d e
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                        2          3    7               2          2   2 6
+--R                 (480A b c + 360B b )d e  + (- 1440A b c  - 2760B b c)d e
+--R               + 
+--R                        3            2  3 5          3 4 4
+--R                 (960A c  + 5280B b c )d e  - 2880B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                         2           3  2 6               2           2   3 5
+--R                 (1920A b c + 1440B b )d e  + (- 5760A b c  - 11040B b c)d e
+--R               + 
+--R                         3             2  4 4           3 5 3
+--R                 (3840A c  + 21120B b c )d e  - 11520B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         2           3  3 5               2           2   4 4
+--R                 (2880A b c + 2160B b )d e  + (- 8640A b c  - 16560B b c)d e
+--R               + 
+--R                         3             2  5 3           3 6 2
+--R                 (5760A c  + 31680B b c )d e  - 17280B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         2           3  4 4               2           2   5 3
+--R                 (1920A b c + 1440B b )d e  + (- 5760A b c  - 11040B b c)d e
+--R               + 
+--R                         3             2  6 2           3 7
+--R                 (3840A c  + 21120B b c )d e  - 11520B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2          3  5 3               2          2   6 2
+--R             (480A b c + 360B b )d e  + (- 1440A b c  - 2760B b c)d e
+--R           + 
+--R                    3            2  7           3 8
+--R             (960A c  + 5280B b c )d e - 2880B c d
+--R        *
+--R                +------------+          +----------+
+--R            +-+ |           2       +-+ |   2
+--R           \|c \|b d e - c d  log(2\|c \|c x  + b x  + 2c x + b)
+--R       + 
+--R                        4 9            3          4    8
+--R                 - 15A b e  + (- 240A b c - 105B b )d e
+--R               + 
+--R                         2 2          3   2 7               3           2 2  3 6
+--R                 (2160A b c  + 2520B b c)d e  + (- 3840A b c  - 10080B b c )d e
+--R               + 
+--R                         4             3  4 5          4 5 4
+--R                 (1920A c  + 13440B b c )d e  - 5760B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                        4   8            3          4  2 7
+--R                 - 60A b d e  + (- 960A b c - 420B b )d e
+--R               + 
+--R                         2 2           3   3 6
+--R                 (8640A b c  + 10080B b c)d e
+--R               + 
+--R                              3           2 2  4 5
+--R                 (- 15360A b c  - 40320B b c )d e
+--R               + 
+--R                         4             3  5 4           4 6 3
+--R                 (7680A c  + 53760B b c )d e  - 23040B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        4 2 7             3          4  3 6
+--R                 - 90A b d e  + (- 1440A b c - 630B b )d e
+--R               + 
+--R                          2 2           3   4 5
+--R                 (12960A b c  + 15120B b c)d e
+--R               + 
+--R                              3           2 2  5 4
+--R                 (- 23040A b c  - 60480B b c )d e
+--R               + 
+--R                          4             3  6 3           4 7 2
+--R                 (11520A c  + 80640B b c )d e  - 34560B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4 3 6            3          4  4 5
+--R                 - 60A b d e  + (- 960A b c - 420B b )d e
+--R               + 
+--R                         2 2           3   5 4
+--R                 (8640A b c  + 10080B b c)d e
+--R               + 
+--R                              3           2 2  6 3
+--R                 (- 15360A b c  - 40320B b c )d e
+--R               + 
+--R                         4             3  7 2           4 8
+--R                 (7680A c  + 53760B b c )d e  - 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                    4 4 5            3          4  5 4
+--R             - 15A b d e  + (- 240A b c - 105B b )d e
+--R           + 
+--R                     2 2          3   6 3               3           2 2  7 2
+--R             (2160A b c  + 2520B b c)d e  + (- 3840A b c  - 10080B b c )d e
+--R           + 
+--R                     4             3  8           4 9
+--R             (1920A c  + 13440B b c )d e - 5760B c d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                     2   7        3 2 6  5
+--R             (96B b c d e  - 96B c d e )x
+--R           + 
+--R                          2         2     7            3            2  2 6
+--R                 (192A b c  + 432B b c)d e  + (- 192A c  - 1008B b c )d e
+--R               + 
+--R                       3 3 5
+--R                 576B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      3 8            2          3    7
+--R                 15A b e  + (- 646A b c - 279B b )d e
+--R               + 
+--R                           2          2   2 6             3            2  3 5
+--R                 (2616A b c  + 4142B b c)d e  + (- 2000A c  - 9848B b c )d e
+--R               + 
+--R                        3 4 4
+--R                 6000B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        3   7             2          3  2 6
+--R                 - 73A b d e  + (- 1132A b c - 511B b )d e
+--R               + 
+--R                           2          2   3 5             3             2  4 4
+--R                 (5320A b c  + 8196B b c)d e  + (- 4160A c  - 20120B b c )d e
+--R               + 
+--R                         3 5 3
+--R                 12480B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 6            2          3  3 5
+--R                 - 55A b d e  + (- 870A b c - 385B b )d e
+--R               + 
+--R                           2          2   4 4             3             2  5 3
+--R                 (4240A b c  + 6430B b c)d e  + (- 3360A c  - 16080B b c )d e
+--R               + 
+--R                         3 6 2
+--R                 10080B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 5            2          3  4 4
+--R             - 15A b d e  + (- 240A b c - 105B b )d e
+--R           + 
+--R                       2          2   5 3            3            2  6 2
+--R             (1200A b c  + 1800B b c)d e  + (- 960A c  - 4560B b c )d e
+--R           + 
+--R                    3 7
+--R             2880B c d e
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                    12         2 11  4          2 11         3 10  3
+--R           (192b d e   - 192c d e  )x  + (768b d e   - 768c d e  )x
+--R         + 
+--R                   3 10          4 9  2          4 9         5 8           5 8
+--R           (1152b d e   - 1152c d e )x  + (768b d e  - 768c d e )x + 192b d e
+--R         + 
+--R                   6 7
+--R           - 192c d e
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ,
+--R
+--R                      4 9          3          4    8
+--R                 15A b e  + (240A b c + 105B b )d e
+--R               + 
+--R                           2 2          3   2 7             3           2 2  3 6
+--R                 (- 2160A b c  - 2520B b c)d e  + (3840A b c  + 10080B b c )d e
+--R               + 
+--R                           4             3  4 5          4 5 4
+--R                 (- 1920A c  - 13440B b c )d e  + 5760B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      4   8          3          4  2 7
+--R                 60A b d e  + (960A b c + 420B b )d e
+--R               + 
+--R                           2 2           3   3 6
+--R                 (- 8640A b c  - 10080B b c)d e
+--R               + 
+--R                            3           2 2  4 5
+--R                 (15360A b c  + 40320B b c )d e
+--R               + 
+--R                           4             3  5 4           4 6 3
+--R                 (- 7680A c  - 53760B b c )d e  + 23040B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      4 2 7           3          4  3 6
+--R                 90A b d e  + (1440A b c + 630B b )d e
+--R               + 
+--R                            2 2           3   4 5
+--R                 (- 12960A b c  - 15120B b c)d e
+--R               + 
+--R                            3           2 2  5 4
+--R                 (23040A b c  + 60480B b c )d e
+--R               + 
+--R                            4             3  6 3           4 7 2
+--R                 (- 11520A c  - 80640B b c )d e  + 34560B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      4 3 6          3          4  4 5
+--R                 60A b d e  + (960A b c + 420B b )d e
+--R               + 
+--R                           2 2           3   5 4
+--R                 (- 8640A b c  - 10080B b c)d e
+--R               + 
+--R                            3           2 2  6 3
+--R                 (15360A b c  + 40320B b c )d e
+--R               + 
+--R                           4             3  7 2           4 8
+--R                 (- 7680A c  - 53760B b c )d e  + 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                  4 4 5          3          4  5 4
+--R             15A b d e  + (240A b c + 105B b )d e
+--R           + 
+--R                       2 2          3   6 3             3           2 2  7 2
+--R             (- 2160A b c  - 2520B b c)d e  + (3840A b c  + 10080B b c )d e
+--R           + 
+--R                       4             3  8           4 9
+--R             (- 1920A c  - 13440B b c )d e + 5760B c d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                         2           3    7               2           2   2 6
+--R                 (1920A b c + 1440B b )d e  + (- 5760A b c  - 11040B b c)d e
+--R               + 
+--R                         3             2  3 5           3 4 4
+--R                 (3840A c  + 21120B b c )d e  - 11520B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                         2           3  2 6                2           2   3 5
+--R                 (7680A b c + 5760B b )d e  + (- 23040A b c  - 44160B b c)d e
+--R               + 
+--R                          3             2  4 4           3 5 3
+--R                 (15360A c  + 84480B b c )d e  - 46080B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                          2           3  3 5                2           2   4 4
+--R                 (11520A b c + 8640B b )d e  + (- 34560A b c  - 66240B b c)d e
+--R               + 
+--R                          3              2  5 3           3 6 2
+--R                 (23040A c  + 126720B b c )d e  - 69120B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         2           3  4 4                2           2   5 3
+--R                 (7680A b c + 5760B b )d e  + (- 23040A b c  - 44160B b c)d e
+--R               + 
+--R                          3             2  6 2           3 7
+--R                 (15360A c  + 84480B b c )d e  - 46080B c d e
+--R            *
+--R               x
+--R           + 
+--R                     2           3  5 3               2           2   6 2
+--R             (1920A b c + 1440B b )d e  + (- 5760A b c  - 11040B b c)d e
+--R           + 
+--R                     3             2  7            3 8
+--R             (3840A c  + 21120B b c )d e - 11520B c d
+--R        *
+--R                                        +----------+
+--R            +--------------+            |   2
+--R            |             2  +---+     \|c x  + b x
+--R           \|- b d e + c d  \|- c atan(-------------)
+--R                                            +---+
+--R                                          x\|- c
+--R       + 
+--R                      2   7         3 2 6  5
+--R             (192B b c d e  - 192B c d e )x
+--R           + 
+--R                          2         2     7            3            2  2 6
+--R                 (384A b c  + 864B b c)d e  + (- 384A c  - 2016B b c )d e
+--R               + 
+--R                        3 3 5
+--R                 1152B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      3 8             2          3    7
+--R                 30A b e  + (- 1292A b c - 558B b )d e
+--R               + 
+--R                           2          2   2 6             3             2  3 5
+--R                 (5232A b c  + 8284B b c)d e  + (- 4000A c  - 19696B b c )d e
+--R               + 
+--R                         3 4 4
+--R                 12000B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         3   7             2           3  2 6
+--R                 - 146A b d e  + (- 2264A b c - 1022B b )d e
+--R               + 
+--R                            2           2   3 5             3             2  4 4
+--R                 (10640A b c  + 16392B b c)d e  + (- 8320A c  - 40240B b c )d e
+--R               + 
+--R                         3 5 3
+--R                 24960B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         3 2 6             2          3  3 5
+--R                 - 110A b d e  + (- 1740A b c - 770B b )d e
+--R               + 
+--R                           2           2   4 4             3             2  5 3
+--R                 (8480A b c  + 12860B b c)d e  + (- 6720A c  - 32160B b c )d e
+--R               + 
+--R                         3 6 2
+--R                 20160B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 5            2          3  4 4
+--R             - 30A b d e  + (- 480A b c - 210B b )d e
+--R           + 
+--R                       2          2   5 3             3            2  6 2
+--R             (2400A b c  + 3600B b c)d e  + (- 1920A c  - 9120B b c )d e
+--R           + 
+--R                    3 7
+--R             5760B c d e
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R                    12         2 11  4           2 11          3 10  3
+--R           (384b d e   - 384c d e  )x  + (1536b d e   - 1536c d e  )x
+--R         + 
+--R                   3 10          4 9  2           4 9          5 8           5 8
+--R           (2304b d e   - 2304c d e )x  + (1536b d e  - 1536c d e )x + 384b d e
+--R         + 
+--R                   6 7
+--R           - 384c d e
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                        4 9            3          4    8
+--R                 - 15A b e  + (- 240A b c - 105B b )d e
+--R               + 
+--R                         2 2          3   2 7               3           2 2  3 6
+--R                 (2160A b c  + 2520B b c)d e  + (- 3840A b c  - 10080B b c )d e
+--R               + 
+--R                         4             3  4 5          4 5 4
+--R                 (1920A c  + 13440B b c )d e  - 5760B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                        4   8            3          4  2 7
+--R                 - 60A b d e  + (- 960A b c - 420B b )d e
+--R               + 
+--R                         2 2           3   3 6
+--R                 (8640A b c  + 10080B b c)d e
+--R               + 
+--R                              3           2 2  4 5
+--R                 (- 15360A b c  - 40320B b c )d e
+--R               + 
+--R                         4             3  5 4           4 6 3
+--R                 (7680A c  + 53760B b c )d e  - 23040B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        4 2 7             3          4  3 6
+--R                 - 90A b d e  + (- 1440A b c - 630B b )d e
+--R               + 
+--R                          2 2           3   4 5
+--R                 (12960A b c  + 15120B b c)d e
+--R               + 
+--R                              3           2 2  5 4
+--R                 (- 23040A b c  - 60480B b c )d e
+--R               + 
+--R                          4             3  6 3           4 7 2
+--R                 (11520A c  + 80640B b c )d e  - 34560B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4 3 6            3          4  4 5
+--R                 - 60A b d e  + (- 960A b c - 420B b )d e
+--R               + 
+--R                         2 2           3   5 4
+--R                 (8640A b c  + 10080B b c)d e
+--R               + 
+--R                              3           2 2  6 3
+--R                 (- 15360A b c  - 40320B b c )d e
+--R               + 
+--R                         4             3  7 2           4 8
+--R                 (7680A c  + 53760B b c )d e  - 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                    4 4 5            3          4  5 4
+--R             - 15A b d e  + (- 240A b c - 105B b )d e
+--R           + 
+--R                     2 2          3   6 3               3           2 2  7 2
+--R             (2160A b c  + 2520B b c)d e  + (- 3840A b c  - 10080B b c )d e
+--R           + 
+--R                     4             3  8           4 9
+--R             (1920A c  + 13440B b c )d e - 5760B c d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                        2          3    7               2          2   2 6
+--R                 (960A b c + 720B b )d e  + (- 2880A b c  - 5520B b c)d e
+--R               + 
+--R                         3             2  3 5          3 4 4
+--R                 (1920A c  + 10560B b c )d e  - 5760B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                         2           3  2 6                2           2   3 5
+--R                 (3840A b c + 2880B b )d e  + (- 11520A b c  - 22080B b c)d e
+--R               + 
+--R                         3             2  4 4           3 5 3
+--R                 (7680A c  + 42240B b c )d e  - 23040B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         2           3  3 5                2           2   4 4
+--R                 (5760A b c + 4320B b )d e  + (- 17280A b c  - 33120B b c)d e
+--R               + 
+--R                          3             2  5 3           3 6 2
+--R                 (11520A c  + 63360B b c )d e  - 34560B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                         2           3  4 4                2           2   5 3
+--R                 (3840A b c + 2880B b )d e  + (- 11520A b c  - 22080B b c)d e
+--R               + 
+--R                         3             2  6 2           3 7
+--R                 (7680A c  + 42240B b c )d e  - 23040B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2          3  5 3               2          2   6 2
+--R             (960A b c + 720B b )d e  + (- 2880A b c  - 5520B b c)d e
+--R           + 
+--R                     3             2  7           3 8
+--R             (1920A c  + 10560B b c )d e - 5760B c d
+--R        *
+--R                                      +----------+
+--R                  +------------+      |   2
+--R            +---+ |           2      \|c x  + b x
+--R           \|- c \|b d e - c d  atan(-------------)
+--R                                          +---+
+--R                                        x\|- c
+--R       + 
+--R                     2   7        3 2 6  5
+--R             (96B b c d e  - 96B c d e )x
+--R           + 
+--R                          2         2     7            3            2  2 6
+--R                 (192A b c  + 432B b c)d e  + (- 192A c  - 1008B b c )d e
+--R               + 
+--R                       3 3 5
+--R                 576B c d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      3 8            2          3    7
+--R                 15A b e  + (- 646A b c - 279B b )d e
+--R               + 
+--R                           2          2   2 6             3            2  3 5
+--R                 (2616A b c  + 4142B b c)d e  + (- 2000A c  - 9848B b c )d e
+--R               + 
+--R                        3 4 4
+--R                 6000B c d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        3   7             2          3  2 6
+--R                 - 73A b d e  + (- 1132A b c - 511B b )d e
+--R               + 
+--R                           2          2   3 5             3             2  4 4
+--R                 (5320A b c  + 8196B b c)d e  + (- 4160A c  - 20120B b c )d e
+--R               + 
+--R                         3 5 3
+--R                 12480B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 6            2          3  3 5
+--R                 - 55A b d e  + (- 870A b c - 385B b )d e
+--R               + 
+--R                           2          2   4 4             3             2  5 3
+--R                 (4240A b c  + 6430B b c)d e  + (- 3360A c  - 16080B b c )d e
+--R               + 
+--R                         3 6 2
+--R                 10080B c d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 5            2          3  4 4
+--R             - 15A b d e  + (- 240A b c - 105B b )d e
+--R           + 
+--R                       2          2   5 3            3            2  6 2
+--R             (1200A b c  + 1800B b c)d e  + (- 960A c  - 4560B b c )d e
+--R           + 
+--R                    3 7
+--R             2880B c d e
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R                    12         2 11  4          2 11         3 10  3
+--R           (192b d e   - 192c d e  )x  + (768b d e   - 768c d e  )x
+--R         + 
+--R                   3 10          4 9  2          4 9         5 8           5 8
+--R           (1152b d e   - 1152c d e )x  + (768b d e  - 768c d e )x + 192b d e
+--R         + 
+--R                   6 7
+--R           - 192c d e
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 471
+
+--S 472 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                  2          3    3              2          2   2 2
+--R           (320A b c + 240B b )d e  + (- 960A b c  - 1840B b c)d e
+--R         + 
+--R                  3            2  3           3 4
+--R           (640A c  + 3520B b c )d e - 1920B c d
+--R      *
+--R        +--------------+                                +----------+
+--R        |             2  +-----------+ +-+ +-+      +-+ |   2
+--R       \|- b d e + c d  \|- b e + c d \|c \|d log(2\|c \|c x  + b x  + 2c x + b)
+--R     + 
+--R               4 5         3         4    4            2 2         3   2 3
+--R           5A b e  + (80A b c + 35B b )d e  + (- 720A b c  - 840B b c)d e
+--R         + 
+--R                     3          2 2  3 2            4            3  4
+--R           (1280A b c  + 3360B b c )d e  + (- 640A c  - 4480B b c )d e
+--R         + 
+--R                  4 5
+--R           1920B c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                    2          3    3             2          2   2 2
+--R           (- 640A b c - 480B b )d e  + (1920A b c  + 3680B b c)d e
+--R         + 
+--R                     3            2  3           3 4
+--R           (- 1280A c  - 7040B b c )d e + 3840B c d
+--R      *
+--R          +--------------+                                  +-+
+--R          |             2  +-----------+ +-+ +-+          x\|c
+--R         \|- b d e + c d  \|- b e + c d \|c \|d atanh(-------------)
+--R                                                       +----------+
+--R                                                       |   2
+--R                                                      \|c x  + b x
+--R     + 
+--R               4 5         3         4    4            2 2         3   2 3
+--R           5A b e  + (80A b c + 35B b )d e  + (- 720A b c  - 840B b c)d e
+--R         + 
+--R                     3          2 2  3 2            4            3  4
+--R           (1280A b c  + 3360B b c )d e  + (- 640A c  - 4480B b c )d e
+--R         + 
+--R                  4 5
+--R           1920B c d
+--R      *
+--R          +--------------+
+--R          |             2              (b e - 2c d)x - b d
+--R         \|- b d e + c d  atanh(--------------------------------)
+--R                                                    +----------+
+--R                                  +-----------+ +-+ |   2
+--R                                2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                             +--------------+
+--R              8         2 7  |             2  +-----------+ +-+
+--R     (128b d e  - 128c d e )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 472
+
+--S 473 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 473
+
+--S 474 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                  2          3    3              2          2   2 2
+--R           (320A b c + 240B b )d e  + (- 960A b c  - 1840B b c)d e
+--R         + 
+--R                  3            2  3           3 4
+--R           (640A c  + 3520B b c )d e - 1920B c d
+--R      *
+--R                              +------------+          +----------+
+--R        +-----------+ +-+ +-+ |           2       +-+ |   2
+--R       \|- b e + c d \|c \|d \|b d e - c d  log(2\|c \|c x  + b x  + 2c x + b)
+--R     + 
+--R                    2          3    3             2          2   2 2
+--R           (- 640A b c - 480B b )d e  + (1920A b c  + 3680B b c)d e
+--R         + 
+--R                     3            2  3           3 4
+--R           (- 1280A c  - 7040B b c )d e + 3840B c d
+--R      *
+--R                                +------------+            +-+
+--R          +-----------+ +-+ +-+ |           2           x\|c
+--R         \|- b e + c d \|c \|d \|b d e - c d  atanh(-------------)
+--R                                                     +----------+
+--R                                                     |   2
+--R                                                    \|c x  + b x
+--R     + 
+--R               4 5         3         4    4            2 2         3   2 3
+--R           5A b e  + (80A b c + 35B b )d e  + (- 720A b c  - 840B b c)d e
+--R         + 
+--R                     3          2 2  3 2            4            3  4
+--R           (1280A b c  + 3360B b c )d e  + (- 640A c  - 4480B b c )d e
+--R         + 
+--R                  4 5
+--R           1920B c d
+--R      *
+--R          +------------+
+--R          |           2              (b e - 2c d)x - b d
+--R         \|b d e - c d  atanh(--------------------------------)
+--R                                                  +----------+
+--R                                +-----------+ +-+ |   2
+--R                              2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  4 5            3         4    4           2 2          3   2 3
+--R           - 10A b e  + (- 160A b c - 70B b )d e  + (1440A b c  + 1680B b c)d e
+--R         + 
+--R                       3          2 2  3 2           4            3  4
+--R           (- 2560A b c  - 6720B b c )d e  + (1280A c  + 8960B b c )d e
+--R         + 
+--R                    4 5
+--R           - 3840B c d
+--R      *
+--R                                 +------------+ +----------+
+--R                                 |           2  |   2
+--R          +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|d atan(----------------------------)
+--R                                        (b e - c d)x
+--R  /
+--R                                               +------------+
+--R              8         2 7  +-----------+ +-+ |           2
+--R     (128b d e  - 128c d e )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 474
+
+--S 475 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 1457
+t0:=(A+B*x)*(d+e*x)^3/sqrt(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R      3 4       3         2  3          2       2   2        2       3        3
+--R   B e x  + (A e  + 3B d e )x  + (3A d e  + 3B d e)x  + (3A d e + B d )x + A d
+--R   ----------------------------------------------------------------------------
+--R                                    +----------+
+--R                                    |   2
+--R                                   \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 476
+
+--S 477 of 1457
+r0:=1/64*(128*A*c^4*d^3+35*b^4*B*e^3+144*b^2*c^2*d*e*(B*d+A*e)-40*b^3*_
+     c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*atanh(x*sqrt(c)/_
+     sqrt(b*x+c*x^2))/c^(9/2)+1/192*(8*A*c*e*(52*c^2*d^2-52*b*c*d*e+_
+     15*b^2*e^2)+B*(96*c^3*d^3-352*b*c^2*d^2*e+346*b^2*c*d*e^2-105*_
+     b^3*e^3))*sqrt(b*x+c*x^2)/c^4+1/24*(6*B*c*d-7*b*B*e+8*A*c*e)*_
+     (d+e*x)^2*sqrt(b*x+c*x^2)/c^2+1/4*B*(d+e*x)^3*sqrt(b*x+c*x^2)/c-_
+     1/96*e*(d*(12*b*B*c*d-48*A*c^2*d-7*b^2*B*e+8*A*b*c*e)-(40*A*c*e*_
+     (2*c*d-b*e)+B*(24*c^2*d^2-64*b*c*d*e+35*b^2*e^2))*x)*sqrt(b*x+c*x^2)/c^3
+--R 
+--R
+--R   (2)
+--R                    3          4  3          2 2         3     2
+--R           (- 120A b c + 105B b )e  + (432A b c  - 360B b c)d e
+--R         + 
+--R                      3         2 2  2           4           3  3
+--R           (- 576A b c  + 432B b c )d e + (384A c  - 192B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                3 3 3          3          2  3         3   2  2
+--R           48B c e x  + ((64A c  - 56B b c )e  + 192B c d e )x
+--R         + 
+--R                      2        2   3          3           2    2         3 2
+--R           ((- 80A b c  + 70B b c)e  + (288A c  - 240B b c )d e  + 288B c d e)x
+--R         + 
+--R                  2          3  3              2         2     2
+--R           (120A b c - 105B b )e  + (- 432A b c  + 360B b c)d e
+--R         + 
+--R                  3           2  2          3 3
+--R           (576A c  - 432B b c )d e + 192B c d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R         4 +-+
+--R     192c \|c
+--R                                                    Type: Expression(Integer)
+--E 477
+
+--S 478 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                    3          4  3            2 2         3     2
+--R             (120A b c - 105B b )e  + (- 432A b c  + 360B b c)d e
+--R           + 
+--R                      3         2 2  2             4           3  3
+--R             (576A b c  - 432B b c )d e + (- 384A c  + 192B b c )d
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                  3 3 3           3           2  3         3   2  2
+--R             96B c e x  + ((128A c  - 112B b c )e  + 384B c d e )x
+--R           + 
+--R                            2         2   3          3           2    2
+--R                 (- 160A b c  + 140B b c)e  + (576A c  - 480B b c )d e
+--R               + 
+--R                       3 2
+--R                 576B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2          3  3              2         2     2
+--R             (240A b c - 210B b )e  + (- 864A b c  + 720B b c)d e
+--R           + 
+--R                     3           2  2          3 3
+--R             (1152A c  - 864B b c )d e + 384B c d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R           4 +-+
+--R       384c \|c
+--R     ,
+--R
+--R                      3          4  3          2 2         3     2
+--R             (- 120A b c + 105B b )e  + (432A b c  - 360B b c)d e
+--R           + 
+--R                        3         2 2  2           4           3  3
+--R             (- 576A b c  + 432B b c )d e + (384A c  - 192B b c )d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                  3 3 3          3          2  3         3   2  2
+--R             48B c e x  + ((64A c  - 56B b c )e  + 192B c d e )x
+--R           + 
+--R                             2        2   3          3           2    2
+--R                   (- 80A b c  + 70B b c)e  + (288A c  - 240B b c )d e
+--R                 + 
+--R                         3 2
+--R                   288B c d e
+--R            *
+--R               x
+--R           + 
+--R                    2          3  3              2         2     2
+--R             (120A b c - 105B b )e  + (- 432A b c  + 360B b c)d e
+--R           + 
+--R                    3           2  2          3 3
+--R             (576A c  - 432B b c )d e + 192B c d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R           4 +---+
+--R       192c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 478
+
+--S 479 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                 3         4  3            2 2         3     2
+--R           (40A b c - 35B b )e  + (- 144A b c  + 120B b c)d e
+--R         + 
+--R                    3         2 2  2             4          3  3
+--R           (192A b c  - 144B b c )d e + (- 128A c  + 64B b c )d
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                 3         4  3            2 2         3     2
+--R           (80A b c - 70B b )e  + (- 288A b c  + 240B b c)d e
+--R         + 
+--R                    3         2 2  2             4           3  3
+--R           (384A b c  - 288B b c )d e + (- 256A c  + 128B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R  /
+--R         4 +-+
+--R     128c \|c
+--R                                                    Type: Expression(Integer)
+--E 479
+
+--S 480 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 480
+
+--S 481 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                 3         4  3            2 2         3     2
+--R           (40A b c - 35B b )e  + (- 144A b c  + 120B b c)d e
+--R         + 
+--R                    3         2 2  2             4          3  3
+--R           (192A b c  - 144B b c )d e + (- 128A c  + 64B b c )d
+--R      *
+--R                           +-+
+--R          +---+          x\|c
+--R         \|- c atanh(-------------)
+--R                      +----------+
+--R                      |   2
+--R                     \|c x  + b x
+--R     + 
+--R                   3         4  3          2 2         3     2
+--R           (- 40A b c + 35B b )e  + (144A b c  - 120B b c)d e
+--R         + 
+--R                      3         2 2  2           4          3  3
+--R           (- 192A b c  + 144B b c )d e + (128A c  - 64B b c )d
+--R      *
+--R                         +----------+
+--R                   +---+ |   2
+--R          +-+     \|- c \|c x  + b x
+--R         \|c atan(-------------------)
+--R                          c x
+--R  /
+--R        4 +---+ +-+
+--R     64c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 481
+
+--S 482 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 482
+
+)clear all
+
+--S 483 of 1457
+t0:=(A+B*x)*(d+e*x)^2/sqrt(b*x+c*x^2)
+--R 
+--R
+--R           2 3       2           2                2        2
+--R        B e x  + (A e  + 2B d e)x  + (2A d e + B d )x + A d
+--R   (1)  ----------------------------------------------------
+--R                             +----------+
+--R                             |   2
+--R                            \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 483
+
+--S 484 of 1457
+r0:=1/8*(16*A*c^3*d^2-5*b^3*B*e^2+6*b^2*c*e*(2*B*d+A*e)-8*b*c^2*d*_
+     (B*d+2*A*e))*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/24*(18*A*c*_
+     e*(2*c*d-b*e)+B*(16*c^2*d^2-34*b*c*d*e+15*b^2*e^2))*sqrt(b*x+_
+     c*x^2)/c^3+1/3*B*(d+e*x)^2*sqrt(b*x+c*x^2)/c-1/12*e*((b*B-6*A*c)*_
+     d-(4*B*c*d-5*b*B*e+6*A*c*e)*x)*sqrt(b*x+c*x^2)/c^2
+--R 
+--R
+--R   (2)
+--R                 2         3  2             2        2
+--R           (18A b c - 15B b )e  + (- 48A b c  + 36B b c)d e
+--R         + 
+--R                 3          2  2
+--R           (48A c  - 24B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R               2 2 2          2            2        2
+--R           8B c e x  + ((12A c  - 10B b c)e  + 24B c d e)x
+--R         + 
+--R                             2  2         2                      2 2
+--R           (- 18A b c + 15B b )e  + (48A c  - 36B b c)d e + 24B c d
+--R      *
+--R              +----------+
+--R          +-+ |   2
+--R         \|c \|c x  + b x
+--R  /
+--R        3 +-+
+--R     24c \|c
+--R                                                    Type: Expression(Integer)
+--E 484
+
+--S 485 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                   2         3  2             2        2
+--R             (18A b c - 15B b )e  + (- 48A b c  + 36B b c)d e
+--R           + 
+--R                   3          2  2
+--R             (48A c  - 24B b c )d
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                  2 2 2          2            2        2
+--R             16B c e x  + ((24A c  - 20B b c)e  + 48B c d e)x
+--R           + 
+--R                               2  2         2                      2 2
+--R             (- 36A b c + 30B b )e  + (96A c  - 72B b c)d e + 48B c d
+--R        *
+--R                +----------+
+--R            +-+ |   2
+--R           \|c \|c x  + b x
+--R    /
+--R          3 +-+
+--R       48c \|c
+--R     ,
+--R
+--R                   2         3  2             2        2
+--R             (18A b c - 15B b )e  + (- 48A b c  + 36B b c)d e
+--R           + 
+--R                   3          2  2
+--R             (48A c  - 24B b c )d
+--R        *
+--R                       +----------+
+--R                 +---+ |   2
+--R                \|- c \|c x  + b x
+--R           atan(-------------------)
+--R                        c x
+--R       + 
+--R                 2 2 2          2            2        2
+--R             8B c e x  + ((12A c  - 10B b c)e  + 24B c d e)x
+--R           + 
+--R                               2  2         2                      2 2
+--R             (- 18A b c + 15B b )e  + (48A c  - 36B b c)d e + 24B c d
+--R        *
+--R                  +----------+
+--R            +---+ |   2
+--R           \|- c \|c x  + b x
+--R    /
+--R          3 +---+
+--R       24c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 485
+
+--S 486 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R               2        3  2             2        2              3         2  2
+--R         ((6A b c - 5B b )e  + (- 16A b c  + 12B b c)d e + (16A c  - 8B b c )d )
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                   2         3  2           2        2
+--R           (- 12A b c + 10B b )e  + (32A b c  - 24B b c)d e
+--R         + 
+--R                   3          2  2
+--R           (- 32A c  + 16B b c )d
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R  /
+--R        3 +-+
+--R     16c \|c
+--R                                                    Type: Expression(Integer)
+--E 486
+
+--S 487 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 487
+
+--S 488 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                    2        3  2           2        2
+--R             (- 6A b c + 5B b )e  + (16A b c  - 12B b c)d e
+--R           + 
+--R                     3         2  2
+--R             (- 16A c  + 8B b c )d
+--R      *
+--R                           +-+
+--R          +---+          x\|c
+--R         \|- c atanh(-------------)
+--R                      +----------+
+--R                      |   2
+--R                     \|c x  + b x
+--R     + 
+--R               2        3  2             2        2              3         2  2
+--R         ((6A b c - 5B b )e  + (- 16A b c  + 12B b c)d e + (16A c  - 8B b c )d )
+--R      *
+--R                         +----------+
+--R                   +---+ |   2
+--R          +-+     \|- c \|c x  + b x
+--R         \|c atan(-------------------)
+--R                          c x
+--R  /
+--R       3 +---+ +-+
+--R     8c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 488
+
+--S 489 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 489
+
+)clear all
+
+--S 490 of 1457
+t0:=(A+B*x)*(d+e*x)/sqrt(b*x+c*x^2)
+--R 
+--R
+--R             2
+--R        B e x  + (A e + B d)x + A d
+--R   (1)  ---------------------------
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 490
+
+--S 491 of 1457
+r0:=1/4*(8*A*c^2*d+3*b^2*B*e-4*b*c*(B*d+A*e))*atanh(x*sqrt(c)/sqrt(b*x+_
+     c*x^2))/c^(5/2)+1/4*(2*B*c*d-3*b*B*e+4*A*c*e)*sqrt(b*x+c*x^2)/c^2+_
+     1/2*B*(d+e*x)*sqrt(b*x+c*x^2)/c
+--R 
+--R
+--R   (2)
+--R                                                            +-+
+--R                        2          2                      x\|c
+--R       ((- 4A b c + 3B b )e + (8A c  - 4B b c)d)atanh(-------------)
+--R                                                       +----------+
+--R                                                       |   2
+--R                                                      \|c x  + b x
+--R     + 
+--R                                                +----------+
+--R                                            +-+ |   2
+--R       (2B c e x + (4A c - 3B b)e + 4B c d)\|c \|c x  + b x
+--R  /
+--R       2 +-+
+--R     4c \|c
+--R                                                    Type: Expression(Integer)
+--E 491
+
+--S 492 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                          2            2
+--R           ((4A b c - 3B b )e + (- 8A c  + 4B b c)d)
+--R        *
+--R                    +----------+
+--R                    |   2                     +-+
+--R           log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                                                  +----------+
+--R                                              +-+ |   2
+--R         (4B c e x + (8A c - 6B b)e + 8B c d)\|c \|c x  + b x
+--R    /
+--R         2 +-+
+--R       8c \|c
+--R     ,
+--R
+--R                                                              +----------+
+--R                                                        +---+ |   2
+--R                          2          2                 \|- c \|c x  + b x
+--R         ((- 4A b c + 3B b )e + (8A c  - 4B b c)d)atan(-------------------)
+--R                                                               c x
+--R       + 
+--R                                                    +----------+
+--R                                              +---+ |   2
+--R         (2B c e x + (4A c - 3B b)e + 4B c d)\|- c \|c x  + b x
+--R    /
+--R         2 +---+
+--R       4c \|- c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 492
+
+--S 493 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                        2            2
+--R         ((4A b c - 3B b )e + (- 8A c  + 4B b c)d)
+--R      *
+--R                  +----------+
+--R                  |   2                     +-+
+--R         log(- 2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                                             +-+
+--R                      2             2                      x\|c
+--R       ((8A b c - 6B b )e + (- 16A c  + 8B b c)d)atanh(-------------)
+--R                                                        +----------+
+--R                                                        |   2
+--R                                                       \|c x  + b x
+--R  /
+--R       2 +-+
+--R     8c \|c
+--R                                                    Type: Expression(Integer)
+--E 493
+
+--S 494 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 494
+
+--S 495 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                                  +-+
+--R                      2            2             +---+          x\|c
+--R       ((4A b c - 3B b )e + (- 8A c  + 4B b c)d)\|- c atanh(-------------)
+--R                                                             +----------+
+--R                                                             |   2
+--R                                                            \|c x  + b x
+--R     + 
+--R                                                                +----------+
+--R                                                          +---+ |   2
+--R                        2          2             +-+     \|- c \|c x  + b x
+--R       ((- 4A b c + 3B b )e + (8A c  - 4B b c)d)\|c atan(-------------------)
+--R                                                                 c x
+--R  /
+--R       2 +---+ +-+
+--R     4c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 495
+
+--S 496 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 496
+
+)clear all
+
+--S 497 of 1457
+t0:=(A+B*x)/sqrt(b*x+c*x^2)
+--R 
+--R
+--R           B x + A
+--R   (1)  -------------
+--R         +----------+
+--R         |   2
+--R        \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 497
+
+--S 498 of 1457
+r0:=-(b*B-2*A*c)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+B*sqrt(b*x+c*x^2)/c
+--R 
+--R
+--R                                +-+              +----------+
+--R                              x\|c           +-+ |   2
+--R        (2A c - B b)atanh(-------------) + B\|c \|c x  + b x
+--R                           +----------+
+--R                           |   2
+--R                          \|c x  + b x
+--R   (2)  -----------------------------------------------------
+--R                                  +-+
+--R                                c\|c
+--R                                                    Type: Expression(Integer)
+--E 498
+
+--S 499 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                       +----------+                            +----------+
+--R                       |   2                     +-+       +-+ |   2
+--R    (2A c - B b)log(2c\|c x  + b x  + (2c x + b)\|c ) + 2B\|c \|c x  + b x
+--R   [-----------------------------------------------------------------------,
+--R                                        +-+
+--R                                     2c\|c
+--R                            +----------+
+--R                      +---+ |   2                   +----------+
+--R                     \|- c \|c x  + b x       +---+ |   2
+--R    (2A c - B b)atan(-------------------) + B\|- c \|c x  + b x
+--R                             c x
+--R    ------------------------------------------------------------]
+--R                                 +---+
+--R                               c\|- c
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 499
+
+--S 500 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                          +----------+
+--R                          |   2                     +-+
+--R       (2A c - B b)log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                  +-+
+--R                                x\|c
+--R       (- 4A c + 2B b)atanh(-------------)
+--R                             +----------+
+--R                             |   2
+--R                            \|c x  + b x
+--R  /
+--R        +-+
+--R     2c\|c
+--R                                                    Type: Expression(Integer)
+--E 500
+
+--S 501 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 501
+
+--S 502 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                       +-+
+--R                      +---+          x\|c
+--R       (- 2A c + B b)\|- c atanh(-------------)
+--R                                  +----------+
+--R                                  |   2
+--R                                 \|c x  + b x
+--R     + 
+--R                                   +----------+
+--R                             +---+ |   2
+--R                    +-+     \|- c \|c x  + b x
+--R       (2A c - B b)\|c atan(-------------------)
+--R                                    c x
+--R  /
+--R       +---+ +-+
+--R     c\|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 502
+
+--S 503 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 503
+
+)clear all
+
+--S 504 of 1457
+t0:=(A+B*x)/((d+e*x)*sqrt(b*x+c*x^2))
+--R 
+--R
+--R                B x + A
+--R   (1)  ----------------------
+--R                  +----------+
+--R                  |   2
+--R        (e x + d)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 504
+
+--S 505 of 1457
+r0:=2*B*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e*sqrt(c))-(B*d-A*e)*atanh(1/2*_
+     (b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/_
+     (e*sqrt(d)*sqrt(c*d-b*e))
+--R 
+--R
+--R   (2)
+--R                                       +-+
+--R          +-----------+ +-+          x\|c
+--R       2B\|- b e + c d \|d atanh(-------------)
+--R                                  +----------+
+--R                                  |   2
+--R                                 \|c x  + b x
+--R     + 
+--R                     +-+             (b e - 2c d)x - b d
+--R       (- A e + B d)\|c atanh(--------------------------------)
+--R                                                  +----------+
+--R                                +-----------+ +-+ |   2
+--R                              2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R       +-----------+ +-+ +-+
+--R     e\|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 505
+
+--S 506 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R           +--------------+       +----------+
+--R           |             2        |   2                     +-+
+--R         B\|- b d e + c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                       +-+
+--R           (A e - B d)\|c
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R    /
+--R         +--------------+
+--R         |             2  +-+
+--R       e\|- b d e + c d  \|c
+--R     ,
+--R
+--R           +------------+       +----------+
+--R           |           2        |   2                     +-+
+--R         B\|b d e - c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                                  +------------+ +----------+
+--R                                  |           2  |   2
+--R                         +-+     \|b d e - c d  \|c x  + b x
+--R         (- 2A e + 2B d)\|c atan(----------------------------)
+--R                                         (b e - c d)x
+--R    /
+--R             +------------+
+--R         +-+ |           2
+--R       e\|c \|b d e - c d
+--R     ,
+--R
+--R                       +---+
+--R           (A e - B d)\|- c
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                                        +----------+
+--R            +--------------+      +---+ |   2
+--R            |             2      \|- c \|c x  + b x
+--R         2B\|- b d e + c d  atan(-------------------)
+--R                                         c x
+--R    /
+--R         +--------------+
+--R         |             2  +---+
+--R       e\|- b d e + c d  \|- c
+--R     ,
+--R
+--R                                    +------------+ +----------+
+--R                                    |           2  |   2
+--R                         +---+     \|b d e - c d  \|c x  + b x
+--R         (- 2A e + 2B d)\|- c atan(----------------------------)
+--R                                           (b e - c d)x
+--R       + 
+--R                                      +----------+
+--R            +------------+      +---+ |   2
+--R            |           2      \|- c \|c x  + b x
+--R         2B\|b d e - c d  atan(-------------------)
+--R                                       c x
+--R    /
+--R               +------------+
+--R         +---+ |           2
+--R       e\|- c \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 506
+
+--S 507 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R         +--------------+                         +----------+
+--R         |             2  +-----------+ +-+       |   2                     +-+
+--R       B\|- b d e + c d  \|- b e + c d \|d log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                     +-----------+ +-+ +-+
+--R         (A e - B d)\|- b e + c d \|c \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R            +--------------+                              +-+
+--R            |             2  +-----------+ +-+          x\|c
+--R       - 2B\|- b d e + c d  \|- b e + c d \|d atanh(-------------)
+--R                                                     +----------+
+--R                                                     |   2
+--R                                                    \|c x  + b x
+--R     + 
+--R                   +--------------+
+--R                   |             2  +-+             (b e - 2c d)x - b d
+--R       (A e - B d)\|- b d e + c d  \|c atanh(--------------------------------)
+--R                                                                 +----------+
+--R                                               +-----------+ +-+ |   2
+--R                                             2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R       +--------------+
+--R       |             2  +-----------+ +-+ +-+
+--R     e\|- b d e + c d  \|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 507
+
+--S 508 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 508
+
+--S 509 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                           +------------+       +----------+
+--R         +-----------+ +-+ |           2        |   2                     +-+
+--R       B\|- b e + c d \|d \|b d e - c d  log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                              +------------+            +-+
+--R            +-----------+ +-+ |           2           x\|c
+--R       - 2B\|- b e + c d \|d \|b d e - c d  atanh(-------------)
+--R                                                   +----------+
+--R                                                   |   2
+--R                                                  \|c x  + b x
+--R     + 
+--R                       +------------+
+--R                   +-+ |           2              (b e - 2c d)x - b d
+--R       (A e - B d)\|c \|b d e - c d  atanh(--------------------------------)
+--R                                                               +----------+
+--R                                             +-----------+ +-+ |   2
+--R                                           2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                                  +------------+ +----------+
+--R                                                  |           2  |   2
+--R                       +-----------+ +-+ +-+     \|b d e - c d  \|c x  + b x
+--R       (- 2A e + 2B d)\|- b e + c d \|c \|d atan(----------------------------)
+--R                                                         (b e - c d)x
+--R  /
+--R                             +------------+
+--R       +-----------+ +-+ +-+ |           2
+--R     e\|- b e + c d \|c \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 509
+
+--S 510 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 510
+
+)clear all
+
+--S 511 of 1457
+t0:=(A+B*x)/((d+e*x)^2*sqrt(b*x+c*x^2))
+--R 
+--R
+--R                     B x + A
+--R   (1)  ---------------------------------
+--R                             +----------+
+--R          2 2             2  |   2
+--R        (e x  + 2d e x + d )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 511
+
+--S 512 of 1457
+r0:=-1/2*(b*B*d-2*A*c*d+A*b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_
+     sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))+(B*d-A*e)*_
+     sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                  2                                              2
+--R         ((- A b e  + (2A c - B b)d e)x - A b d e + (2A c - B b)d )
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                       +----------+
+--R                     +-----------+ +-+ |   2
+--R       (2A e - 2B d)\|- b e + c d \|d \|c x  + b x
+--R  /
+--R             2       2          2        3  +-----------+ +-+
+--R     ((2b d e  - 2c d e)x + 2b d e - 2c d )\|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 512
+
+--S 513 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                  2                                                  2
+--R           ((A b e  + (- 2A c + B b)d e)x + A b d e + (- 2A c + B b)d )
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                       +--------------+ +----------+
+--R                       |             2  |   2
+--R         (2A e - 2B d)\|- b d e + c d  \|c x  + b x
+--R    /
+--R                                              +--------------+
+--R               2       2          2        3  |             2
+--R       ((2b d e  - 2c d e)x + 2b d e - 2c d )\|- b d e + c d
+--R     ,
+--R
+--R                    2                                              2
+--R           ((- A b e  + (2A c - B b)d e)x - A b d e + (2A c - B b)d )
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                     +------------+ +----------+
+--R                     |           2  |   2
+--R         (A e - B d)\|b d e - c d  \|c x  + b x
+--R    /
+--R                                          +------------+
+--R              2      2         2       3  |           2
+--R       ((b d e  - c d e)x + b d e - c d )\|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 513
+
+--S 514 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                   +-----------+ +-+
+--R         (A b e + (- 2A c + B b)d)\|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                   +--------------+
+--R                                   |             2
+--R         (A b e + (- 2A c + B b)d)\|- b d e + c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                      +--------------+
+--R                   2  |             2  +-----------+ +-+
+--R     (2b d e - 2c d )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 514
+
+--S 515 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 515
+
+--S 516 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                   +------------+
+--R                                   |           2
+--R         (A b e + (- 2A c + B b)d)\|b d e - c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                     +-----------+ +-+
+--R         (- 2A b e + (4A c - 2B b)d)\|- b e + c d \|d
+--R      *
+--R               +------------+ +----------+
+--R               |           2  |   2
+--R              \|b d e - c d  \|c x  + b x
+--R         atan(----------------------------)
+--R                      (b e - c d)x
+--R  /
+--R                                        +------------+
+--R                   2  +-----------+ +-+ |           2
+--R     (2b d e - 2c d )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 516
+
+--S 517 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 517
+
+)clear all
+
+--S 518 of 1457
+t0:=(A+B*x)/((d+e*x)^3*sqrt(b*x+c*x^2))
+--R 
+--R
+--R                          B x + A
+--R   (1)  -------------------------------------------
+--R                                       +----------+
+--R          3 3       2 2     2       3  |   2
+--R        (e x  + 3d e x  + 3d e x + d )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 518
+
+--S 519 of 1457
+r0:=1/8*(8*A*c^2*d^2-4*b*c*d*(B*d+2*A*e)+b^2*e*(B*d+3*A*e))*atanh(1/2*(b*d+_
+     (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*_
+     (c*d-b*e)^(5/2))+1/2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_
+     (d+e*x)^2)-1/4*(3*A*e*(2*c*d-b*e)-B*d*(2*c*d+b*e))*sqrt(b*x+c*x^2)/_
+     (d^2*(c*d-b*e)^2*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                  2 4                2    3          2           2 2  2
+--R           (- 3A b e  + (8A b c - B b )d e  + (- 8A c  + 4B b c)d e )x
+--R         + 
+--R                  2   3                  2  2 2           2           3
+--R           (- 6A b d e  + (16A b c - 2B b )d e  + (- 16A c  + 8B b c)d e)x
+--R         + 
+--R                 2 2 2                2  3           2           4
+--R           - 3A b d e  + (8A b c - B b )d e + (- 8A c  + 4B b c)d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  3                      2         2               2
+--R           (6A b e  + (- 12A c + 2B b)d e  + 4B c d e)x + 10A b d e
+--R         + 
+--R                            2          3
+--R           (- 16A c - 2B b)d e + 8B c d
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R            2 2 4          3 3     2 4 2  2       2 3 3          4 2      2 5
+--R         (8b d e  - 16b c d e  + 8c d e )x  + (16b d e  - 32b c d e  + 16c d e)x
+--R       + 
+--R           2 4 2          5      2 6
+--R         8b d e  - 16b c d e + 8c d
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 519
+
+--S 520 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                  2 4                  2    3        2           2 2  2
+--R             (3A b e  + (- 8A b c + B b )d e  + (8A c  - 4B b c)d e )x
+--R           + 
+--R                  2   3                    2  2 2         2           3
+--R             (6A b d e  + (- 16A b c + 2B b )d e  + (16A c  - 8B b c)d e)x
+--R           + 
+--R                 2 2 2                  2  3         2           4
+--R             3A b d e  + (- 8A b c + B b )d e + (8A c  - 4B b c)d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                    3                      2         2               2
+--R             (6A b e  + (- 12A c + 2B b)d e  + 4B c d e)x + 10A b d e
+--R           + 
+--R                              2          3
+--R             (- 16A c - 2B b)d e + 8B c d
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R              2 2 4          3 3     2 4 2  2
+--R           (8b d e  - 16b c d e  + 8c d e )x
+--R         + 
+--R               2 3 3          4 2      2 5        2 4 2          5      2 6
+--R           (16b d e  - 32b c d e  + 16c d e)x + 8b d e  - 16b c d e + 8c d
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                    2 4                2    3          2           2 2  2
+--R             (- 3A b e  + (8A b c - B b )d e  + (- 8A c  + 4B b c)d e )x
+--R           + 
+--R                    2   3                  2  2 2           2           3
+--R             (- 6A b d e  + (16A b c - 2B b )d e  + (- 16A c  + 8B b c)d e)x
+--R           + 
+--R                   2 2 2                2  3           2           4
+--R             - 3A b d e  + (8A b c - B b )d e + (- 8A c  + 4B b c)d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                    3                    2         2              2
+--R             (3A b e  + (- 6A c + B b)d e  + 2B c d e)x + 5A b d e
+--R           + 
+--R                            2          3
+--R             (- 8A c - B b)d e + 4B c d
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R              2 2 4         3 3     2 4 2  2      2 3 3          4 2     2 5
+--R           (4b d e  - 8b c d e  + 4c d e )x  + (8b d e  - 16b c d e  + 8c d e)x
+--R         + 
+--R             2 4 2         5      2 6
+--R           4b d e  - 8b c d e + 4c d
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 520
+
+--S 521 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R              2 2                  2            2           2  +-----------+ +-+
+--R         (3A b e  + (- 8A b c + B b )d e + (8A c  - 4B b c)d )\|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                                               +--------------+
+--R              2 2                  2            2           2  |             2
+--R         (3A b e  + (- 8A b c + B b )d e + (8A c  - 4B b c)d )\|- b d e + c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                   +--------------+
+--R        2 2 2          3      2 4  |             2  +-----------+ +-+
+--R     (8b d e  - 16b c d e + 8c d )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 521
+
+--S 522 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 522
+
+--S 523 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                               +------------+
+--R              2 2                  2            2           2  |           2
+--R         (3A b e  + (- 8A b c + B b )d e + (8A c  - 4B b c)d )\|b d e - c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                2 2                  2               2           2
+--R         (- 6A b e  + (16A b c - 2B b )d e + (- 16A c  + 8B b c)d )
+--R      *
+--R                                 +------------+ +----------+
+--R                                 |           2  |   2
+--R          +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|d atan(----------------------------)
+--R                                        (b e - c d)x
+--R  /
+--R                                                     +------------+
+--R        2 2 2          3      2 4  +-----------+ +-+ |           2
+--R     (8b d e  - 16b c d e + 8c d )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 523
+
+--S 524 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 524
+
+)clear all
+
+--S 525 of 1457
+t0:=(A+B*x)/((d+e*x)^4*sqrt(b*x+c*x^2))
+--R 
+--R
+--R                               B x + A
+--R   (1)  -----------------------------------------------------
+--R                                                 +----------+
+--R          4 4       3 3     2 2 2     3       4  |   2
+--R        (e x  + 4d e x  + 6d e x  + 4d e x + d )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 525
+
+--S 526 of 1457
+r0:=1/16*(16*A*c^3*d^3-8*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(B*d+5*A*e)+_
+     2*b^2*c*d*e*(2*B*d+9*A*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_
+     sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+_
+     1/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^3)-_
+     1/12*(5*A*e*(2*c*d-b*e)-B*d*(4*c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*_
+     (c*d-b*e)^2*(d+e*x)^2)+1/24*(B*d*(8*c^2*d^2+10*b*c*d*e-3*b^2*e^2)-_
+     A*e*(44*c^2*d^2-44*b*c*d*e+15*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*_
+     (c*d-b*e)^3*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                      3 6         2        3    5             2        2   2 4
+--R               - 15A b e  + (54A b c - 3B b )d e  + (- 72A b c  + 12B b c)d e
+--R             + 
+--R                     3          2  3 3
+--R               (48A c  - 24B b c )d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      3   5          2        3  2 4
+--R               - 45A b d e  + (162A b c - 9B b )d e
+--R             + 
+--R                          2        2   3 3          3          2  4 2
+--R               (- 216A b c  + 36B b c)d e  + (144A c  - 72B b c )d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      3 2 4          2        3  3 3
+--R               - 45A b d e  + (162A b c - 9B b )d e
+--R             + 
+--R                          2        2   4 2          3          2  5
+--R               (- 216A b c  + 36B b c)d e  + (144A c  - 72B b c )d e
+--R          *
+--R             x
+--R         + 
+--R                  3 3 3         2        3  4 2             2        2   5
+--R           - 15A b d e  + (54A b c - 3B b )d e  + (- 72A b c  + 12B b c)d e
+--R         + 
+--R                 3          2  6
+--R           (48A c  - 24B b c )d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                    2 5                    2    4         2            2 3
+--R               30A b e  + (- 88A b c + 6B b )d e  + (88A c  - 20B b c)d e
+--R             + 
+--R                      2 3 2
+--R               - 16B c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    2   4                      2  2 3          2            3 2
+--R               80A b d e  + (- 236A b c + 16B b )d e  + (216A c  - 28B b c)d e
+--R             + 
+--R                      2 4
+--R               - 48B c d e
+--R          *
+--R             x
+--R         + 
+--R                2 2 3                     2  3 2          2            4
+--R           66A b d e  + (- 180A b c - 6B b )d e  + (144A c  + 24B b c)d e
+--R         + 
+--R                  2 5
+--R           - 48B c d
+--R      *
+--R                            +----------+
+--R          +-----------+ +-+ |   2
+--R         \|- b e + c d \|d \|c x  + b x
+--R  /
+--R             3 3 6       2   4 5         2 5 4      3 6 3  3
+--R         (48b d e  - 144b c d e  + 144b c d e  - 48c d e )x
+--R       + 
+--R              3 4 5       2   5 4         2 6 3       3 7 2  2
+--R         (144b d e  - 432b c d e  + 432b c d e  - 144c d e )x
+--R       + 
+--R              3 5 4       2   6 3         2 7 2       3 8         3 6 3
+--R         (144b d e  - 432b c d e  + 432b c d e  - 144c d e)x + 48b d e
+--R       + 
+--R               2   7 2         2 8       3 9
+--R         - 144b c d e  + 144b c d e - 48c d
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 526
+
+--S 527 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                      3 6           2        3    5           2        2   2 4
+--R                 15A b e  + (- 54A b c + 3B b )d e  + (72A b c  - 12B b c)d e
+--R               + 
+--R                         3          2  3 3
+--R                 (- 48A c  + 24B b c )d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      3   5            2        3  2 4
+--R                 45A b d e  + (- 162A b c + 9B b )d e
+--R               + 
+--R                          2        2   3 3            3          2  4 2
+--R                 (216A b c  - 36B b c)d e  + (- 144A c  + 72B b c )d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      3 2 4            2        3  3 3
+--R                 45A b d e  + (- 162A b c + 9B b )d e
+--R               + 
+--R                          2        2   4 2            3          2  5
+--R                 (216A b c  - 36B b c)d e  + (- 144A c  + 72B b c )d e
+--R            *
+--R               x
+--R           + 
+--R                  3 3 3           2        3  4 2           2        2   5
+--R             15A b d e  + (- 54A b c + 3B b )d e  + (72A b c  - 12B b c)d e
+--R           + 
+--R                     3          2  6
+--R             (- 48A c  + 24B b c )d
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                      2 5                    2    4         2            2 3
+--R                 30A b e  + (- 88A b c + 6B b )d e  + (88A c  - 20B b c)d e
+--R               + 
+--R                        2 3 2
+--R                 - 16B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      2   4                      2  2 3
+--R                 80A b d e  + (- 236A b c + 16B b )d e
+--R               + 
+--R                        2            3 2        2 4
+--R                 (216A c  - 28B b c)d e  - 48B c d e
+--R            *
+--R               x
+--R           + 
+--R                  2 2 3                     2  3 2          2            4
+--R             66A b d e  + (- 180A b c - 6B b )d e  + (144A c  + 24B b c)d e
+--R           + 
+--R                    2 5
+--R             - 48B c d
+--R        *
+--R            +--------------+ +----------+
+--R            |             2  |   2
+--R           \|- b d e + c d  \|c x  + b x
+--R    /
+--R               3 3 6       2   4 5         2 5 4      3 6 3  3
+--R           (48b d e  - 144b c d e  + 144b c d e  - 48c d e )x
+--R         + 
+--R                3 4 5       2   5 4         2 6 3       3 7 2  2
+--R           (144b d e  - 432b c d e  + 432b c d e  - 144c d e )x
+--R         + 
+--R                3 5 4       2   6 3         2 7 2       3 8         3 6 3
+--R           (144b d e  - 432b c d e  + 432b c d e  - 144c d e)x + 48b d e
+--R         + 
+--R                 2   7 2         2 8       3 9
+--R           - 144b c d e  + 144b c d e - 48c d
+--R      *
+--R          +--------------+
+--R          |             2
+--R         \|- b d e + c d
+--R     ,
+--R
+--R                        3 6         2        3    5             2        2   2 4
+--R                 - 15A b e  + (54A b c - 3B b )d e  + (- 72A b c  + 12B b c)d e
+--R               + 
+--R                       3          2  3 3
+--R                 (48A c  - 24B b c )d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        3   5          2        3  2 4
+--R                 - 45A b d e  + (162A b c - 9B b )d e
+--R               + 
+--R                            2        2   3 3          3          2  4 2
+--R                 (- 216A b c  + 36B b c)d e  + (144A c  - 72B b c )d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        3 2 4          2        3  3 3
+--R                 - 45A b d e  + (162A b c - 9B b )d e
+--R               + 
+--R                            2        2   4 2          3          2  5
+--R                 (- 216A b c  + 36B b c)d e  + (144A c  - 72B b c )d e
+--R            *
+--R               x
+--R           + 
+--R                    3 3 3         2        3  4 2             2        2   5
+--R             - 15A b d e  + (54A b c - 3B b )d e  + (- 72A b c  + 12B b c)d e
+--R           + 
+--R                   3          2  6
+--R             (48A c  - 24B b c )d
+--R        *
+--R                 +------------+ +----------+
+--R                 |           2  |   2
+--R                \|b d e - c d  \|c x  + b x
+--R           atan(----------------------------)
+--R                        (b e - c d)x
+--R       + 
+--R                      2 5                    2    4         2            2 3
+--R                 15A b e  + (- 44A b c + 3B b )d e  + (44A c  - 10B b c)d e
+--R               + 
+--R                       2 3 2
+--R                 - 8B c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      2   4                     2  2 3          2            3 2
+--R                 40A b d e  + (- 118A b c + 8B b )d e  + (108A c  - 14B b c)d e
+--R               + 
+--R                        2 4
+--R                 - 24B c d e
+--R            *
+--R               x
+--R           + 
+--R                  2 2 3                    2  3 2         2            4
+--R             33A b d e  + (- 90A b c - 3B b )d e  + (72A c  + 12B b c)d e
+--R           + 
+--R                    2 5
+--R             - 24B c d
+--R        *
+--R            +------------+ +----------+
+--R            |           2  |   2
+--R           \|b d e - c d  \|c x  + b x
+--R    /
+--R               3 3 6      2   4 5        2 5 4      3 6 3  3
+--R           (24b d e  - 72b c d e  + 72b c d e  - 24c d e )x
+--R         + 
+--R               3 4 5       2   5 4         2 6 3      3 7 2  2
+--R           (72b d e  - 216b c d e  + 216b c d e  - 72c d e )x
+--R         + 
+--R               3 5 4       2   6 3         2 7 2      3 8         3 6 3
+--R           (72b d e  - 216b c d e  + 216b c d e  - 72c d e)x + 24b d e
+--R         + 
+--R                2   7 2        2 8       3 9
+--R           - 72b c d e  + 72b c d e - 24c d
+--R      *
+--R          +------------+
+--R          |           2
+--R         \|b d e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 527
+
+--S 528 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R               3 3           2       3    2           2       2   2
+--R           5A b e  + (- 18A b c + B b )d e  + (24A b c  - 4B b c)d e
+--R         + 
+--R                   3         2  3
+--R           (- 16A c  + 8B b c )d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R               3 3           2       3    2           2       2   2
+--R           5A b e  + (- 18A b c + B b )d e  + (24A b c  - 4B b c)d e
+--R         + 
+--R                   3         2  3
+--R           (- 16A c  + 8B b c )d
+--R      *
+--R          +--------------+
+--R          |             2              (b e - 2c d)x - b d
+--R         \|- b d e + c d  atanh(--------------------------------)
+--R                                                    +----------+
+--R                                  +-----------+ +-+ |   2
+--R                                2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                                    +--------------+
+--R           3 3 3      2   4 2        2 5       3 6  |             2
+--R       (16b d e  - 48b c d e  + 48b c d e - 16c d )\|- b d e + c d
+--R    *
+--R        +-----------+ +-+
+--R       \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 528
+
+--S 529 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 529
+
+--S 530 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R               3 3           2       3    2           2       2   2
+--R           5A b e  + (- 18A b c + B b )d e  + (24A b c  - 4B b c)d e
+--R         + 
+--R                   3         2  3
+--R           (- 16A c  + 8B b c )d
+--R      *
+--R          +------------+
+--R          |           2              (b e - 2c d)x - b d
+--R         \|b d e - c d  atanh(--------------------------------)
+--R                                                  +----------+
+--R                                +-----------+ +-+ |   2
+--R                              2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  3 3         2        3    2             2       2   2
+--R           - 10A b e  + (36A b c - 2B b )d e  + (- 48A b c  + 8B b c)d e
+--R         + 
+--R                 3          2  3
+--R           (32A c  - 16B b c )d
+--R      *
+--R                                 +------------+ +----------+
+--R                                 |           2  |   2
+--R          +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|d atan(----------------------------)
+--R                                        (b e - c d)x
+--R  /
+--R           3 3 3      2   4 2        2 5       3 6  +-----------+ +-+
+--R       (16b d e  - 48b c d e  + 48b c d e - 16c d )\|- b e + c d \|d
+--R    *
+--R        +------------+
+--R        |           2
+--R       \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 530
+
+--S 531 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 531
+
+)clear all
+
+--S 532 of 1457
+t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(3/2)
+--R 
+--R
+--R   (1)
+--R      3 4       3         2  3          2       2   2        2       3        3
+--R   B e x  + (A e  + 3B d e )x  + (3A d e  + 3B d e)x  + (3A d e + B d )x + A d
+--R   ----------------------------------------------------------------------------
+--R                                          +----------+
+--R                                 2        |   2
+--R                             (c x  + b x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 532
+
+--S 533 of 1457
+r0:=3/4*e*(4*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-12*b*c*d*e+5*b^2*e^2))*_
+     atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2*(A*b-(b*B-2*A*c)*x)*_
+     (d+e*x)^3/(b^2*sqrt(b*x+c*x^2))+1/4*e*(32*A*c^3*d^2-15*b^3*B*e^2-_
+     16*b*c^2*d*(B*d+2*A*e)+2*b^2*c*e*(17*B*d+6*A*e))*sqrt(b*x+c*x^2)/_
+     (b^2*c^3)-2*(b*B-2*A*c)*e*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^2*c)+_
+     1/2*e^2*(b*(b*B+4*A*c)*d+(8*A*c^2*d+5*b^2*B*e-4*b*c*(B*d+A*e))*x)*_
+     sqrt(b*x+c*x^2)/(b^2*c^2)
+--R 
+--R
+--R   (2)
+--R                  3         4  3         2 2        3     2        2 2 2
+--R         ((- 12A b c + 15B b )e  + (24A b c  - 36B b c)d e  + 24B b c d e)
+--R      *
+--R          +----------+            +-+
+--R          |   2                 x\|c
+--R         \|c x  + b x atanh(-------------)
+--R                             +----------+
+--R                             |   2
+--R                            \|c x  + b x
+--R     + 
+--R               2 2 3 3         2 2       3   3        2 2   2  2
+--R           2B b c e x  + ((4A b c  - 5B b c)e  + 12B b c d e )x
+--R         + 
+--R                     3         4  3           2 2        3     2
+--R               (12A b c - 15B b )e  + (- 24A b c  + 36B b c)d e
+--R             + 
+--R                       3        2 2  2            4         3  3
+--R               (24A b c  - 24B b c )d e + (- 16A c  + 8B b c )d
+--R          *
+--R             x
+--R         + 
+--R                   3 3
+--R           - 8A b c d
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R               +----------+
+--R       2 3 +-+ |   2
+--R     4b c \|c \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 533
+
+--S 534 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                    3         4  3         2 2        3     2        2 2 2
+--R           ((- 12A b c + 15B b )e  + (24A b c  - 36B b c)d e  + 24B b c d e)
+--R        *
+--R            +----------+       +----------+
+--R            |   2              |   2                     +-+
+--R           \|c x  + b x log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                 2 2 3 3         2 2        3   3        2 2   2  2
+--R             4B b c e x  + ((8A b c  - 10B b c)e  + 24B b c d e )x
+--R           + 
+--R                       3         4  3           2 2        3     2
+--R                 (24A b c - 30B b )e  + (- 48A b c  + 72B b c)d e
+--R               + 
+--R                         3        2 2  2            4          3  3
+--R                 (48A b c  - 48B b c )d e + (- 32A c  + 16B b c )d
+--R            *
+--R               x
+--R           + 
+--R                      3 3
+--R             - 16A b c d
+--R        *
+--R            +-+
+--R           \|c
+--R    /
+--R                 +----------+
+--R         2 3 +-+ |   2
+--R       8b c \|c \|c x  + b x
+--R     ,
+--R
+--R                    3         4  3         2 2        3     2        2 2 2
+--R           ((- 12A b c + 15B b )e  + (24A b c  - 36B b c)d e  + 24B b c d e)
+--R        *
+--R                                    +----------+
+--R            +----------+      +---+ |   2
+--R            |   2            \|- c \|c x  + b x
+--R           \|c x  + b x atan(-------------------)
+--R                                     c x
+--R       + 
+--R                 2 2 3 3         2 2       3   3        2 2   2  2
+--R             2B b c e x  + ((4A b c  - 5B b c)e  + 12B b c d e )x
+--R           + 
+--R                       3         4  3           2 2        3     2
+--R                 (12A b c - 15B b )e  + (- 24A b c  + 36B b c)d e
+--R               + 
+--R                         3        2 2  2            4         3  3
+--R                 (24A b c  - 24B b c )d e + (- 16A c  + 8B b c )d
+--R            *
+--R               x
+--R           + 
+--R                     3 3
+--R             - 8A b c d
+--R        *
+--R            +---+
+--R           \|- c
+--R    /
+--R                   +----------+
+--R         2 3 +---+ |   2
+--R       4b c \|- c \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 534
+
+--S 535 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                            2  3         2              2        2 2
+--R         ((- 12A b c + 15B b )e  + (24A c  - 36B b c)d e  + 24B c d e)
+--R      *
+--R                +----------+
+--R                |   2                     +-+
+--R         log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                          2  3           2              2        2 2
+--R         ((24A b c - 30B b )e  + (- 48A c  + 72B b c)d e  - 48B c d e)
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R  /
+--R       3 +-+
+--R     8c \|c
+--R                                                    Type: Expression(Integer)
+--E 535
+
+--S 536 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 536
+
+--S 537 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                          2  3           2              2        2 2   +---+
+--R         ((12A b c - 15B b )e  + (- 24A c  + 36B b c)d e  - 24B c d e)\|- c
+--R      *
+--R                     +-+
+--R                   x\|c
+--R         atanh(-------------)
+--R                +----------+
+--R                |   2
+--R               \|c x  + b x
+--R     + 
+--R                            2  3         2              2        2 2   +-+
+--R         ((- 12A b c + 15B b )e  + (24A c  - 36B b c)d e  + 24B c d e)\|c
+--R      *
+--R                     +----------+
+--R               +---+ |   2
+--R              \|- c \|c x  + b x
+--R         atan(-------------------)
+--R                      c x
+--R  /
+--R       3 +---+ +-+
+--R     4c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 537
+
+--S 538 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 538
+
+)clear all
+
+--S 539 of 1457
+t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(3/2)
+--R 
+--R
+--R           2 3       2           2                2        2
+--R        B e x  + (A e  + 2B d e)x  + (2A d e + B d )x + A d
+--R   (1)  ----------------------------------------------------
+--R                                   +----------+
+--R                          2        |   2
+--R                      (c x  + b x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 539
+
+--S 540 of 1457
+r0:=e*(4*B*c*d-3*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-_
+     2*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*sqrt(b*x+c*x^2))+e*(8*A*c^2*d+_
+     3*b^2*B*e-4*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/(b^2*c^2)+2*e^2*(A*b-_
+     (b*B-2*A*c)*x)*sqrt(b*x+c*x^2)/(b^2*c)
+--R 
+--R
+--R   (2)
+--R                                         +----------+            +-+
+--R             2        3  2       2       |   2                 x\|c
+--R       ((2A b c - 3B b )e  + 4B b c d e)\|c x  + b x atanh(-------------)
+--R                                                            +----------+
+--R                                                            |   2
+--R                                                           \|c x  + b x
+--R     + 
+--R              2   2 2
+--R           B b c e x
+--R         + 
+--R                      2        3  2          2       2
+--R               (- 2A b c + 3B b )e  + (4A b c  - 4B b c)d e
+--R             + 
+--R                      3         2  2
+--R               (- 4A c  + 2B b c )d
+--R          *
+--R             x
+--R         + 
+--R                   2 2
+--R           - 2A b c d
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R              +----------+
+--R      2 2 +-+ |   2
+--R     b c \|c \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 540
+
+--S 541 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                                             +----------+
+--R                 2        3  2       2       |   2
+--R           ((2A b c - 3B b )e  + 4B b c d e)\|c x  + b x
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                 2   2 2
+--R             2B b c e x
+--R           + 
+--R                        2        3  2          2       2
+--R                 (- 4A b c + 6B b )e  + (8A b c  - 8B b c)d e
+--R               + 
+--R                        3         2  2
+--R                 (- 8A c  + 4B b c )d
+--R            *
+--R               x
+--R           + 
+--R                     2 2
+--R             - 4A b c d
+--R        *
+--R            +-+
+--R           \|c
+--R    /
+--R                 +----------+
+--R         2 2 +-+ |   2
+--R       2b c \|c \|c x  + b x
+--R     ,
+--R
+--R                                                                   +----------+
+--R                                           +----------+      +---+ |   2
+--R               2        3  2       2       |   2            \|- c \|c x  + b x
+--R         ((2A b c - 3B b )e  + 4B b c d e)\|c x  + b x atan(-------------------)
+--R                                                                    c x
+--R       + 
+--R                2   2 2
+--R             B b c e x
+--R           + 
+--R                        2        3  2          2       2
+--R                 (- 2A b c + 3B b )e  + (4A b c  - 4B b c)d e
+--R               + 
+--R                        3         2  2
+--R                 (- 4A c  + 2B b c )d
+--R            *
+--R               x
+--R           + 
+--R                     2 2
+--R             - 2A b c d
+--R        *
+--R            +---+
+--R           \|- c
+--R    /
+--R                  +----------+
+--R        2 2 +---+ |   2
+--R       b c \|- c \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 541
+
+--S 542 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                          +----------+
+--R                      2                   |   2                     +-+
+--R       ((2A c - 3B b)e  + 4B c d e)log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                                 +-+
+--R                        2                      x\|c
+--R       ((- 4A c + 6B b)e  - 8B c d e)atanh(-------------)
+--R                                            +----------+
+--R                                            |   2
+--R                                           \|c x  + b x
+--R  /
+--R       2 +-+
+--R     2c \|c
+--R                                                    Type: Expression(Integer)
+--E 542
+
+--S 543 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 543
+
+--S 544 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                       +-+
+--R                        2             +---+          x\|c
+--R       ((- 2A c + 3B b)e  - 4B c d e)\|- c atanh(-------------)
+--R                                                  +----------+
+--R                                                  |   2
+--R                                                 \|c x  + b x
+--R     + 
+--R                                                   +----------+
+--R                                             +---+ |   2
+--R                      2             +-+     \|- c \|c x  + b x
+--R       ((2A c - 3B b)e  + 4B c d e)\|c atan(-------------------)
+--R                                                    c x
+--R  /
+--R      2 +---+ +-+
+--R     c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 544
+
+--S 545 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 545
+
+)clear all
+
+--S 546 of 1457
+t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(3/2)
+--R 
+--R
+--R             2
+--R        B e x  + (A e + B d)x + A d
+--R   (1)  ---------------------------
+--R                      +----------+
+--R             2        |   2
+--R         (c x  + b x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 546
+
+--S 547 of 1457
+r0:=2*B*e*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-2*(A*b-(b*B-2*A*c)*x)*_
+     (d+e*x)/(b^2*sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*e*sqrt(b*x+c*x^2)/(b^2*c)
+--R 
+--R
+--R   (2)
+--R              +----------+            +-+
+--R           2  |   2                 x\|c
+--R       2B b e\|c x  + b x atanh(-------------)
+--R                                 +----------+
+--R                                 |   2
+--R                                \|c x  + b x
+--R     + 
+--R                       2            2                          +-+
+--R       (((2A b c - 2B b )e + (- 4A c  + 2B b c)d)x - 2A b c d)\|c
+--R  /
+--R             +----------+
+--R      2  +-+ |   2
+--R     b c\|c \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 547
+
+--S 548 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R               +----------+       +----------+
+--R            2  |   2              |   2                     +-+
+--R         B b e\|c x  + b x log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                         2            2                          +-+
+--R         (((2A b c - 2B b )e + (- 4A c  + 2B b c)d)x - 2A b c d)\|c
+--R    /
+--R               +----------+
+--R        2  +-+ |   2
+--R       b c\|c \|c x  + b x
+--R     ,
+--R
+--R                                        +----------+
+--R                +----------+      +---+ |   2
+--R             2  |   2            \|- c \|c x  + b x
+--R         2B b e\|c x  + b x atan(-------------------)
+--R                                         c x
+--R       + 
+--R                         2            2                          +---+
+--R         (((2A b c - 2B b )e + (- 4A c  + 2B b c)d)x - 2A b c d)\|- c
+--R    /
+--R                 +----------+
+--R        2  +---+ |   2
+--R       b c\|- c \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 548
+
+--S 549 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R                   +----------+                                      +-+
+--R                   |   2                     +-+                   x\|c
+--R        B e log(2c\|c x  + b x  + (2c x + b)\|c ) - 2B e atanh(-------------)
+--R                                                                +----------+
+--R                                                                |   2
+--R                                                               \|c x  + b x
+--R   (4)  ---------------------------------------------------------------------
+--R                                          +-+
+--R                                        c\|c
+--R                                                    Type: Expression(Integer)
+--E 549
+
+--S 550 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 550
+
+--S 551 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R                                                               +----------+
+--R                                +-+                      +---+ |   2
+--R               +---+          x\|c              +-+     \|- c \|c x  + b x
+--R        - 2B e\|- c atanh(-------------) + 2B e\|c atan(-------------------)
+--R                           +----------+                         c x
+--R                           |   2
+--R                          \|c x  + b x
+--R   (6)  --------------------------------------------------------------------
+--R                                       +---+ +-+
+--R                                     c\|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 551
+
+--S 552 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 552
+
+)clear all
+
+--S 553 of 1457
+t0:=(A+B*x)/(b*x+c*x^2)^(3/2)
+--R 
+--R
+--R                 B x + A
+--R   (1)  -------------------------
+--R                     +----------+
+--R            2        |   2
+--R        (c x  + b x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 553
+
+--S 554 of 1457
+r0:=-2*(A*b-(b*B-2*A*c)*x)/(b^2*sqrt(b*x+c*x^2))
+--R 
+--R
+--R        (- 4A c + 2B b)x - 2A b
+--R   (2)  -----------------------
+--R               +----------+
+--R             2 |   2
+--R            b \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 554
+
+--S 555 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R        (- 4A c + 2B b)x - 2A b
+--R   (3)  -----------------------
+--R               +----------+
+--R             2 |   2
+--R            b \|c x  + b x
+--R                                         Type: Union(Expression(Integer),...)
+--E 555
+
+--S 556 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 556
+
+--S 557 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 557
+
+)clear all
+
+--S 558 of 1457
+t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(3/2))
+--R 
+--R
+--R                           B x + A
+--R   (1)  ---------------------------------------------
+--R                                         +----------+
+--R              3               2          |   2
+--R        (c e x  + (b e + c d)x  + b d x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 558
+
+--S 559 of 1457
+r0:=-e*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_
+     sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))-2*(A*b*(c*d-b*e)+_
+     c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*sqrt(b*x+c*x^2))
+--R 
+--R
+--R   (2)
+--R                          +----------+
+--R           2 2      2     |   2                    (b e - 2c d)x - b d
+--R       (A b e  - B b d e)\|c x  + b x atanh(--------------------------------)
+--R                                                                +----------+
+--R                                              +-----------+ +-+ |   2
+--R                                            2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                         2                    2              +-----------+ +-+
+--R     ((- 2A b c e + (4A c  - 2B b c)d)x - 2A b e + 2A b c d)\|- b e + c d \|d
+--R  /
+--R                                        +----------+
+--R       3       2   2  +-----------+ +-+ |   2
+--R     (b d e - b c d )\|- b e + c d \|d \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 559
+
+--S 560 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                              +----------+
+--R               2 2      2     |   2
+--R           (A b e  - B b d e)\|c x  + b x
+--R        *
+--R           log
+--R                                   +----------+
+--R                                2  |   2
+--R                  (2b d e - 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                                                               +--------------+
+--R                           2                    2              |             2
+--R       ((- 2A b c e + (4A c  - 2B b c)d)x - 2A b e + 2A b c d)\|- b d e + c d
+--R    /
+--R                        +--------------+ +----------+
+--R         3       2   2  |             2  |   2
+--R       (b d e - b c d )\|- b d e + c d  \|c x  + b x
+--R     ,
+--R
+--R                                                +------------+ +----------+
+--R                              +----------+      |           2  |   2
+--R              2 2       2     |   2            \|b d e - c d  \|c x  + b x
+--R         (2A b e  - 2B b d e)\|c x  + b x atan(----------------------------)
+--R                                                       (b e - c d)x
+--R       + 
+--R                                                                 +------------+
+--R                             2                    2              |           2
+--R         ((- 2A b c e + (4A c  - 2B b c)d)x - 2A b e + 2A b c d)\|b d e - c d
+--R    /
+--R                        +------------+ +----------+
+--R         3       2   2  |           2  |   2
+--R       (b d e - b c d )\|b d e - c d  \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 560
+
+--S 561 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R             2          +-----------+ +-+
+--R         (A e  - B d e)\|- b e + c d \|d
+--R      *
+--R         log
+--R                                 +----------+
+--R                              2  |   2
+--R                (2b d e - 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                        +--------------+
+--R             2          |             2              (b e - 2c d)x - b d
+--R       (- A e  + B d e)\|- b d e + c d  atanh(--------------------------------)
+--R                                                                  +----------+
+--R                                                +-----------+ +-+ |   2
+--R                                              2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                    +--------------+
+--R                 2  |             2  +-----------+ +-+
+--R     (b d e - c d )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 561
+
+--S 562 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 562
+
+--S 563 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                        +------------+
+--R             2          |           2              (b e - 2c d)x - b d
+--R       (- A e  + B d e)\|b d e - c d  atanh(--------------------------------)
+--R                                                                +----------+
+--R                                              +-----------+ +-+ |   2
+--R                                            2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                               +------------+ +----------+
+--R                                               |           2  |   2
+--R            2           +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R       (2A e  - 2B d e)\|- b e + c d \|d atan(----------------------------)
+--R                                                      (b e - c d)x
+--R  /
+--R                                      +------------+
+--R                 2  +-----------+ +-+ |           2
+--R     (b d e - c d )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 563
+
+--S 564 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 564
+
+)clear all
+
+--S 565 of 1457
+t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(3/2))
+--R 
+--R
+--R                                       B x + A
+--R   (1)  ---------------------------------------------------------------------
+--R                                                                 +----------+
+--R            2 4       2           3                2  2      2   |   2
+--R        (c e x  + (b e  + 2c d e)x  + (2b d e + c d )x  + b d x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 565
+
+--S 566 of 1457
+r0:=1/2*e*(3*A*e*(2*c*d-b*e)-B*d*(4*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-_
+     b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-_
+     b*e)^(5/2))-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*_
+     (c*d-b*e)*(d+e*x)*sqrt(b*x+c*x^2))-e*(4*A*c^2*d^2-b^2*e*(B*d-_
+     3*A*e)-2*b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                3 4          2       3    3       2   2 2         3   3
+--R           (3A b e  + (- 6A b c - B b )d e  + 4B b c d e )x + 3A b d e
+--R         + 
+--R                  2       3  2 2       2   3
+--R           (- 6A b c - B b )d e  + 4B b c d e
+--R      *
+--R          +----------+
+--R          |   2                    (b e - 2c d)x - b d
+--R         \|c x  + b x atanh(--------------------------------)
+--R                                                +----------+
+--R                              +-----------+ +-+ |   2
+--R                            2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  2   3          2       2     2          3         2  2   2
+--R           (- 6A b c e  + (8A b c  + 2B b c)d e  + (- 8A c  + 4B b c )d e)x
+--R         + 
+--R                     3 3        2        3    2         2 2
+--R               - 6A b e  + (4A b c + 2B b )d e  + 4A b c d e
+--R             + 
+--R                      3         2  3
+--R               (- 8A c  + 4B b c )d
+--R          *
+--R             x
+--R         + 
+--R                 3   2       2   2          2 3
+--R           - 4A b d e  + 8A b c d e - 4A b c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R  /
+--R           4 2 3     3   3 2     2 2 4        4 3 2     3   4      2 2 5
+--R       ((2b d e  - 4b c d e  + 2b c d e)x + 2b d e  - 4b c d e + 2b c d )
+--R    *
+--R                          +----------+
+--R        +-----------+ +-+ |   2
+--R       \|- b e + c d \|d \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 566
+
+--S 567 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                  3 4          2       3    3       2   2 2         3   3
+--R             (3A b e  + (- 6A b c - B b )d e  + 4B b c d e )x + 3A b d e
+--R           + 
+--R                    2       3  2 2       2   3
+--R             (- 6A b c - B b )d e  + 4B b c d e
+--R        *
+--R            +----------+
+--R            |   2
+--R           \|c x  + b x
+--R        *
+--R           log
+--R                                   +----------+
+--R                                2  |   2
+--R                  (2b d e - 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                    2   3          2       2     2          3         2  2   2
+--R             (- 6A b c e  + (8A b c  + 2B b c)d e  + (- 8A c  + 4B b c )d e)x
+--R           + 
+--R                       3 3        2        3    2         2 2
+--R                 - 6A b e  + (4A b c + 2B b )d e  + 4A b c d e
+--R               + 
+--R                        3         2  3
+--R                 (- 8A c  + 4B b c )d
+--R            *
+--R               x
+--R           + 
+--R                   3   2       2   2          2 3
+--R             - 4A b d e  + 8A b c d e - 4A b c d
+--R        *
+--R            +--------------+
+--R            |             2
+--R           \|- b d e + c d
+--R    /
+--R             4 2 3     3   3 2     2 2 4        4 3 2     3   4      2 2 5
+--R         ((2b d e  - 4b c d e  + 2b c d e)x + 2b d e  - 4b c d e + 2b c d )
+--R      *
+--R          +--------------+ +----------+
+--R          |             2  |   2
+--R         \|- b d e + c d  \|c x  + b x
+--R     ,
+--R
+--R                  3 4          2       3    3       2   2 2         3   3
+--R             (3A b e  + (- 6A b c - B b )d e  + 4B b c d e )x + 3A b d e
+--R           + 
+--R                    2       3  2 2       2   3
+--R             (- 6A b c - B b )d e  + 4B b c d e
+--R        *
+--R                              +------------+ +----------+
+--R            +----------+      |           2  |   2
+--R            |   2            \|b d e - c d  \|c x  + b x
+--R           \|c x  + b x atan(----------------------------)
+--R                                     (b e - c d)x
+--R       + 
+--R                    2   3          2      2     2          3         2  2   2
+--R             (- 3A b c e  + (4A b c  + B b c)d e  + (- 4A c  + 2B b c )d e)x
+--R           + 
+--R                       3 3        2       3    2         2 2
+--R                 - 3A b e  + (2A b c + B b )d e  + 2A b c d e
+--R               + 
+--R                        3         2  3
+--R                 (- 4A c  + 2B b c )d
+--R            *
+--R               x
+--R           + 
+--R                   3   2       2   2          2 3
+--R             - 2A b d e  + 4A b c d e - 2A b c d
+--R        *
+--R            +------------+
+--R            |           2
+--R           \|b d e - c d
+--R    /
+--R            4 2 3     3   3 2    2 2 4       4 3 2     3   4     2 2 5
+--R         ((b d e  - 2b c d e  + b c d e)x + b d e  - 2b c d e + b c d )
+--R      *
+--R          +------------+ +----------+
+--R          |           2  |   2
+--R         \|b d e - c d  \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 567
+
+--S 568 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                3                    2         2   +-----------+ +-+
+--R         (3A b e  + (- 6A c - B b)d e  + 4B c d e)\|- b e + c d \|d
+--R      *
+--R         log
+--R                                 +----------+
+--R                              2  |   2
+--R                (2b d e - 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                                   +--------------+
+--R                  3                  2         2   |             2
+--R         (- 3A b e  + (6A c + B b)d e  - 4B c d e)\|- b d e + c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                  +--------------+
+--R        2 2 2         3      2 4  |             2  +-----------+ +-+
+--R     (2b d e  - 4b c d e + 2c d )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 568
+
+--S 569 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 569
+
+--S 570 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                   +------------+
+--R                  3                  2         2   |           2
+--R         (- 3A b e  + (6A c + B b)d e  - 4B c d e)\|b d e - c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                3                      2         2   +-----------+ +-+
+--R         (6A b e  + (- 12A c - 2B b)d e  + 8B c d e)\|- b e + c d \|d
+--R      *
+--R               +------------+ +----------+
+--R               |           2  |   2
+--R              \|b d e - c d  \|c x  + b x
+--R         atan(----------------------------)
+--R                      (b e - c d)x
+--R  /
+--R                                                    +------------+
+--R        2 2 2         3      2 4  +-----------+ +-+ |           2
+--R     (2b d e  - 4b c d e + 2c d )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 570
+
+--S 571 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 571
+
+)clear all
+
+--S 572 of 1457
+t0:=(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^(3/2))
+--R 
+--R
+--R   (1)
+--R     B x + A
+--R  /
+--R            3 5       3         2  4          2       2   3        2       3  2
+--R         c e x  + (b e  + 3c d e )x  + (3b d e  + 3c d e)x  + (3b d e + c d )x
+--R       + 
+--R            3
+--R         b d x
+--R    *
+--R        +----------+
+--R        |   2
+--R       \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 572
+
+--S 573 of 1457
+r0:=-3/8*e*(B*d*(8*c^2*d^2-4*b*c*d*e+b^2*e^2)-A*e*(16*c^2*d^2-16*b*c*d*e+_
+     5*b^2*e^2))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_
+     sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))-2*(A*b*(c*d-b*e)+_
+     c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^2*sqrt(b*x+_
+     c*x^2))-1/2*e*(8*A*c^2*d^2-b^2*e*(B*d-5*A*e)-4*b*c*d*(B*d+2*A*e))*_
+     sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^2)-1/4*e*(16*A*c^3*d^3-_
+     2*b^2*c*d*e*(5*B*d-19*A*e)+3*b^3*e^2*(B*d-5*A*e)-8*b*c^2*d^2*_
+     (B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                    4 6           3        4    5         2 2        3   2 4
+--R               15A b e  + (- 48A b c - 3B b )d e  + (48A b c  + 12B b c)d e
+--R             + 
+--R                      2 2 3 3
+--R               - 24B b c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    4   5           3        4  2 4         2 2        3   3 3
+--R               30A b d e  + (- 96A b c - 6B b )d e  + (96A b c  + 24B b c)d e
+--R             + 
+--R                      2 2 4 2
+--R               - 48B b c d e
+--R          *
+--R             x
+--R         + 
+--R                4 2 4           3        4  3 3         2 2        3   4 2
+--R           15A b d e  + (- 48A b c - 3B b )d e  + (48A b c  + 12B b c)d e
+--R         + 
+--R                  2 2 5
+--R           - 24B b c d e
+--R      *
+--R          +----------+
+--R          |   2                    (b e - 2c d)x - b d
+--R         \|c x  + b x atanh(--------------------------------)
+--R                                                +----------+
+--R                              +-----------+ +-+ |   2
+--R                            2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                      3   5         2 2       3     4
+--R               - 30A b c e  + (76A b c  + 6B b c)d e
+--R             + 
+--R                         3        2 2  2 3         4          3  3 2
+--R               (- 48A b c  - 20B b c )d e  + (32A c  - 16B b c )d e
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      4 5         3        4    4         2 2        3   2 3
+--R               - 30A b e  + (26A b c + 6B b )d e  + (80A b c  - 10B b c)d e
+--R             + 
+--R                         3        2 2  3 2         4          3  4
+--R               (- 80A b c  - 24B b c )d e  + (64A c  - 32B b c )d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                      4   4          3         4  2 3
+--R               - 50A b d e  + (112A b c + 10B b )d e
+--R             + 
+--R                       2 2        3   3 2          3 4          4          3  5
+--R               (- 48A b c  - 24B b c)d e  - 16A b c d e + (32A c  - 16B b c )d
+--R          *
+--R             x
+--R         + 
+--R                  4 2 3        3   3 2        2 2 4           3 5
+--R           - 16A b d e  + 48A b c d e  - 48A b c d e + 16A b c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R  /
+--R            5 3 5      4   4 4      3 2 5 3     2 3 6 2  2
+--R         (8b d e  - 24b c d e  + 24b c d e  - 8b c d e )x
+--R       + 
+--R             5 4 4      4   5 3      3 2 6 2      2 3 7        5 5 3
+--R         (16b d e  - 48b c d e  + 48b c d e  - 16b c d e)x + 8b d e
+--R       + 
+--R              4   6 2      3 2 7      2 3 8
+--R         - 24b c d e  + 24b c d e - 8b c d
+--R    *
+--R                          +----------+
+--R        +-----------+ +-+ |   2
+--R       \|- b e + c d \|d \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 573
+
+--S 574 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                        4 6         3        4    5           2 2        3   2 4
+--R                 - 15A b e  + (48A b c + 3B b )d e  + (- 48A b c  - 12B b c)d e
+--R               + 
+--R                      2 2 3 3
+--R                 24B b c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4   5         3        4  2 4
+--R                 - 30A b d e  + (96A b c + 6B b )d e
+--R               + 
+--R                         2 2        3   3 3        2 2 4 2
+--R                 (- 96A b c  - 24B b c)d e  + 48B b c d e
+--R            *
+--R               x
+--R           + 
+--R                    4 2 4         3        4  3 3           2 2        3   4 2
+--R             - 15A b d e  + (48A b c + 3B b )d e  + (- 48A b c  - 12B b c)d e
+--R           + 
+--R                  2 2 5
+--R             24B b c d e
+--R        *
+--R            +----------+
+--R            |   2
+--R           \|c x  + b x
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                        3   5         2 2       3     4
+--R                 - 30A b c e  + (76A b c  + 6B b c)d e
+--R               + 
+--R                           3        2 2  2 3         4          3  3 2
+--R                 (- 48A b c  - 20B b c )d e  + (32A c  - 16B b c )d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        4 5         3        4    4         2 2        3   2 3
+--R                 - 30A b e  + (26A b c + 6B b )d e  + (80A b c  - 10B b c)d e
+--R               + 
+--R                           3        2 2  3 2         4          3  4
+--R                 (- 80A b c  - 24B b c )d e  + (64A c  - 32B b c )d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4   4          3         4  2 3
+--R                 - 50A b d e  + (112A b c + 10B b )d e
+--R               + 
+--R                       2 2        3   3 2          3 4          4          3  5
+--R               (- 48A b c  - 24B b c)d e  - 16A b c d e + (32A c  - 16B b c )d
+--R            *
+--R               x
+--R           + 
+--R                    4 2 3        3   3 2        2 2 4           3 5
+--R             - 16A b d e  + 48A b c d e  - 48A b c d e + 16A b c d
+--R        *
+--R            +--------------+
+--R            |             2
+--R           \|- b d e + c d
+--R    /
+--R              5 3 5      4   4 4      3 2 5 3     2 3 6 2  2
+--R           (8b d e  - 24b c d e  + 24b c d e  - 8b c d e )x
+--R         + 
+--R               5 4 4      4   5 3      3 2 6 2      2 3 7        5 5 3
+--R           (16b d e  - 48b c d e  + 48b c d e  - 16b c d e)x + 8b d e
+--R         + 
+--R                4   6 2      3 2 7      2 3 8
+--R           - 24b c d e  + 24b c d e - 8b c d
+--R      *
+--R          +--------------+ +----------+
+--R          |             2  |   2
+--R         \|- b d e + c d  \|c x  + b x
+--R     ,
+--R
+--R                      4 6           3        4    5         2 2        3   2 4
+--R                 15A b e  + (- 48A b c - 3B b )d e  + (48A b c  + 12B b c)d e
+--R               + 
+--R                        2 2 3 3
+--R                 - 24B b c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      4   5           3        4  2 4         2 2        3   3 3
+--R                 30A b d e  + (- 96A b c - 6B b )d e  + (96A b c  + 24B b c)d e
+--R               + 
+--R                        2 2 4 2
+--R                 - 48B b c d e
+--R            *
+--R               x
+--R           + 
+--R                  4 2 4           3        4  3 3         2 2        3   4 2
+--R             15A b d e  + (- 48A b c - 3B b )d e  + (48A b c  + 12B b c)d e
+--R           + 
+--R                    2 2 5
+--R             - 24B b c d e
+--R        *
+--R                              +------------+ +----------+
+--R            +----------+      |           2  |   2
+--R            |   2            \|b d e - c d  \|c x  + b x
+--R           \|c x  + b x atan(----------------------------)
+--R                                     (b e - c d)x
+--R       + 
+--R                        3   5         2 2       3     4
+--R                 - 15A b c e  + (38A b c  + 3B b c)d e
+--R               + 
+--R                           3        2 2  2 3         4         3  3 2
+--R                 (- 24A b c  - 10B b c )d e  + (16A c  - 8B b c )d e
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        4 5         3        4    4         2 2       3   2 3
+--R                 - 15A b e  + (13A b c + 3B b )d e  + (40A b c  - 5B b c)d e
+--R               + 
+--R                           3        2 2  3 2         4          3  4
+--R                 (- 40A b c  - 12B b c )d e  + (32A c  - 16B b c )d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                        4   4         3        4  2 3
+--R                 - 25A b d e  + (56A b c + 5B b )d e
+--R               + 
+--R                         2 2        3   3 2         3 4          4         3  5
+--R                 (- 24A b c  - 12B b c)d e  - 8A b c d e + (16A c  - 8B b c )d
+--R            *
+--R               x
+--R           + 
+--R                   4 2 3        3   3 2        2 2 4          3 5
+--R             - 8A b d e  + 24A b c d e  - 24A b c d e + 8A b c d
+--R        *
+--R            +------------+
+--R            |           2
+--R           \|b d e - c d
+--R    /
+--R              5 3 5      4   4 4      3 2 5 3     2 3 6 2  2
+--R           (4b d e  - 12b c d e  + 12b c d e  - 4b c d e )x
+--R         + 
+--R              5 4 4      4   5 3      3 2 6 2     2 3 7        5 5 3
+--R           (8b d e  - 24b c d e  + 24b c d e  - 8b c d e)x + 4b d e
+--R         + 
+--R                4   6 2      3 2 7      2 3 8
+--R           - 12b c d e  + 12b c d e - 4b c d
+--R      *
+--R          +------------+ +----------+
+--R          |           2  |   2
+--R         \|b d e - c d  \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 574
+
+--S 575 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                  2 4                  2    3           2            2 2
+--R           - 15A b e  + (48A b c + 3B b )d e  + (- 48A c  - 12B b c)d e
+--R         + 
+--R                2 3
+--R           24B c d e
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                  2 4                  2    3           2            2 2
+--R           - 15A b e  + (48A b c + 3B b )d e  + (- 48A c  - 12B b c)d e
+--R         + 
+--R                2 3
+--R           24B c d e
+--R      *
+--R          +--------------+
+--R          |             2              (b e - 2c d)x - b d
+--R         \|- b d e + c d  atanh(--------------------------------)
+--R                                                    +----------+
+--R                                  +-----------+ +-+ |   2
+--R                                2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                                  +--------------+
+--R          3 3 3      2   4 2        2 5      3 6  |             2  +-----------+
+--R       (8b d e  - 24b c d e  + 24b c d e - 8c d )\|- b d e + c d  \|- b e + c d
+--R    *
+--R        +-+
+--R       \|d
+--R                                                    Type: Expression(Integer)
+--E 575
+
+--S 576 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 576
+
+--S 577 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                  2 4                  2    3           2            2 2
+--R           - 15A b e  + (48A b c + 3B b )d e  + (- 48A c  - 12B b c)d e
+--R         + 
+--R                2 3
+--R           24B c d e
+--R      *
+--R          +------------+
+--R          |           2              (b e - 2c d)x - b d
+--R         \|b d e - c d  atanh(--------------------------------)
+--R                                                  +----------+
+--R                                +-----------+ +-+ |   2
+--R                              2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                  2 4                    2    3         2            2 2
+--R             30A b e  + (- 96A b c - 6B b )d e  + (96A c  + 24B b c)d e
+--R           + 
+--R                    2 3
+--R             - 48B c d e
+--R      *
+--R                                 +------------+ +----------+
+--R                                 |           2  |   2
+--R          +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R         \|- b e + c d \|d atan(----------------------------)
+--R                                        (b e - c d)x
+--R  /
+--R                                                                  +------------+
+--R        3 3 3      2   4 2        2 5      3 6  +-----------+ +-+ |           2
+--R     (8b d e  - 24b c d e  + 24b c d e - 8c d )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 577
+
+--S 578 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 578
+
+)clear all
+
+--S 579 of 1457
+t0:=(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^(5/2)
+--R 
+--R
+--R   (1)
+--R          4 5       4         3  4          3       2 2  3
+--R       B e x  + (A e  + 4B d e )x  + (4A d e  + 6B d e )x
+--R     + 
+--R            2 2       3   2        3       4        4
+--R       (6A d e  + 4B d e)x  + (4A d e + B d )x + A d
+--R  /
+--R                             +----------+
+--R       2 4         3    2 2  |   2
+--R     (c x  + 2b c x  + b x )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 579
+
+--S 580 of 1457
+r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^4/(b^2*(b*x+c*x^2)^(3/2))+e^3*(8*B*c*d-_
+     5*b*B*e+2*A*c*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-8/3*_
+     (d+e*x)^3*(b*(b*B*d-2*A*c*d+2*A*b*e)-(4*A*c^2*d-b^2*B*e-2*b*c*(B*d+_
+     A*e))*x)/(b^4*sqrt(b*x+c*x^2))-1/3*e*(64*A*c^4*d^3-15*b^4*B*e^3-_
+     32*b*c^3*d^2*(B*d+3*A*e)+2*b^3*c*e^2*(11*B*d+3*A*e)+4*b^2*c^2*d*_
+     e*(4*B*d+5*A*e))*sqrt(b*x+c*x^2)/(b^4*c^3)-8/3*e*(4*A*c^2*d-b^2*B*e-_
+     2*b*c*(B*d+A*e))*(d+e*x)^2*sqrt(b*x+c*x^2)/(b^4*c)+2/3*e^2*(b*d*_
+     (4*b*B*c*d-8*A*c^2*d-b^2*B*e+10*A*b*c*e)-(16*A*c^3*d^2+5*b^3*B*e^2-_
+     2*A*b^2*c*e^2-8*b*c^2*d*(B*d+2*A*e))*x)*sqrt(b*x+c*x^2)/(b^4*c^2)
+--R 
+--R
+--R   (2)
+--R                 4 2        5   4        4 2   3  2
+--R           ((6A b c  - 15B b c)e  + 24B b c d e )x
+--R         + 
+--R                 5         6  4        5     3
+--R           ((6A b c - 15B b )e  + 24B b c d e )x
+--R      *
+--R          +----------+            +-+
+--R          |   2                 x\|c
+--R         \|c x  + b x atanh(-------------)
+--R                             +----------+
+--R                             |   2
+--R                            \|c x  + b x
+--R     + 
+--R               4 2 4 4
+--R           3B b c e x
+--R         + 
+--R                      4 2        5   4        3 3        4 2    3
+--R               (- 8A b c  + 20B b c)e  + (8A b c  - 32B b c )d e
+--R             + 
+--R                     2 4        3 3  2 2             5        2 4  3
+--R               (24A b c  + 12B b c )d e  + (- 64A b c  + 16B b c )d e
+--R             + 
+--R                     6          5  4
+--R               (32A c  - 16B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                      5         6  4        5     3        3 3 2 2
+--R               (- 6A b c + 15B b )e  - 24B b c d e  + 36A b c d e
+--R             + 
+--R                       2 4        3 3  3            5        2 4  4
+--R               (- 96A b c  + 24B b c )d e + (48A b c  - 24B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                   3 3 3          2 4       3 3  4         3 3 4
+--R           (- 24A b c d e + (12A b c  - 6B b c )d )x - 2A b c d
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R                            +----------+
+--R        4 4 2     5 3   +-+ |   2
+--R     (3b c x  + 3b c x)\|c \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 580
+
+--S 581 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                   4 2        5   4        4 2   3  2
+--R             ((6A b c  - 15B b c)e  + 24B b c d e )x
+--R           + 
+--R                   5         6  4        5     3
+--R             ((6A b c - 15B b )e  + 24B b c d e )x
+--R        *
+--R            +----------+       +----------+
+--R            |   2              |   2                     +-+
+--R           \|c x  + b x log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                 4 2 4 4
+--R             6B b c e x
+--R           + 
+--R                         4 2        5   4         3 3        4 2    3
+--R                 (- 16A b c  + 40B b c)e  + (16A b c  - 64B b c )d e
+--R               + 
+--R                       2 4        3 3  2 2              5        2 4  3
+--R                 (48A b c  + 24B b c )d e  + (- 128A b c  + 32B b c )d e
+--R               + 
+--R                       6          5  4
+--R                 (64A c  - 32B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                         5         6  4        5     3        3 3 2 2
+--R                 (- 12A b c + 30B b )e  - 48B b c d e  + 72A b c d e
+--R               + 
+--R                          2 4        3 3  3            5        2 4  4
+--R                 (- 192A b c  + 48B b c )d e + (96A b c  - 48B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     3 3 3          2 4        3 3  4         3 3 4
+--R             (- 48A b c d e + (24A b c  - 12B b c )d )x - 4A b c d
+--R        *
+--R            +-+
+--R           \|c
+--R    /
+--R                              +----------+
+--R          4 4 2     5 3   +-+ |   2
+--R       (6b c x  + 6b c x)\|c \|c x  + b x
+--R     ,
+--R
+--R                   4 2        5   4        4 2   3  2
+--R             ((6A b c  - 15B b c)e  + 24B b c d e )x
+--R           + 
+--R                   5         6  4        5     3
+--R             ((6A b c - 15B b )e  + 24B b c d e )x
+--R        *
+--R                                    +----------+
+--R            +----------+      +---+ |   2
+--R            |   2            \|- c \|c x  + b x
+--R           \|c x  + b x atan(-------------------)
+--R                                     c x
+--R       + 
+--R                 4 2 4 4
+--R             3B b c e x
+--R           + 
+--R                        4 2        5   4        3 3        4 2    3
+--R                 (- 8A b c  + 20B b c)e  + (8A b c  - 32B b c )d e
+--R               + 
+--R                       2 4        3 3  2 2             5        2 4  3
+--R                 (24A b c  + 12B b c )d e  + (- 64A b c  + 16B b c )d e
+--R               + 
+--R                       6          5  4
+--R                 (32A c  - 16B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                        5         6  4        5     3        3 3 2 2
+--R                 (- 6A b c + 15B b )e  - 24B b c d e  + 36A b c d e
+--R               + 
+--R                         2 4        3 3  3            5        2 4  4
+--R                 (- 96A b c  + 24B b c )d e + (48A b c  - 24B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     3 3 3          2 4       3 3  4         3 3 4
+--R             (- 24A b c d e + (12A b c  - 6B b c )d )x - 2A b c d
+--R        *
+--R            +---+
+--R           \|- c
+--R    /
+--R                                +----------+
+--R          4 4 2     5 3   +---+ |   2
+--R       (3b c x  + 3b c x)\|- c \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 581
+
+--S 582 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                           +----------+
+--R                      4           3        |   2                     +-+
+--R       ((2A c - 5B b)e  + 8B c d e )log(2c\|c x  + b x  + (2c x + b)\|c )
+--R     + 
+--R                                                    +-+
+--R                         4            3           x\|c
+--R       ((- 4A c + 10B b)e  - 16B c d e )atanh(-------------)
+--R                                               +----------+
+--R                                               |   2
+--R                                              \|c x  + b x
+--R  /
+--R       3 +-+
+--R     2c \|c
+--R                                                    Type: Expression(Integer)
+--E 582
+
+--S 583 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 583
+
+--S 584 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                        +-+
+--R                        4           3  +---+          x\|c
+--R       ((- 2A c + 5B b)e  - 8B c d e )\|- c atanh(-------------)
+--R                                                   +----------+
+--R                                                   |   2
+--R                                                  \|c x  + b x
+--R     + 
+--R                                                    +----------+
+--R                                              +---+ |   2
+--R                      4           3  +-+     \|- c \|c x  + b x
+--R       ((2A c - 5B b)e  + 8B c d e )\|c atan(-------------------)
+--R                                                     c x
+--R  /
+--R      3 +---+ +-+
+--R     c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 584
+
+--S 585 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 585
+
+)clear all
+
+--S 586 of 1457
+t0:=(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(5/2)
+--R 
+--R
+--R   (1)
+--R      3 4       3         2  3          2       2   2        2       3        3
+--R   B e x  + (A e  + 3B d e )x  + (3A d e  + 3B d e)x  + (3A d e + B d )x + A d
+--R   ----------------------------------------------------------------------------
+--R                                               +----------+
+--R                         2 4         3    2 2  |   2
+--R                       (c x  + 2b c x  + b x )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 586
+
+--S 587 of 1457
+r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^3/(b^2*(b*x+c*x^2)^(3/2))+2*B*e^3*_
+     atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-4/3*(d+e*x)^2*(b*(2*b*B*d-_
+     4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)/(b^4*_
+     sqrt(b*x+c*x^2))-2/3*e*(32*A*c^3*d^2+3*b^3*B*e^2-16*b*c^2*d*(B*d+_
+     2*A*e)+2*b^2*c*e*(2*B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^4*c^2)+4/3*e^2*_
+     (b*(2*b*B*d-4*A*c*d+3*A*b*e)-(8*A*c^2*d-b^2*B*e-4*b*c*(B*d+A*e))*x)*_
+     sqrt(b*x+c*x^2)/(b^4*c)
+--R 
+--R
+--R   (2)
+--R                                +----------+            +-+
+--R            4   3 2       5 3   |   2                 x\|c
+--R       (6B b c e x  + 6B b e x)\|c x  + b x atanh(-------------)
+--R                                                   +----------+
+--R                                                   |   2
+--R                                                  \|c x  + b x
+--R     + 
+--R                    3 2       4   3         2 3       3 2    2
+--R               (2A b c  - 8B b c)e  + (12A b c  + 6B b c )d e
+--R             + 
+--R                         4        2 3  2          5          4  3
+--R               (- 48A b c  + 12B b c )d e + (32A c  - 16B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                     5 3        3 2   2           2 3        3 2  2
+--R               - 6B b e  + 18A b c d e  + (- 72A b c  + 18B b c )d e
+--R             + 
+--R                       4        2 3  3
+--R               (48A b c  - 24B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                   3 2 2          2 3       3 2  3         3 2 3
+--R           (- 18A b c d e + (12A b c  - 6B b c )d )x - 2A b c d
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R                            +----------+
+--R        4 3 2     5 2   +-+ |   2
+--R     (3b c x  + 3b c x)\|c \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 587
+
+--S 588 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                                    +----------+
+--R                4   3 2       5 3   |   2
+--R           (3B b c e x  + 3B b e x)\|c x  + b x
+--R        *
+--R                  +----------+
+--R                  |   2                     +-+
+--R           log(2c\|c x  + b x  + (2c x + b)\|c )
+--R       + 
+--R                      3 2       4   3         2 3       3 2    2
+--R                 (2A b c  - 8B b c)e  + (12A b c  + 6B b c )d e
+--R               + 
+--R                           4        2 3  2          5          4  3
+--R                 (- 48A b c  + 12B b c )d e + (32A c  - 16B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                       5 3        3 2   2           2 3        3 2  2
+--R                 - 6B b e  + 18A b c d e  + (- 72A b c  + 18B b c )d e
+--R               + 
+--R                         4        2 3  3
+--R                 (48A b c  - 24B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     3 2 2          2 3       3 2  3         3 2 3
+--R             (- 18A b c d e + (12A b c  - 6B b c )d )x - 2A b c d
+--R        *
+--R            +-+
+--R           \|c
+--R    /
+--R                              +----------+
+--R          4 3 2     5 2   +-+ |   2
+--R       (3b c x  + 3b c x)\|c \|c x  + b x
+--R     ,
+--R
+--R                                                          +----------+
+--R                                  +----------+      +---+ |   2
+--R              4   3 2       5 3   |   2            \|- c \|c x  + b x
+--R         (6B b c e x  + 6B b e x)\|c x  + b x atan(-------------------)
+--R                                                           c x
+--R       + 
+--R                      3 2       4   3         2 3       3 2    2
+--R                 (2A b c  - 8B b c)e  + (12A b c  + 6B b c )d e
+--R               + 
+--R                           4        2 3  2          5          4  3
+--R                 (- 48A b c  + 12B b c )d e + (32A c  - 16B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                       5 3        3 2   2           2 3        3 2  2
+--R                 - 6B b e  + 18A b c d e  + (- 72A b c  + 18B b c )d e
+--R               + 
+--R                         4        2 3  3
+--R                 (48A b c  - 24B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     3 2 2          2 3       3 2  3         3 2 3
+--R             (- 18A b c d e + (12A b c  - 6B b c )d )x - 2A b c d
+--R        *
+--R            +---+
+--R           \|- c
+--R    /
+--R                                +----------+
+--R          4 3 2     5 2   +---+ |   2
+--R       (3b c x  + 3b c x)\|- c \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 588
+
+--S 589 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R                   +----------+                                      +-+
+--R           3       |   2                     +-+        3          x\|c
+--R        B e log(2c\|c x  + b x  + (2c x + b)\|c ) - 2B e atanh(-------------)
+--R                                                                +----------+
+--R                                                                |   2
+--R                                                               \|c x  + b x
+--R   (4)  ---------------------------------------------------------------------
+--R                                         2 +-+
+--R                                        c \|c
+--R                                                    Type: Expression(Integer)
+--E 589
+
+--S 590 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 590
+
+--S 591 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R                                                                 +----------+
+--R                                 +-+                       +---+ |   2
+--R              3 +---+          x\|c             3 +-+     \|- c \|c x  + b x
+--R        - 2B e \|- c atanh(-------------) + 2B e \|c atan(-------------------)
+--R                            +----------+                          c x
+--R                            |   2
+--R                           \|c x  + b x
+--R   (6)  ----------------------------------------------------------------------
+--R                                      2 +---+ +-+
+--R                                     c \|- c \|c
+--R                                                    Type: Expression(Integer)
+--E 591
+
+--S 592 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 592
+
+)clear all
+
+--S 593 of 1457
+t0:=(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(5/2)
+--R 
+--R
+--R           2 3       2           2                2        2
+--R        B e x  + (A e  + 2B d e)x  + (2A d e + B d )x + A d
+--R   (1)  ----------------------------------------------------
+--R                                        +----------+
+--R                  2 4         3    2 2  |   2
+--R                (c x  + 2b c x  + b x )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 593
+
+--S 594 of 1457
+r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*(b*x+c*x^2)^(3/2))-_
+     8/3*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)/(b^4*sqrt(b*x+c*x^2))
+--R 
+--R
+--R   (2)
+--R             2        3  2             2       2              3          2  2  3
+--R       ((4A b c + 2B b )e  + (- 32A b c  + 8B b c)d e + (32A c  - 16B b c )d )x
+--R     + 
+--R            3 2           2         3               2        2   2  2
+--R       (6A b e  + (- 48A b c + 12B b )d e + (48A b c  - 24B b c)d )x
+--R     + 
+--R               3            2        3  2         3 2
+--R       (- 12A b d e + (12A b c - 6B b )d )x - 2A b d
+--R  /
+--R                      +----------+
+--R        4   2     5   |   2
+--R     (3b c x  + 3b x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 594
+
+--S 595 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R             2        3  2             2       2              3          2  2  3
+--R       ((4A b c + 2B b )e  + (- 32A b c  + 8B b c)d e + (32A c  - 16B b c )d )x
+--R     + 
+--R            3 2           2         3               2        2   2  2
+--R       (6A b e  + (- 48A b c + 12B b )d e + (48A b c  - 24B b c)d )x
+--R     + 
+--R               3            2        3  2         3 2
+--R       (- 12A b d e + (12A b c - 6B b )d )x - 2A b d
+--R  /
+--R                      +----------+
+--R        4   2     5   |   2
+--R     (3b c x  + 3b x)\|c x  + b x
+--R                                         Type: Union(Expression(Integer),...)
+--E 595
+
+--S 596 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 596
+
+--S 597 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 597
+
+)clear all
+
+--S 598 of 1457
+t0:=(A+B*x)*(d+e*x)/(b*x+c*x^2)^(5/2)
+--R 
+--R
+--R                  2
+--R             B e x  + (A e + B d)x + A d
+--R   (1)  ------------------------------------
+--R                                +----------+
+--R          2 4         3    2 2  |   2
+--R        (c x  + 2b c x  + b x )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 598
+
+--S 599 of 1457
+r0:=-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-_
+     4/3*(b*(2*b*B*d-4*A*c*d+A*b*e)-(8*A*c^2*d+b^2*B*e-_
+     4*b*c*(B*d+A*e))*x)/(b^4*sqrt(b*x+c*x^2))
+--R 
+--R
+--R   (2)
+--R                  2       2            3          2    3
+--R       ((- 16A b c  + 4B b c)e + (32A c  - 16B b c )d)x
+--R     + 
+--R                2        3             2        2     2
+--R       ((- 24A b c + 6B b )e + (48A b c  - 24B b c)d)x
+--R     + 
+--R              3          2        3           3
+--R       (- 6A b e + (12A b c - 6B b )d)x - 2A b d
+--R  /
+--R                      +----------+
+--R        4   2     5   |   2
+--R     (3b c x  + 3b x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 599
+
+--S 600 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  2       2            3          2    3
+--R       ((- 16A b c  + 4B b c)e + (32A c  - 16B b c )d)x
+--R     + 
+--R                2        3             2        2     2
+--R       ((- 24A b c + 6B b )e + (48A b c  - 24B b c)d)x
+--R     + 
+--R              3          2        3           3
+--R       (- 6A b e + (12A b c - 6B b )d)x - 2A b d
+--R  /
+--R                      +----------+
+--R        4   2     5   |   2
+--R     (3b c x  + 3b x)\|c x  + b x
+--R                                         Type: Union(Expression(Integer),...)
+--E 600
+
+--S 601 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 601
+
+--S 602 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 602
+
+)clear all
+
+--S 603 of 1457
+t0:=(A+B*x)/(b*x+c*x^2)^(5/2)
+--R 
+--R
+--R                       B x + A
+--R   (1)  ------------------------------------
+--R                                +----------+
+--R          2 4         3    2 2  |   2
+--R        (c x  + 2b c x  + b x )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 603
+
+--S 604 of 1457
+r0:=-2/3*(A*b-(b*B-2*A*c)*x)/(b^2*(b*x+c*x^2)^(3/2))+8/3*(b*B-2*A*c)/_
+     (b^3*sqrt(b*x+c*x^2))-16/3*(b*B-2*A*c)*sqrt(b*x+c*x^2)/(b^4*x)
+--R 
+--R
+--R   (2)
+--R         3          2  3           2        2   2         2        3         3
+--R   (32A c  - 16B b c )x  + (48A b c  - 24B b c)x  + (12A b c - 6B b )x - 2A b
+--R   ---------------------------------------------------------------------------
+--R                                           +----------+
+--R                             4   2     5   |   2
+--R                          (3b c x  + 3b x)\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 604
+
+--S 605 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R         3          2  3           2        2   2         2        3         3
+--R   (32A c  - 16B b c )x  + (48A b c  - 24B b c)x  + (12A b c - 6B b )x - 2A b
+--R   ---------------------------------------------------------------------------
+--R                                           +----------+
+--R                             4   2     5   |   2
+--R                          (3b c x  + 3b x)\|c x  + b x
+--R                                         Type: Union(Expression(Integer),...)
+--E 605
+
+--S 606 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 606
+
+--S 607 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 607
+
+)clear all
+
+--S 608 of 1457
+t0:=(A+B*x)/((d+e*x)*(b*x+c*x^2)^(5/2))
+--R 
+--R
+--R                                       B x + A
+--R   (1)  --------------------------------------------------------------------
+--R                                                                +----------+
+--R          2   5              2   4     2            3    2   2  |   2
+--R        (c e x  + (2b c e + c d)x  + (b e + 2b c d)x  + b d x )\|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 608
+
+--S 609 of 1457
+r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_
+     (b*x+c*x^2)^(3/2))-e^3*(B*d-A*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_
+     (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+_
+     2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+3*b^2*e*(B*d-A*e)-4*b*c*d*(B*d+A*e))+_
+     c*(16*A*c^3*d^3-3*b^3*e^2*(B*d-A*e)+2*b^2*c*d*e*(7*B*d+A*e)-_
+     8*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2))
+--R 
+--R
+--R   (2)
+--R                                                                    +----------+
+--R                 4   4       4     3  2          5 4       5   3    |   2
+--R         ((- 3A b c e  + 3B b c d e )x  + (- 3A b e  + 3B b d e )x)\|c x  + b x
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                   3 2 3        2 3       3 2    2             4        2 3  2
+--R               6A b c e  + (4A b c  - 6B b c )d e  + (- 48A b c  + 28B b c )d e
+--R             + 
+--R                     5          4  3
+--R               (32A c  - 16B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                    4   3        3 2        4     2           2 3        3 2  2
+--R               12A b c e  + (6A b c  - 12B b c)d e  + (- 72A b c  + 42B b c )d e
+--R             + 
+--R                       4        2 3  3
+--R               (48A b c  - 24B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                   5 3       5   2           3 2        4   2
+--R               6A b e  - 6B b d e  + (- 18A b c  + 12B b c)d e
+--R             + 
+--R                     2 3       3 2  3
+--R               (12A b c  - 6B b c )d
+--R          *
+--R             x
+--R         + 
+--R                 5   2       4   2        3 2 3
+--R           - 2A b d e  + 4A b c d e - 2A b c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R  /
+--R           6   2 2     5 2 3      4 3 4  2      7 2 2     6   3      5 2 4
+--R       ((3b c d e  - 6b c d e + 3b c d )x  + (3b d e  - 6b c d e + 3b c d )x)
+--R    *
+--R                          +----------+
+--R        +-----------+ +-+ |   2
+--R       \|- b e + c d \|d \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 609
+
+--S 610 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                                                                  +----------+
+--R                 4   4       4     3  2        5 4       5   3    |   2
+--R           ((3A b c e  - 3B b c d e )x  + (3A b e  - 3B b d e )x)\|c x  + b x
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                     3 2 3        2 3       3 2    2
+--R                 6A b c e  + (4A b c  - 6B b c )d e
+--R               + 
+--R                           4        2 3  2          5          4  3
+--R                 (- 48A b c  + 28B b c )d e + (32A c  - 16B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      4   3        3 2        4     2
+--R                 12A b c e  + (6A b c  - 12B b c)d e
+--R               + 
+--R                         2 3        3 2  2            4        2 3  3
+--R                 (- 72A b c  + 42B b c )d e + (48A b c  - 24B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     5 3       5   2           3 2        4   2
+--R                 6A b e  - 6B b d e  + (- 18A b c  + 12B b c)d e
+--R               + 
+--R                       2 3       3 2  3
+--R                 (12A b c  - 6B b c )d
+--R            *
+--R               x
+--R           + 
+--R                   5   2       4   2        3 2 3
+--R             - 2A b d e  + 4A b c d e - 2A b c d
+--R        *
+--R            +--------------+
+--R            |             2
+--R           \|- b d e + c d
+--R    /
+--R             6   2 2     5 2 3      4 3 4  2      7 2 2     6   3      5 2 4
+--R         ((3b c d e  - 6b c d e + 3b c d )x  + (3b d e  - 6b c d e + 3b c d )x)
+--R      *
+--R          +--------------+ +----------+
+--R          |             2  |   2
+--R         \|- b d e + c d  \|c x  + b x
+--R     ,
+--R
+--R                   4   4       4     3  2          5 4       5   3
+--R           ((- 6A b c e  + 6B b c d e )x  + (- 6A b e  + 6B b d e )x)
+--R        *
+--R                              +------------+ +----------+
+--R            +----------+      |           2  |   2
+--R            |   2            \|b d e - c d  \|c x  + b x
+--R           \|c x  + b x atan(----------------------------)
+--R                                     (b e - c d)x
+--R       + 
+--R                     3 2 3        2 3       3 2    2
+--R                 6A b c e  + (4A b c  - 6B b c )d e
+--R               + 
+--R                           4        2 3  2          5          4  3
+--R                 (- 48A b c  + 28B b c )d e + (32A c  - 16B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      4   3        3 2        4     2
+--R                 12A b c e  + (6A b c  - 12B b c)d e
+--R               + 
+--R                         2 3        3 2  2            4        2 3  3
+--R                 (- 72A b c  + 42B b c )d e + (48A b c  - 24B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     5 3       5   2           3 2        4   2
+--R                 6A b e  - 6B b d e  + (- 18A b c  + 12B b c)d e
+--R               + 
+--R                       2 3       3 2  3
+--R                 (12A b c  - 6B b c )d
+--R            *
+--R               x
+--R           + 
+--R                   5   2       4   2        3 2 3
+--R             - 2A b d e  + 4A b c d e - 2A b c d
+--R        *
+--R            +------------+
+--R            |           2
+--R           \|b d e - c d
+--R    /
+--R             6   2 2     5 2 3      4 3 4  2      7 2 2     6   3      5 2 4
+--R         ((3b c d e  - 6b c d e + 3b c d )x  + (3b d e  - 6b c d e + 3b c d )x)
+--R      *
+--R          +------------+ +----------+
+--R          |           2  |   2
+--R         \|b d e - c d  \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 610
+
+--S 611 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R             4        3  +-----------+ +-+
+--R         (A e  - B d e )\|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                       +--------------+
+--R           4        3  |             2              (b e - 2c d)x - b d
+--R       (A e  - B d e )\|- b d e + c d  atanh(--------------------------------)
+--R                                                                 +----------+
+--R                                               +-----------+ +-+ |   2
+--R                                             2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                +--------------+
+--R       2 2 2         3     2 4  |             2  +-----------+ +-+
+--R     (b d e  - 2b c d e + c d )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 611
+
+--S 612 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 612
+
+--S 613 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                       +------------+
+--R           4        3  |           2              (b e - 2c d)x - b d
+--R       (A e  - B d e )\|b d e - c d  atanh(--------------------------------)
+--R                                                               +----------+
+--R                                             +-----------+ +-+ |   2
+--R                                           2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                                                  +------------+ +----------+
+--R                                                  |           2  |   2
+--R              4         3  +-----------+ +-+     \|b d e - c d  \|c x  + b x
+--R       (- 2A e  + 2B d e )\|- b e + c d \|d atan(----------------------------)
+--R                                                         (b e - c d)x
+--R  /
+--R                                                  +------------+
+--R       2 2 2         3     2 4  +-----------+ +-+ |           2
+--R     (b d e  - 2b c d e + c d )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 613
+
+--S 614 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 614
+
+)clear all
+
+--S 615 of 1457
+t0:=(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(5/2))
+--R 
+--R
+--R   (1)
+--R     B x + A
+--R  /
+--R          2 2 6          2     2     5     2 2               2 2  4
+--R         c e x  + (2b c e  + 2c d e)x  + (b e  + 4b c d e + c d )x
+--R       + 
+--R            2            2  3    2 2 2
+--R         (2b d e + 2b c d )x  + b d x
+--R    *
+--R        +----------+
+--R        |   2
+--R       \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 615
+
+--S 616 of 1457
+r0:=-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*_
+     (d+e*x)*(b*x+c*x^2)^(3/2))-1/2*e^3*(B*d*(8*c*d-3*b*e)-5*A*e*_
+     (2*c*d-b*e))*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_
+     sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+2/3*(b*(c*d-b*e)*_
+     (8*A*c^2*d^2+b^2*e*(3*B*d-5*A*e)-2*b*c*d*(2*B*d+A*e))+c*(16*A*c^3*d^3-_
+     b^3*e^2*(3*B*d-5*A*e)+2*b^2*c*d*e*(8*B*d-A*e)-8*b*c^2*d^2*(B*d+_
+     3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*(d+e*x)*sqrt(b*x+c*x^2))+1/3*e*_
+     (32*A*c^4*d^4-2*b^3*c*d*e^2*(9*B*d-10*A*e)+3*b^4*e^3*(3*B*d-5*A*e)+_
+     4*b^2*c^2*d^2*e*(10*B*d+3*A*e)-16*b*c^3*d^3*(B*d+4*A*e))*sqrt(b*x+_
+     c*x^2)/(b^4*d^3*(c*d-b*e)^3*(d+e*x))
+--R 
+--R
+--R   (2)
+--R                   5   6         4 2       5     5        4 2 2 4  3
+--R           (- 15A b c e  + (30A b c  + 9B b c)d e  - 24B b c d e )x
+--R         + 
+--R                      6 6         5        6    5         4 2        5   2 4
+--R               - 15A b e  + (15A b c + 9B b )d e  + (30A b c  - 15B b c)d e
+--R             + 
+--R                      4 2 3 3
+--R               - 24B b c d e
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                   6   5         5        6  2 4        5   3 3
+--R           (- 15A b d e  + (30A b c + 9B b )d e  - 24B b c d e )x
+--R      *
+--R          +----------+
+--R          |   2                    (b e - 2c d)x - b d
+--R         \|c x  + b x atanh(--------------------------------)
+--R                                                +----------+
+--R                              +-----------+ +-+ |   2
+--R                            2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                    4 2 5           3 3        4 2    4
+--R               30A b c e  + (- 40A b c  - 18B b c )d e
+--R             + 
+--R                       2 4        3 3  2 3            5        2 4  3 2
+--R               (- 24A b c  + 36B b c )d e  + (128A b c  - 80B b c )d e
+--R             + 
+--R                       6          5  4
+--R               (- 64A c  + 32B b c )d e
+--R          *
+--R              4
+--R             x
+--R         + 
+--R                    5   5           4 2        5     4
+--R               60A b c e  + (- 60A b c  - 36B b c)d e
+--R             + 
+--R                       3 3        4 2  2 3          2 4        3 3  3 2
+--R               (- 76A b c  + 60B b c )d e  + (168A b c  - 84B b c )d e
+--R             + 
+--R                       5        2 4  4            6          5  5
+--R               (32A b c  - 32B b c )d e + (- 64A c  + 32B b c )d
+--R          *
+--R              3
+--R             x
+--R         + 
+--R                    6 5        6   4           4 2        5   2 3
+--R               30A b e  - 18B b d e  + (- 84A b c  + 12B b c)d e
+--R             + 
+--R                     3 3        4 2  3 2          2 4         3 3  4
+--R               (12A b c  + 36B b c )d e  + (168A b c  - 108B b c )d e
+--R             + 
+--R                         5        2 4  5
+--R               (- 96A b c  + 48B b c )d
+--R          *
+--R              2
+--R             x
+--R         + 
+--R                    6   4           5         6  2 3
+--R               20A b d e  + (- 36A b c - 12B b )d e
+--R             + 
+--R                       4 2        5   3 2         3 3        4 2  4
+--R               (- 12A b c  + 36B b c)d e  + (52A b c  - 36B b c )d e
+--R             + 
+--R                       2 4        3 3  5
+--R               (- 24A b c  + 12B b c )d
+--R          *
+--R             x
+--R         + 
+--R                 6 2 3        5   3 2        4 2 4        3 3 5
+--R           - 4A b d e  + 12A b c d e  - 12A b c d e + 4A b c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R  /
+--R            7   3 4      6 2 4 3      5 3 5 2     4 4 6   3
+--R         (6b c d e  - 18b c d e  + 18b c d e  - 6b c d e)x
+--R       + 
+--R            8 3 4      7   4 3      5 3 6      4 4 7  2
+--R         (6b d e  - 12b c d e  + 12b c d e - 6b c d )x
+--R       + 
+--R            8 4 3      7   5 2      6 2 6      5 3 7
+--R         (6b d e  - 18b c d e  + 18b c d e - 6b c d )x
+--R    *
+--R                          +----------+
+--R        +-----------+ +-+ |   2
+--R       \|- b e + c d \|d \|c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 616
+
+--S 617 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                   5   6           4 2       5     5        4 2 2 4  3
+--R             (15A b c e  + (- 30A b c  - 9B b c)d e  + 24B b c d e )x
+--R           + 
+--R                      6 6           5        6    5           4 2        5   2 4
+--R                 15A b e  + (- 15A b c - 9B b )d e  + (- 30A b c  + 15B b c)d e
+--R               + 
+--R                      4 2 3 3
+--R                 24B b c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                   6   5           5        6  2 4        5   3 3
+--R             (15A b d e  + (- 30A b c - 9B b )d e  + 24B b c d e )x
+--R        *
+--R            +----------+
+--R            |   2
+--R           \|c x  + b x
+--R        *
+--R           log
+--R                                     +----------+
+--R                                  2  |   2
+--R                  (- 2b d e + 2c d )\|c x  + b x
+--R                + 
+--R                                          +--------------+
+--R                                          |             2
+--R                  ((- b e + 2c d)x + b d)\|- b d e + c d
+--R             /
+--R                e x + d
+--R       + 
+--R                      4 2 5           3 3        4 2    4
+--R                 30A b c e  + (- 40A b c  - 18B b c )d e
+--R               + 
+--R                         2 4        3 3  2 3            5        2 4  3 2
+--R                 (- 24A b c  + 36B b c )d e  + (128A b c  - 80B b c )d e
+--R               + 
+--R                         6          5  4
+--R                 (- 64A c  + 32B b c )d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      5   5           4 2        5     4
+--R                 60A b c e  + (- 60A b c  - 36B b c)d e
+--R               + 
+--R                         3 3        4 2  2 3          2 4        3 3  3 2
+--R                 (- 76A b c  + 60B b c )d e  + (168A b c  - 84B b c )d e
+--R               + 
+--R                         5        2 4  4            6          5  5
+--R                 (32A b c  - 32B b c )d e + (- 64A c  + 32B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      6 5        6   4           4 2        5   2 3
+--R                 30A b e  - 18B b d e  + (- 84A b c  + 12B b c)d e
+--R               + 
+--R                       3 3        4 2  3 2          2 4         3 3  4
+--R                 (12A b c  + 36B b c )d e  + (168A b c  - 108B b c )d e
+--R               + 
+--R                           5        2 4  5
+--R                 (- 96A b c  + 48B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      6   4           5         6  2 3
+--R                 20A b d e  + (- 36A b c - 12B b )d e
+--R               + 
+--R                         4 2        5   3 2         3 3        4 2  4
+--R                 (- 12A b c  + 36B b c)d e  + (52A b c  - 36B b c )d e
+--R               + 
+--R                         2 4        3 3  5
+--R                 (- 24A b c  + 12B b c )d
+--R            *
+--R               x
+--R           + 
+--R                   6 2 3        5   3 2        4 2 4        3 3 5
+--R             - 4A b d e  + 12A b c d e  - 12A b c d e + 4A b c d
+--R        *
+--R            +--------------+
+--R            |             2
+--R           \|- b d e + c d
+--R    /
+--R              7   3 4      6 2 4 3      5 3 5 2     4 4 6   3
+--R           (6b c d e  - 18b c d e  + 18b c d e  - 6b c d e)x
+--R         + 
+--R              8 3 4      7   4 3      5 3 6      4 4 7  2
+--R           (6b d e  - 12b c d e  + 12b c d e - 6b c d )x
+--R         + 
+--R              8 4 3      7   5 2      6 2 6      5 3 7
+--R           (6b d e  - 18b c d e  + 18b c d e - 6b c d )x
+--R      *
+--R          +--------------+ +----------+
+--R          |             2  |   2
+--R         \|- b d e + c d  \|c x  + b x
+--R     ,
+--R
+--R                     5   6         4 2       5     5        4 2 2 4  3
+--R             (- 15A b c e  + (30A b c  + 9B b c)d e  - 24B b c d e )x
+--R           + 
+--R                        6 6         5        6    5         4 2        5   2 4
+--R                 - 15A b e  + (15A b c + 9B b )d e  + (30A b c  - 15B b c)d e
+--R               + 
+--R                        4 2 3 3
+--R                 - 24B b c d e
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                     6   5         5        6  2 4        5   3 3
+--R             (- 15A b d e  + (30A b c + 9B b )d e  - 24B b c d e )x
+--R        *
+--R                              +------------+ +----------+
+--R            +----------+      |           2  |   2
+--R            |   2            \|b d e - c d  \|c x  + b x
+--R           \|c x  + b x atan(----------------------------)
+--R                                     (b e - c d)x
+--R       + 
+--R                      4 2 5           3 3       4 2    4
+--R                 15A b c e  + (- 20A b c  - 9B b c )d e
+--R               + 
+--R                         2 4        3 3  2 3           5        2 4  3 2
+--R                 (- 12A b c  + 18B b c )d e  + (64A b c  - 40B b c )d e
+--R               + 
+--R                         6          5  4
+--R                 (- 32A c  + 16B b c )d e
+--R            *
+--R                4
+--R               x
+--R           + 
+--R                      5   5           4 2        5     4
+--R                 30A b c e  + (- 30A b c  - 18B b c)d e
+--R               + 
+--R                         3 3        4 2  2 3         2 4        3 3  3 2
+--R                 (- 38A b c  + 30B b c )d e  + (84A b c  - 42B b c )d e
+--R               + 
+--R                         5        2 4  4            6          5  5
+--R                 (16A b c  - 16B b c )d e + (- 32A c  + 16B b c )d
+--R            *
+--R                3
+--R               x
+--R           + 
+--R                      6 5       6   4           4 2       5   2 3
+--R                 15A b e  - 9B b d e  + (- 42A b c  + 6B b c)d e
+--R               + 
+--R                      3 3        4 2  3 2         2 4        3 3  4
+--R                 (6A b c  + 18B b c )d e  + (84A b c  - 54B b c )d e
+--R               + 
+--R                           5        2 4  5
+--R                 (- 48A b c  + 24B b c )d
+--R            *
+--R                2
+--R               x
+--R           + 
+--R                      6   4           5        6  2 3
+--R                 10A b d e  + (- 18A b c - 6B b )d e
+--R               + 
+--R                        4 2        5   3 2         3 3        4 2  4
+--R                 (- 6A b c  + 18B b c)d e  + (26A b c  - 18B b c )d e
+--R               + 
+--R                         2 4       3 3  5
+--R                 (- 12A b c  + 6B b c )d
+--R            *
+--R               x
+--R           + 
+--R                   6 2 3       5   3 2       4 2 4        3 3 5
+--R             - 2A b d e  + 6A b c d e  - 6A b c d e + 2A b c d
+--R        *
+--R            +------------+
+--R            |           2
+--R           \|b d e - c d
+--R    /
+--R              7   3 4     6 2 4 3     5 3 5 2     4 4 6   3
+--R           (3b c d e  - 9b c d e  + 9b c d e  - 3b c d e)x
+--R         + 
+--R              8 3 4     7   4 3     5 3 6      4 4 7  2
+--R           (3b d e  - 6b c d e  + 6b c d e - 3b c d )x
+--R         + 
+--R              8 4 3     7   5 2     6 2 6      5 3 7
+--R           (3b d e  - 9b c d e  + 9b c d e - 3b c d )x
+--R      *
+--R          +------------+ +----------+
+--R          |           2  |   2
+--R         \|b d e - c d  \|c x  + b x
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 617
+
+--S 618 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                5                      4         2 3  +-----------+ +-+
+--R         (5A b e  + (- 10A c - 3B b)d e  + 8B c d e )\|- b e + c d \|d
+--R      *
+--R         log
+--R                                   +----------+
+--R                                2  |   2
+--R                (- 2b d e + 2c d )\|c x  + b x
+--R              + 
+--R                                        +--------------+
+--R                                        |             2
+--R                ((- b e + 2c d)x + b d)\|- b d e + c d
+--R           /
+--R              e x + d
+--R     + 
+--R                                                      +--------------+
+--R                5                      4         2 3  |             2
+--R         (5A b e  + (- 10A c - 3B b)d e  + 8B c d e )\|- b d e + c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R  /
+--R                                              +--------------+
+--R        3 3 3     2   4 2       2 5      3 6  |             2  +-----------+ +-+
+--R     (2b d e  - 6b c d e  + 6b c d e - 2c d )\|- b d e + c d  \|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 618
+
+--S 619 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 619
+
+--S 620 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                                      +------------+
+--R                5                      4         2 3  |           2
+--R         (5A b e  + (- 10A c - 3B b)d e  + 8B c d e )\|b d e - c d
+--R      *
+--R                      (b e - 2c d)x - b d
+--R         atanh(--------------------------------)
+--R                                   +----------+
+--R                 +-----------+ +-+ |   2
+--R               2\|- b e + c d \|d \|c x  + b x
+--R     + 
+--R                   5                    4          2 3  +-----------+ +-+
+--R         (- 10A b e  + (20A c + 6B b)d e  - 16B c d e )\|- b e + c d \|d
+--R      *
+--R               +------------+ +----------+
+--R               |           2  |   2
+--R              \|b d e - c d  \|c x  + b x
+--R         atan(----------------------------)
+--R                      (b e - c d)x
+--R  /
+--R                                                                +------------+
+--R        3 3 3     2   4 2       2 5      3 6  +-----------+ +-+ |           2
+--R     (2b d e  - 6b c d e  + 6b c d e - 2c d )\|- b e + c d \|d \|b d e - c d
+--R                                                    Type: Expression(Integer)
+--E 620
+
+--S 621 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 621
+
+)clear all
+
+--S 622 of 1457
+t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R            3 6                3           2  5
+--R       B c e x  + ((A c + B b)e  + 3B c d e )x
+--R     + 
+--R             3                   2         2   4
+--R       (A b e  + (3A c + 3B b)d e  + 3B c d e)x
+--R     + 
+--R                2                 2         3  3          2                3  2
+--R       (3A b d e  + (3A c + 3B b)d e + B c d )x  + (3A b d e + (A c + B b)d )x
+--R     + 
+--R            3
+--R       A b d x
+--R  *
+--R      +-------+
+--R     \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 622
+
+--S 623 of 1457
+r0:=-2/9*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(9/2)/e^4+2/11*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^4-2/13*(3*B*c*d-b*B*e-A*c*e)*_
+     (d+e*x)^(13/2)/e^4+2/15*B*c*(d+e*x)^(15/2)/e^4
+--R 
+--R
+--R   (2)
+--R                 7 7                      7              6  6
+--R         858B c e x  + ((990A c + 990B b)e  + 3036B c d e )x
+--R       + 
+--R                   7                         6            2 5  5
+--R         (1170A b e  + (3600A c + 3600B b)d e  + 3708B c d e )x
+--R       + 
+--R                     6                       2 5            3 4  4
+--R         (4420A b d e  + (4580A c + 4580B b)d e  + 1600B c d e )x
+--R       + 
+--R                   2 5                       3 4          4 3  3
+--R         (5980A b d e  + (2120A c + 2120B b)d e  + 10B c d e )x
+--R       + 
+--R                   3 4                   4 3          5 2  2
+--R         (3120A b d e  + (30A c + 30B b)d e  - 12B c d e )x
+--R       + 
+--R                  4 3                     5 2          6              5 2
+--R         (130A b d e  + (- 40A c - 40B b)d e  + 16B c d e)x - 260A b d e
+--R       + 
+--R                         6           7
+--R         (80A c + 80B b)d e - 32B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R          4
+--R     6435e
+--R                                                    Type: Expression(Integer)
+--E 623
+
+--S 624 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                 7 7                      7              6  6
+--R         858B c e x  + ((990A c + 990B b)e  + 3036B c d e )x
+--R       + 
+--R                   7                         6            2 5  5
+--R         (1170A b e  + (3600A c + 3600B b)d e  + 3708B c d e )x
+--R       + 
+--R                     6                       2 5            3 4  4
+--R         (4420A b d e  + (4580A c + 4580B b)d e  + 1600B c d e )x
+--R       + 
+--R                   2 5                       3 4          4 3  3
+--R         (5980A b d e  + (2120A c + 2120B b)d e  + 10B c d e )x
+--R       + 
+--R                   3 4                   4 3          5 2  2
+--R         (3120A b d e  + (30A c + 30B b)d e  - 12B c d e )x
+--R       + 
+--R                  4 3                     5 2          6              5 2
+--R         (130A b d e  + (- 40A c - 40B b)d e  + 16B c d e)x - 260A b d e
+--R       + 
+--R                         6           7
+--R         (80A c + 80B b)d e - 32B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R          4
+--R     6435e
+--R                                         Type: Union(Expression(Integer),...)
+--E 624
+
+--S 625 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 625
+
+--S 626 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 626
+
+)clear all
+
+--S 627 of 1457
+t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R            2 5                2             4
+--R       B c e x  + ((A c + B b)e  + 2B c d e)x
+--R     + 
+--R             2                           2  3                           2  2
+--R       (A b e  + (2A c + 2B b)d e + B c d )x  + (2A b d e + (A c + B b)d )x
+--R     + 
+--R            2
+--R       A b d x
+--R  *
+--R      +-------+
+--R     \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 627
+
+--S 628 of 1457
+r0:=-2/7*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(7/2)/e^4+2/9*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^4-2/11*(3*B*c*d-b*B*e-A*c*e)*_
+     (d+e*x)^(11/2)/e^4+2/13*B*c*(d+e*x)^(13/2)/e^4
+--R 
+--R
+--R   (2)
+--R                  6 6                        6              5  5
+--R         1386B c e x  + ((1638A c + 1638B b)e  + 3402B c d e )x
+--R       + 
+--R                   6                         5            2 4  4
+--R         (2002A b e  + (4186A c + 4186B b)d e  + 2226B c d e )x
+--R       + 
+--R                     5                       2 4          3 3  3
+--R         (5434A b d e  + (2938A c + 2938B b)d e  + 30B c d e )x
+--R       + 
+--R                   2 4                   3 3          4 2  2
+--R         (4290A b d e  + (78A c + 78B b)d e  - 36B c d e )x
+--R       + 
+--R                  3 3                       4 2          5              4 2
+--R         (286A b d e  + (- 104A c - 104B b)d e  + 48B c d e)x - 572A b d e
+--R       + 
+--R                           5           6
+--R         (208A c + 208B b)d e - 96B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R          4
+--R     9009e
+--R                                                    Type: Expression(Integer)
+--E 628
+
+--S 629 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  6 6                        6              5  5
+--R         1386B c e x  + ((1638A c + 1638B b)e  + 3402B c d e )x
+--R       + 
+--R                   6                         5            2 4  4
+--R         (2002A b e  + (4186A c + 4186B b)d e  + 2226B c d e )x
+--R       + 
+--R                     5                       2 4          3 3  3
+--R         (5434A b d e  + (2938A c + 2938B b)d e  + 30B c d e )x
+--R       + 
+--R                   2 4                   3 3          4 2  2
+--R         (4290A b d e  + (78A c + 78B b)d e  - 36B c d e )x
+--R       + 
+--R                  3 3                       4 2          5              4 2
+--R         (286A b d e  + (- 104A c - 104B b)d e  + 48B c d e)x - 572A b d e
+--R       + 
+--R                           5           6
+--R         (208A c + 208B b)d e - 96B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R          4
+--R     9009e
+--R                                         Type: Union(Expression(Integer),...)
+--E 629
+
+--S 630 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 630
+
+--S 631 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 631
+
+)clear all
+
+--S 632 of 1457
+t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R             4                          3                          2
+--R     (B c e x  + ((A c + B b)e + B c d)x  + (A b e + (A c + B b)d)x  + A b d x)
+--R  *
+--R      +-------+
+--R     \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 632
+
+--S 633 of 1457
+r0:=-2/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(5/2)/e^4+2/7*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^4-2/9*(3*B*c*d-b*B*e-A*c*e)*_
+     (d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4
+--R 
+--R
+--R   (2)
+--R                 5 5                      5             4  4
+--R         630B c e x  + ((770A c + 770B b)e  + 840B c d e )x
+--R       + 
+--R                  5                         4          2 3  3
+--R         (990A b e  + (1100A c + 1100B b)d e  + 30B c d e )x
+--R       + 
+--R                     4                   2 3          3 2  2
+--R         (1584A b d e  + (66A c + 66B b)d e  - 36B c d e )x
+--R       + 
+--R                  2 3                     3 2          4              3 2
+--R         (198A b d e  + (- 88A c - 88B b)d e  + 48B c d e)x - 396A b d e
+--R       + 
+--R                           4           5
+--R         (176A c + 176B b)d e - 96B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R          4
+--R     3465e
+--R                                                    Type: Expression(Integer)
+--E 633
+
+--S 634 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                 5 5                      5             4  4
+--R         630B c e x  + ((770A c + 770B b)e  + 840B c d e )x
+--R       + 
+--R                  5                         4          2 3  3
+--R         (990A b e  + (1100A c + 1100B b)d e  + 30B c d e )x
+--R       + 
+--R                     4                   2 3          3 2  2
+--R         (1584A b d e  + (66A c + 66B b)d e  - 36B c d e )x
+--R       + 
+--R                  2 3                     3 2          4              3 2
+--R         (198A b d e  + (- 88A c - 88B b)d e  + 48B c d e)x - 396A b d e
+--R       + 
+--R                           4           5
+--R         (176A c + 176B b)d e - 96B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R          4
+--R     3465e
+--R                                         Type: Union(Expression(Integer),...)
+--E 634
+
+--S 635 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 635
+
+--S 636 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 636
+
+)clear all
+
+--S 637 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)*sqrt(d+e*x)
+--R 
+--R
+--R              3               2          +-------+
+--R   (1)  (B c x  + (A c + B b)x  + A b x)\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 637
+
+--S 638 of 1457
+r0:=-2/3*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(3/2)/e^4+2/5*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^4-2/7*(3*B*c*d-b*B*e-A*c*e)*_
+     (d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4
+--R 
+--R
+--R   (2)
+--R                4 4                    4            3  3
+--R         70B c e x  + ((90A c + 90B b)e  + 10B c d e )x
+--R       + 
+--R                  4                     3          2 2  2
+--R         (126A b e  + (18A c + 18B b)d e  - 12B c d e )x
+--R       + 
+--R                   3                     2 2          3             2 2
+--R         (42A b d e  + (- 24A c - 24B b)d e  + 16B c d e)x - 84A b d e
+--R       + 
+--R                         3           4
+--R         (48A c + 48B b)d e - 32B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R         4
+--R     315e
+--R                                                    Type: Expression(Integer)
+--E 638
+
+--S 639 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                4 4                    4            3  3
+--R         70B c e x  + ((90A c + 90B b)e  + 10B c d e )x
+--R       + 
+--R                  4                     3          2 2  2
+--R         (126A b e  + (18A c + 18B b)d e  - 12B c d e )x
+--R       + 
+--R                   3                     2 2          3             2 2
+--R         (42A b d e  + (- 24A c - 24B b)d e  + 16B c d e)x - 84A b d e
+--R       + 
+--R                         3           4
+--R         (48A c + 48B b)d e - 32B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R         4
+--R     315e
+--R                                         Type: Union(Expression(Integer),...)
+--E 639
+
+--S 640 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 640
+
+--S 641 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 641
+
+)clear all
+
+--S 642 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/sqrt(d+e*x)
+--R 
+--R
+--R             3               2
+--R        B c x  + (A c + B b)x  + A b x
+--R   (1)  ------------------------------
+--R                   +-------+
+--R                  \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 642
+
+--S 643 of 1457
+r0:=2/3*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^4-2/5*(3*B*c*d-_
+     b*B*e-A*c*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-2*d*_
+     (B*d-A*e)*(c*d-b*e)*sqrt(d+e*x)/e^4
+--R 
+--R
+--R   (2)
+--R                3 3                    3            2  2
+--R         30B c e x  + ((42A c + 42B b)e  - 36B c d e )x
+--R       + 
+--R                 3                       2          2                2
+--R         (70A b e  + (- 56A c - 56B b)d e  + 48B c d e)x - 140A b d e
+--R       + 
+--R                           2           3
+--R         (112A c + 112B b)d e - 96B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R         4
+--R     105e
+--R                                                    Type: Expression(Integer)
+--E 643
+
+--S 644 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                3 3                    3            2  2
+--R         30B c e x  + ((42A c + 42B b)e  - 36B c d e )x
+--R       + 
+--R                 3                       2          2                2
+--R         (70A b e  + (- 56A c - 56B b)d e  + 48B c d e)x - 140A b d e
+--R       + 
+--R                           2           3
+--R         (112A c + 112B b)d e - 96B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R         4
+--R     105e
+--R                                         Type: Union(Expression(Integer),...)
+--E 644
+
+--S 645 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 645
+
+--S 646 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 646
+
+)clear all
+
+--S 647 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(3/2)
+--R 
+--R
+--R             3               2
+--R        B c x  + (A c + B b)x  + A b x
+--R   (1)  ------------------------------
+--R                        +-------+
+--R              (e x + d)\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 647
+
+--S 648 of 1457
+r0:=-2/3*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+_
+     2*d*(B*d-A*e)*(c*d-b*e)/(e^4*sqrt(d+e*x))+2*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^4
+--R 
+--R
+--R   (2)
+--R             3 3                    3            2  2
+--R       6B c e x  + ((10A c + 10B b)e  - 12B c d e )x
+--R     + 
+--R               3                       2          2               2
+--R       (30A b e  + (- 40A c - 40B b)d e  + 48B c d e)x + 60A b d e
+--R     + 
+--R                         2           3
+--R       (- 80A c - 80B b)d e + 96B c d
+--R  /
+--R        4 +-------+
+--R     15e \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 648
+
+--S 649 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R             3 3                    3            2  2
+--R       6B c e x  + ((10A c + 10B b)e  - 12B c d e )x
+--R     + 
+--R               3                       2          2               2
+--R       (30A b e  + (- 40A c - 40B b)d e  + 48B c d e)x + 60A b d e
+--R     + 
+--R                         2           3
+--R       (- 80A c - 80B b)d e + 96B c d
+--R  /
+--R        4 +-------+
+--R     15e \|e x + d
+--R                                         Type: Union(Expression(Integer),...)
+--E 649
+
+--S 650 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 650
+
+--S 651 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 651
+
+)clear all
+
+--S 652 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(5/2)
+--R 
+--R
+--R             3               2
+--R        B c x  + (A c + B b)x  + A b x
+--R   (1)  ------------------------------
+--R          2 2             2  +-------+
+--R        (e x  + 2d e x + d )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 652
+
+--S 653 of 1457
+r0:=2/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(3/2))+2/3*B*c*(d+e*x)^(3/2)/e^4-_
+     2*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))/(e^4*sqrt(d+e*x))-_
+     2*(3*B*c*d-b*B*e-A*c*e)*sqrt(d+e*x)/e^4
+--R 
+--R
+--R   (2)
+--R             3 3                  3            2  2
+--R       2B c e x  + ((6A c + 6B b)e  - 12B c d e )x
+--R     + 
+--R                3                     2          2              2
+--R       (- 6A b e  + (24A c + 24B b)d e  - 48B c d e)x - 4A b d e
+--R     + 
+--R                       2           3
+--R       (16A c + 16B b)d e - 32B c d
+--R  /
+--R        5        4  +-------+
+--R     (3e x + 3d e )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 653
+
+--S 654 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R             3 3                  3            2  2
+--R       2B c e x  + ((6A c + 6B b)e  - 12B c d e )x
+--R     + 
+--R                3                     2          2              2
+--R       (- 6A b e  + (24A c + 24B b)d e  - 48B c d e)x - 4A b d e
+--R     + 
+--R                       2           3
+--R       (16A c + 16B b)d e - 32B c d
+--R  /
+--R        5        4  +-------+
+--R     (3e x + 3d e )\|e x + d
+--R                                         Type: Union(Expression(Integer),...)
+--E 654
+
+--S 655 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 655
+
+--S 656 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 656
+
+)clear all
+
+--S 657 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)/(d+e*x)^(7/2)
+--R 
+--R
+--R                  3               2
+--R             B c x  + (A c + B b)x  + A b x
+--R   (1)  ----------------------------------------
+--R          3 3       2 2     2       3  +-------+
+--R        (e x  + 3d e x  + 3d e x + d )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 657
+
+--S 658 of 1457
+r0:=2/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(5/2))-2/3*(B*d*(3*c*d-2*b*e)-_
+     A*e*(2*c*d-b*e))/(e^4*(d+e*x)^(3/2))+2*(3*B*c*d-b*B*e-A*c*e)/_
+     (e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4
+--R 
+--R
+--R   (2)
+--R              3 3                      3             2  2
+--R       30B c e x  + ((- 30A c - 30B b)e  + 180B c d e )x
+--R     + 
+--R                 3                       2           2              2
+--R       (- 10A b e  + (- 40A c - 40B b)d e  + 240B c d e)x - 4A b d e
+--R     + 
+--R                         2           3
+--R       (- 16A c - 16B b)d e + 96B c d
+--R  /
+--R         6 2        5       2 4  +-------+
+--R     (15e x  + 30d e x + 15d e )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 658
+
+--S 659 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R              3 3                      3             2  2
+--R       30B c e x  + ((- 30A c - 30B b)e  + 180B c d e )x
+--R     + 
+--R                 3                       2           2              2
+--R       (- 10A b e  + (- 40A c - 40B b)d e  + 240B c d e)x - 4A b d e
+--R     + 
+--R                         2           3
+--R       (- 16A c - 16B b)d e + 96B c d
+--R  /
+--R         6 2        5       2 4  +-------+
+--R     (15e x  + 30d e x + 15d e )\|e x + d
+--R                                         Type: Union(Expression(Integer),...)
+--E 659
+
+--S 660 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 660
+
+--S 661 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 661
+
+)clear all
+
+--S 662 of 1457
+t0:=(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R          2 3 8        2           3       2   2  7
+--R       B c e x  + ((A c  + 2B b c)e  + 3B c d e )x
+--R     + 
+--R                     2  3        2             2       2 2   6
+--R       ((2A b c + B b )e  + (3A c  + 6B b c)d e  + 3B c d e)x
+--R     + 
+--R           2 3                 2    2        2           2       2 3  5
+--R       (A b e  + (6A b c + 3B b )d e  + (3A c  + 6B b c)d e + B c d )x
+--R     + 
+--R            2   2                 2  2        2           3  4
+--R       (3A b d e  + (6A b c + 3B b )d e + (A c  + 2B b c)d )x
+--R     + 
+--R            2 2                 2  3  3      2 3 2
+--R       (3A b d e + (2A b c + B b )d )x  + A b d x
+--R  *
+--R      +-------+
+--R     \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 662
+
+--S 663 of 1457
+r0:=-2/9*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(9/2)/e^6+2/11*d*(c*d-b*e)*_
+     (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^6+_
+     2/13*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_
+     3*b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*(2*A*c*e*(2*c*d-b*e)-_
+     B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(15/2)/e^6-2/17*c*_
+     (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(17/2)/e^6+2/19*B*c^2*(d+e*x)^(19/2)/e^6
+--R 
+--R
+--R   (2)
+--R                  2 9 9              2                9            2   8  8
+--R         218790B c e x  + ((244530A c  + 489060B b c)e  + 746460B c d e )x
+--R       + 
+--R                                     2  9             2                   8
+--R             (554268A b c + 277134B b )e  + (847704A c  + 1695408B b c)d e
+--R           + 
+--R                      2 2 7
+--R             866580B c d e
+--R        *
+--R            7
+--R           x
+--R       + 
+--R                      2 9                            2    8
+--R             319770A b e  + (1961256A b c + 980628B b )d e
+--R           + 
+--R                        2                 2 7            2 3 6
+--R             (1005708A c  + 2011416B b c)d e  + 345840B c d e
+--R        *
+--R            6
+--R           x
+--R       + 
+--R                       2   8                             2  2 7
+--R             1162800A b d e  + (2395368A b c + 1197684B b )d e
+--R           + 
+--R                       2                3 6         2 4 5
+--R             (414504A c  + 829008B b c)d e  + 630B c d e
+--R        *
+--R            5
+--R           x
+--R       + 
+--R                       2 2 7                            2  3 6
+--R             1479340A b d e  + (1033600A b c + 516800B b )d e
+--R           + 
+--R                     2              4 5         2 5 4
+--R             (1330A c  + 2660B b c)d e  - 700B c d e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                      2 3 6                       2  4 5
+--R             684760A b d e  + (6460A b c + 3230B b )d e
+--R           + 
+--R                       2              5 4         2 6 3
+--R             (- 1520A c  - 3040B b c)d e  + 800B c d e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                    2 4 5                         2  5 4
+--R             9690A b d e  + (- 7752A b c - 3876B b )d e
+--R           + 
+--R                     2              6 3         2 7 2
+--R             (1824A c  + 3648B b c)d e  - 960B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                       2 5 4                        2  6 3
+--R             - 12920A b d e  + (10336A b c + 5168B b )d e
+--R           + 
+--R                       2              7 2          2 8
+--R             (- 2432A c  - 4864B b c)d e  + 1280B c d e
+--R        *
+--R           x
+--R       + 
+--R                 2 6 3                           2  7 2
+--R         25840A b d e  + (- 20672A b c - 10336B b )d e
+--R       + 
+--R                 2              8           2 9
+--R         (4864A c  + 9728B b c)d e - 2560B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R             6
+--R     2078505e
+--R                                                    Type: Expression(Integer)
+--E 663
+
+--S 664 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                  2 9 9              2                9            2   8  8
+--R         218790B c e x  + ((244530A c  + 489060B b c)e  + 746460B c d e )x
+--R       + 
+--R                                     2  9             2                   8
+--R             (554268A b c + 277134B b )e  + (847704A c  + 1695408B b c)d e
+--R           + 
+--R                      2 2 7
+--R             866580B c d e
+--R        *
+--R            7
+--R           x
+--R       + 
+--R                      2 9                            2    8
+--R             319770A b e  + (1961256A b c + 980628B b )d e
+--R           + 
+--R                        2                 2 7            2 3 6
+--R             (1005708A c  + 2011416B b c)d e  + 345840B c d e
+--R        *
+--R            6
+--R           x
+--R       + 
+--R                       2   8                             2  2 7
+--R             1162800A b d e  + (2395368A b c + 1197684B b )d e
+--R           + 
+--R                       2                3 6         2 4 5
+--R             (414504A c  + 829008B b c)d e  + 630B c d e
+--R        *
+--R            5
+--R           x
+--R       + 
+--R                       2 2 7                            2  3 6
+--R             1479340A b d e  + (1033600A b c + 516800B b )d e
+--R           + 
+--R                     2              4 5         2 5 4
+--R             (1330A c  + 2660B b c)d e  - 700B c d e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                      2 3 6                       2  4 5
+--R             684760A b d e  + (6460A b c + 3230B b )d e
+--R           + 
+--R                       2              5 4         2 6 3
+--R             (- 1520A c  - 3040B b c)d e  + 800B c d e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                    2 4 5                         2  5 4
+--R             9690A b d e  + (- 7752A b c - 3876B b )d e
+--R           + 
+--R                     2              6 3         2 7 2
+--R             (1824A c  + 3648B b c)d e  - 960B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                       2 5 4                        2  6 3
+--R             - 12920A b d e  + (10336A b c + 5168B b )d e
+--R           + 
+--R                       2              7 2          2 8
+--R             (- 2432A c  - 4864B b c)d e  + 1280B c d e
+--R        *
+--R           x
+--R       + 
+--R                 2 6 3                           2  7 2
+--R         25840A b d e  + (- 20672A b c - 10336B b )d e
+--R       + 
+--R                 2              8           2 9
+--R         (4864A c  + 9728B b c)d e - 2560B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R             6
+--R     2078505e
+--R                                         Type: Union(Expression(Integer),...)
+--E 664
+
+--S 665 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 665
+
+--S 666 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 666
+
+)clear all
+
+--S 667 of 1457
+t0:=(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R          2 2 7        2           2       2     6
+--R       B c e x  + ((A c  + 2B b c)e  + 2B c d e)x
+--R     + 
+--R                     2  2        2                   2 2  5
+--R       ((2A b c + B b )e  + (2A c  + 4B b c)d e + B c d )x
+--R     + 
+--R           2 2                 2           2           2  4
+--R       (A b e  + (4A b c + 2B b )d e + (A c  + 2B b c)d )x
+--R     + 
+--R            2                   2  2  3      2 2 2
+--R       (2A b d e + (2A b c + B b )d )x  + A b d x
+--R  *
+--R      +-------+
+--R     \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 667
+
+--S 668 of 1457
+r0:=-2/7*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(7/2)/e^6+2/9*d*(c*d-b*e)*_
+     (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^6+2/11*_
+     (A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_
+     3*b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*(2*A*c*e*(2*c*d-b*e)-_
+     B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*c*_
+     (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(15/2)/e^6+2/17*B*c^2*(d+e*x)^(17/2)/e^6
+--R 
+--R
+--R   (2)
+--R                 2 8 8              2                8            2   7  7
+--R         90090B c e x  + ((102102A c  + 204204B b c)e  + 210210B c d e )x
+--R       + 
+--R                                     2  8             2                  7
+--R             (235620A b c + 117810B b )e  + (243474A c  + 486948B b c)d e
+--R           + 
+--R                      2 2 6
+--R             127050B c d e
+--R        *
+--R            6
+--R           x
+--R       + 
+--R                      2 8                           2    7
+--R             139230A b e  + (578340A b c + 289170B b )d e
+--R           + 
+--R                       2                2 6         2 3 5
+--R             (152082A c  + 304164B b c)d e  + 630B c d e
+--R        *
+--R            5
+--R           x
+--R       + 
+--R                      2   7                           2  2 6
+--R             355810A b d e  + (378420A b c + 189210B b )d e
+--R           + 
+--R                     2              3 5         2 4 4
+--R             (1190A c  + 2380B b c)d e  - 700B c d e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                      2 2 6                       2  3 5
+--R             249730A b d e  + (5100A b c + 2550B b )d e
+--R           + 
+--R                       2              4 4         2 5 3
+--R             (- 1360A c  - 2720B b c)d e  + 800B c d e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                    2 3 5                         2  4 4
+--R             6630A b d e  + (- 6120A b c - 3060B b )d e
+--R           + 
+--R                     2              5 3         2 6 2
+--R             (1632A c  + 3264B b c)d e  - 960B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                      2 4 4                       2  5 3
+--R             - 8840A b d e  + (8160A b c + 4080B b )d e
+--R           + 
+--R                       2              6 2          2 7
+--R             (- 2176A c  - 4352B b c)d e  + 1280B c d e
+--R        *
+--R           x
+--R       + 
+--R                 2 5 3                          2  6 2
+--R         17680A b d e  + (- 16320A b c - 8160B b )d e
+--R       + 
+--R                 2              7           2 8
+--R         (4352A c  + 8704B b c)d e - 2560B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R            6
+--R     765765e
+--R                                                    Type: Expression(Integer)
+--E 668
+
+--S 669 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                 2 8 8              2                8            2   7  7
+--R         90090B c e x  + ((102102A c  + 204204B b c)e  + 210210B c d e )x
+--R       + 
+--R                                     2  8             2                  7
+--R             (235620A b c + 117810B b )e  + (243474A c  + 486948B b c)d e
+--R           + 
+--R                      2 2 6
+--R             127050B c d e
+--R        *
+--R            6
+--R           x
+--R       + 
+--R                      2 8                           2    7
+--R             139230A b e  + (578340A b c + 289170B b )d e
+--R           + 
+--R                       2                2 6         2 3 5
+--R             (152082A c  + 304164B b c)d e  + 630B c d e
+--R        *
+--R            5
+--R           x
+--R       + 
+--R                      2   7                           2  2 6
+--R             355810A b d e  + (378420A b c + 189210B b )d e
+--R           + 
+--R                     2              3 5         2 4 4
+--R             (1190A c  + 2380B b c)d e  - 700B c d e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                      2 2 6                       2  3 5
+--R             249730A b d e  + (5100A b c + 2550B b )d e
+--R           + 
+--R                       2              4 4         2 5 3
+--R             (- 1360A c  - 2720B b c)d e  + 800B c d e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                    2 3 5                         2  4 4
+--R             6630A b d e  + (- 6120A b c - 3060B b )d e
+--R           + 
+--R                     2              5 3         2 6 2
+--R             (1632A c  + 3264B b c)d e  - 960B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                      2 4 4                       2  5 3
+--R             - 8840A b d e  + (8160A b c + 4080B b )d e
+--R           + 
+--R                       2              6 2          2 7
+--R             (- 2176A c  - 4352B b c)d e  + 1280B c d e
+--R        *
+--R           x
+--R       + 
+--R                 2 5 3                          2  6 2
+--R         17680A b d e  + (- 16320A b c - 8160B b )d e
+--R       + 
+--R                 2              7           2 8
+--R         (4352A c  + 8704B b c)d e - 2560B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R            6
+--R     765765e
+--R                                         Type: Union(Expression(Integer),...)
+--E 669
+
+--S 670 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 670
+
+--S 671 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 671
+
+)clear all
+
+--S 672 of 1457
+t0:=(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2)^2
+--R 
+--R
+--R   (1)
+--R          2   6        2                 2   5
+--R       B c e x  + ((A c  + 2B b c)e + B c d)x
+--R     + 
+--R                     2         2             4       2                 2    3
+--R       ((2A b c + B b )e + (A c  + 2B b c)d)x  + (A b e + (2A b c + B b )d)x
+--R     + 
+--R          2   2
+--R       A b d x
+--R  *
+--R      +-------+
+--R     \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 672
+
+--S 673 of 1457
+r0:=-2/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(5/2)/e^6+2/7*d*(c*d-b*e)*_
+     (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^6+2/9*(A*e*_
+     (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_
+     (d+e*x)^(9/2)/e^6-2/11*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+_
+     b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*c*(5*B*c*d-2*b*B*e-A*c*e)*_
+     (d+e*x)^(13/2)/e^6+2/15*B*c^2*(d+e*x)^(15/2)/e^6
+--R 
+--R
+--R   (2)
+--R                2 7 7            2               7          2   6  6
+--R         6006B c e x  + ((6930A c  + 13860B b c)e  + 7392B c d e )x
+--R       + 
+--R                                    2  7           2                 6
+--R               (16380A b c + 8190B b )e  + (8820A c  + 17640B b c)d e
+--R             + 
+--R                     2 2 5
+--R               126B c d e
+--R        *
+--R            5
+--R           x
+--R       + 
+--R                     2 7                         2    6
+--R             10010A b e  + (21840A b c + 10920B b )d e
+--R           + 
+--R                    2             2 5         2 3 4
+--R             (210A c  + 420B b c)d e  - 140B c d e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                     2   6                     2  2 5
+--R             14300A b d e  + (780A b c + 390B b )d e
+--R           + 
+--R                      2             3 4         2 4 3
+--R             (- 240A c  - 480B b c)d e  + 160B c d e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                   2 2 5                       2  3 4          2             4 3
+--R             858A b d e  + (- 936A b c - 468B b )d e  + (288A c  + 576B b c)d e
+--R           + 
+--R                     2 5 2
+--R             - 192B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                      2 3 4                      2  4 3
+--R             - 1144A b d e  + (1248A b c + 624B b )d e
+--R           + 
+--R                      2             5 2         2 6
+--R             (- 384A c  - 768B b c)d e  + 256B c d e
+--R        *
+--R           x
+--R       + 
+--R                2 4 3                         2  5 2          2              6
+--R         2288A b d e  + (- 2496A b c - 1248B b )d e  + (768A c  + 1536B b c)d e
+--R       + 
+--R                 2 7
+--R         - 512B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R           6
+--R     45045e
+--R                                                    Type: Expression(Integer)
+--E 673
+
+--S 674 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                2 7 7            2               7          2   6  6
+--R         6006B c e x  + ((6930A c  + 13860B b c)e  + 7392B c d e )x
+--R       + 
+--R                                    2  7           2                 6
+--R               (16380A b c + 8190B b )e  + (8820A c  + 17640B b c)d e
+--R             + 
+--R                     2 2 5
+--R               126B c d e
+--R        *
+--R            5
+--R           x
+--R       + 
+--R                     2 7                         2    6
+--R             10010A b e  + (21840A b c + 10920B b )d e
+--R           + 
+--R                    2             2 5         2 3 4
+--R             (210A c  + 420B b c)d e  - 140B c d e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                     2   6                     2  2 5
+--R             14300A b d e  + (780A b c + 390B b )d e
+--R           + 
+--R                      2             3 4         2 4 3
+--R             (- 240A c  - 480B b c)d e  + 160B c d e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                   2 2 5                       2  3 4          2             4 3
+--R             858A b d e  + (- 936A b c - 468B b )d e  + (288A c  + 576B b c)d e
+--R           + 
+--R                     2 5 2
+--R             - 192B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                      2 3 4                      2  4 3
+--R             - 1144A b d e  + (1248A b c + 624B b )d e
+--R           + 
+--R                      2             5 2         2 6
+--R             (- 384A c  - 768B b c)d e  + 256B c d e
+--R        *
+--R           x
+--R       + 
+--R                2 4 3                         2  5 2          2              6
+--R         2288A b d e  + (- 2496A b c - 1248B b )d e  + (768A c  + 1536B b c)d e
+--R       + 
+--R                 2 7
+--R         - 512B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R           6
+--R     45045e
+--R                                         Type: Union(Expression(Integer),...)
+--E 674
+
+--S 675 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 675
+
+--S 676 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 676
+
+)clear all
+
+--S 677 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2*sqrt(d+e*x)
+--R 
+--R
+--R            2 5       2           4                2  3      2 2  +-------+
+--R   (1)  (B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 677
+
+--S 678 of 1457
+r0:=-2/3*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(3/2)/e^6+2/5*d*(c*d-b*e)*_
+     (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^6+2/7*(A*e*_
+     (6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*_
+     (d+e*x)^(7/2)/e^6-2/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_
+     8*b*c*d*e+b^2*e^2))*(d+e*x)^(9/2)/e^6-2/11*c*(5*B*c*d-2*b*B*e-A*c*e)*_
+     (d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6
+--R 
+--R
+--R   (2)
+--R                2 6 6            2               6         2   5  5
+--R         6930B c e x  + ((8190A c  + 16380B b c)e  + 630B c d e )x
+--R       + 
+--R                                     2  6          2                5
+--R               (20020A b c + 10010B b )e  + (910A c  + 1820B b c)d e
+--R             + 
+--R                       2 2 4
+--R               - 700B c d e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                     2 6                       2    5
+--R             12870A b e  + (2860A b c + 1430B b )d e
+--R           + 
+--R                       2              2 4         2 3 3
+--R             (- 1040A c  - 2080B b c)d e  + 800B c d e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                    2   5                         2  2 4
+--R             2574A b d e  + (- 3432A b c - 1716B b )d e
+--R           + 
+--R                     2              3 3         2 4 2
+--R             (1248A c  + 2496B b c)d e  - 960B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                      2 2 4                       2  3 3
+--R             - 3432A b d e  + (4576A b c + 2288B b )d e
+--R           + 
+--R                       2              4 2          2 5
+--R             (- 1664A c  - 3328B b c)d e  + 1280B c d e
+--R        *
+--R           x
+--R       + 
+--R                2 3 3                         2  4 2           2              5
+--R         6864A b d e  + (- 9152A b c - 4576B b )d e  + (3328A c  + 6656B b c)d e
+--R       + 
+--R                  2 6
+--R         - 2560B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R           6
+--R     45045e
+--R                                                    Type: Expression(Integer)
+--E 678
+
+--S 679 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R                2 6 6            2               6         2   5  5
+--R         6930B c e x  + ((8190A c  + 16380B b c)e  + 630B c d e )x
+--R       + 
+--R                                     2  6          2                5
+--R               (20020A b c + 10010B b )e  + (910A c  + 1820B b c)d e
+--R             + 
+--R                       2 2 4
+--R               - 700B c d e
+--R        *
+--R            4
+--R           x
+--R       + 
+--R                     2 6                       2    5
+--R             12870A b e  + (2860A b c + 1430B b )d e
+--R           + 
+--R                       2              2 4         2 3 3
+--R             (- 1040A c  - 2080B b c)d e  + 800B c d e
+--R        *
+--R            3
+--R           x
+--R       + 
+--R                    2   5                         2  2 4
+--R             2574A b d e  + (- 3432A b c - 1716B b )d e
+--R           + 
+--R                     2              3 3         2 4 2
+--R             (1248A c  + 2496B b c)d e  - 960B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                      2 2 4                       2  3 3
+--R             - 3432A b d e  + (4576A b c + 2288B b )d e
+--R           + 
+--R                       2              4 2          2 5
+--R             (- 1664A c  - 3328B b c)d e  + 1280B c d e
+--R        *
+--R           x
+--R       + 
+--R                2 3 3                         2  4 2           2              5
+--R         6864A b d e  + (- 9152A b c - 4576B b )d e  + (3328A c  + 6656B b c)d e
+--R       + 
+--R                  2 6
+--R         - 2560B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R           6
+--R     45045e
+--R                                         Type: Union(Expression(Integer),...)
+--E 679
+
+--S 680 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 680
+
+--S 681 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 681
+
+)clear all
+
+--S 682 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2/sqrt(d+e*x)
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R        B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R   (1)  -------------------------------------------------------
+--R                                +-------+
+--R                               \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 682
+
+--S 683 of 1457
+r0:=2/3*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^6+_
+     2/5*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_
+     3*b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_
+     8*b*c*d*e+b^2*e^2))*(d+e*x)^(7/2)/e^6-2/9*c*(5*B*c*d-2*b*B*e-A*c*e)*_
+     (d+e*x)^(9/2)/e^6+2/11*B*c^2*(d+e*x)^(11/2)/e^6-2*d^2*(B*d-A*e)*_
+     (c*d-b*e)^2*sqrt(d+e*x)/e^6
+--R 
+--R
+--R   (2)
+--R               2 5 5           2              5         2   4  4
+--R         630B c e x  + ((770A c  + 1540B b c)e  - 700B c d e )x
+--R       + 
+--R                             2  5            2                4         2 2 3  3
+--R         ((1980A b c + 990B b )e  + (- 880A c  - 1760B b c)d e  + 800B c d e )x
+--R       + 
+--R                    2 5                         2    4
+--R             1386A b e  + (- 2376A b c - 1188B b )d e
+--R           + 
+--R                     2              2 3         2 3 2
+--R             (1056A c  + 2112B b c)d e  - 960B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                      2   4                       2  2 3
+--R             - 1848A b d e  + (3168A b c + 1584B b )d e
+--R           + 
+--R                       2              3 2          2 4
+--R             (- 1408A c  - 2816B b c)d e  + 1280B c d e
+--R        *
+--R           x
+--R       + 
+--R                2 2 3                         2  3 2           2              4
+--R         3696A b d e  + (- 6336A b c - 3168B b )d e  + (2816A c  + 5632B b c)d e
+--R       + 
+--R                  2 5
+--R         - 2560B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R          6
+--R     3465e
+--R                                                    Type: Expression(Integer)
+--E 683
+
+--S 684 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R               2 5 5           2              5         2   4  4
+--R         630B c e x  + ((770A c  + 1540B b c)e  - 700B c d e )x
+--R       + 
+--R                             2  5            2                4         2 2 3  3
+--R         ((1980A b c + 990B b )e  + (- 880A c  - 1760B b c)d e  + 800B c d e )x
+--R       + 
+--R                    2 5                         2    4
+--R             1386A b e  + (- 2376A b c - 1188B b )d e
+--R           + 
+--R                     2              2 3         2 3 2
+--R             (1056A c  + 2112B b c)d e  - 960B c d e
+--R        *
+--R            2
+--R           x
+--R       + 
+--R                      2   4                       2  2 3
+--R             - 1848A b d e  + (3168A b c + 1584B b )d e
+--R           + 
+--R                       2              3 2          2 4
+--R             (- 1408A c  - 2816B b c)d e  + 1280B c d e
+--R        *
+--R           x
+--R       + 
+--R                2 2 3                         2  3 2           2              4
+--R         3696A b d e  + (- 6336A b c - 3168B b )d e  + (2816A c  + 5632B b c)d e
+--R       + 
+--R                  2 5
+--R         - 2560B c d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R          6
+--R     3465e
+--R                                         Type: Union(Expression(Integer),...)
+--E 684
+
+--S 685 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 685
+
+--S 686 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 686
+
+)clear all
+
+--S 687 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(3/2)
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R        B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R   (1)  -------------------------------------------------------
+--R                                    +-------+
+--R                          (e x + d)\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 687
+
+--S 688 of 1457
+r0:=2/3*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_
+     3*b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_
+     8*b*c*d*e+b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*c*(5*B*c*d-2*b*B*e-A*c*e)*_
+     (d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+2*d^2*(B*d-A*e)*_
+     (c*d-b*e)^2/(e^6*sqrt(d+e*x))+2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-_
+     2*A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^6
+--R 
+--R
+--R   (2)
+--R            2 5 5          2             5         2   4  4
+--R       70B c e x  + ((90A c  + 180B b c)e  - 100B c d e )x
+--R     + 
+--R                          2  5            2               4         2 2 3  3
+--R       ((252A b c + 126B b )e  + (- 144A c  - 288B b c)d e  + 160B c d e )x
+--R     + 
+--R                 2 5                       2    4          2             2 3
+--R           210A b e  + (- 504A b c - 252B b )d e  + (288A c  + 576B b c)d e
+--R         + 
+--R                   2 3 2
+--R           - 320B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                   2   4                       2  2 3
+--R           - 840A b d e  + (2016A b c + 1008B b )d e
+--R         + 
+--R                     2              3 2          2 4
+--R           (- 1152A c  - 2304B b c)d e  + 1280B c d e
+--R      *
+--R         x
+--R     + 
+--R                2 2 3                       2  3 2             2              4
+--R       - 1680A b d e  + (4032A b c + 2016B b )d e  + (- 2304A c  - 4608B b c)d e
+--R     + 
+--R              2 5
+--R       2560B c d
+--R  /
+--R         6 +-------+
+--R     315e \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 688
+
+--S 689 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R            2 5 5          2             5         2   4  4
+--R       70B c e x  + ((90A c  + 180B b c)e  - 100B c d e )x
+--R     + 
+--R                          2  5            2               4         2 2 3  3
+--R       ((252A b c + 126B b )e  + (- 144A c  - 288B b c)d e  + 160B c d e )x
+--R     + 
+--R                 2 5                       2    4          2             2 3
+--R           210A b e  + (- 504A b c - 252B b )d e  + (288A c  + 576B b c)d e
+--R         + 
+--R                   2 3 2
+--R           - 320B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                   2   4                       2  2 3
+--R           - 840A b d e  + (2016A b c + 1008B b )d e
+--R         + 
+--R                     2              3 2          2 4
+--R           (- 1152A c  - 2304B b c)d e  + 1280B c d e
+--R      *
+--R         x
+--R     + 
+--R                2 2 3                       2  3 2             2              4
+--R       - 1680A b d e  + (4032A b c + 2016B b )d e  + (- 2304A c  - 4608B b c)d e
+--R     + 
+--R              2 5
+--R       2560B c d
+--R  /
+--R         6 +-------+
+--R     315e \|e x + d
+--R                                         Type: Union(Expression(Integer),...)
+--E 689
+
+--S 690 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 690
+
+--S 691 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 691
+
+)clear all
+
+--S 692 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(5/2)
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R        B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R   (1)  -------------------------------------------------------
+--R                       2 2             2  +-------+
+--R                     (e x  + 2d e x + d )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 692
+
+--S 693 of 1457
+r0:=2/3*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(3/2))-2/3*(2*A*c*e*(2*c*d-_
+     b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*c*_
+     (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-_
+     2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*sqrt(d+e*x))+_
+     2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_
+     3*b^2*e^2))*sqrt(d+e*x)/e^6
+--R 
+--R
+--R   (2)
+--R            2 5 5          2            5        2   4  4
+--R       30B c e x  + ((42A c  + 84B b c)e  - 60B c d e )x
+--R     + 
+--R                         2  5            2               4         2 2 3  3
+--R       ((140A b c + 70B b )e  + (- 112A c  - 224B b c)d e  + 160B c d e )x
+--R     + 
+--R                 2 5                       2    4          2              2 3
+--R           210A b e  + (- 840A b c - 420B b )d e  + (672A c  + 1344B b c)d e
+--R         + 
+--R                   2 3 2
+--R           - 960B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                 2   4                         2  2 3
+--R           840A b d e  + (- 3360A b c - 1680B b )d e
+--R         + 
+--R                   2              3 2          2 4
+--R           (2688A c  + 5376B b c)d e  - 3840B c d e
+--R      *
+--R         x
+--R     + 
+--R             2 2 3                         2  3 2           2              4
+--R       560A b d e  + (- 2240A b c - 1120B b )d e  + (1792A c  + 3584B b c)d e
+--R     + 
+--R                2 5
+--R       - 2560B c d
+--R  /
+--R          7          6  +-------+
+--R     (105e x + 105d e )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 693
+
+--S 694 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R            2 5 5          2            5        2   4  4
+--R       30B c e x  + ((42A c  + 84B b c)e  - 60B c d e )x
+--R     + 
+--R                         2  5            2               4         2 2 3  3
+--R       ((140A b c + 70B b )e  + (- 112A c  - 224B b c)d e  + 160B c d e )x
+--R     + 
+--R                 2 5                       2    4          2              2 3
+--R           210A b e  + (- 840A b c - 420B b )d e  + (672A c  + 1344B b c)d e
+--R         + 
+--R                   2 3 2
+--R           - 960B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                 2   4                         2  2 3
+--R           840A b d e  + (- 3360A b c - 1680B b )d e
+--R         + 
+--R                   2              3 2          2 4
+--R           (2688A c  + 5376B b c)d e  - 3840B c d e
+--R      *
+--R         x
+--R     + 
+--R             2 2 3                         2  3 2           2              4
+--R       560A b d e  + (- 2240A b c - 1120B b )d e  + (1792A c  + 3584B b c)d e
+--R     + 
+--R                2 5
+--R       - 2560B c d
+--R  /
+--R          7          6  +-------+
+--R     (105e x + 105d e )\|e x + d
+--R                                         Type: Union(Expression(Integer),...)
+--E 694
+
+--S 695 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 695
+
+--S 696 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 696
+
+)clear all
+
+--S 697 of 1457
+t0:=(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(7/2)
+--R 
+--R
+--R           2 5       2           4                2  3      2 2
+--R        B c x  + (A c  + 2B b c)x  + (2A b c + B b )x  + A b x
+--R   (1)  -------------------------------------------------------
+--R                  3 3       2 2     2       3  +-------+
+--R                (e x  + 3d e x  + 3d e x + d )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 697
+
+--S 698 of 1457
+r0:=2/5*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(5/2))-2/3*d*(c*d-b*e)*_
+     (B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^(3/2))-2/3*c*_
+     (5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6-_
+     2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+_
+     3*b^2*e^2))/(e^6*sqrt(d+e*x))-2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-_
+     8*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/e^6
+--R 
+--R
+--R   (2)
+--R           2 5 5          2            5        2   4  4
+--R       6B c e x  + ((10A c  + 20B b c)e  - 20B c d e )x
+--R     + 
+--R                        2  5           2               4         2 2 3  3
+--R       ((60A b c + 30B b )e  + (- 80A c  - 160B b c)d e  + 160B c d e )x
+--R     + 
+--R                  2 5                     2    4            2             2 3
+--R           - 30A b e  + (360A b c + 180B b )d e  + (- 480A c  - 960B b c)d e
+--R         + 
+--R                 2 3 2
+--R           960B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                  2   4                     2  2 3            2              3 2
+--R           - 40A b d e  + (480A b c + 240B b )d e  + (- 640A c  - 1280B b c)d e
+--R         + 
+--R                  2 4
+--R           1280B c d e
+--R      *
+--R         x
+--R     + 
+--R              2 2 3                    2  3 2            2             4
+--R       - 16A b d e  + (192A b c + 96B b )d e  + (- 256A c  - 512B b c)d e
+--R     + 
+--R             2 5
+--R       512B c d
+--R  /
+--R         8 2        7       2 6  +-------+
+--R     (15e x  + 30d e x + 15d e )\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 698
+
+--S 699 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R           2 5 5          2            5        2   4  4
+--R       6B c e x  + ((10A c  + 20B b c)e  - 20B c d e )x
+--R     + 
+--R                        2  5           2               4         2 2 3  3
+--R       ((60A b c + 30B b )e  + (- 80A c  - 160B b c)d e  + 160B c d e )x
+--R     + 
+--R                  2 5                     2    4            2             2 3
+--R           - 30A b e  + (360A b c + 180B b )d e  + (- 480A c  - 960B b c)d e
+--R         + 
+--R                 2 3 2
+--R           960B c d e
+--R      *
+--R          2
+--R         x
+--R     + 
+--R                  2   4                     2  2 3            2              3 2
+--R           - 40A b d e  + (480A b c + 240B b )d e  + (- 640A c  - 1280B b c)d e
+--R         + 
+--R                  2 4
+--R           1280B c d e
+--R      *
+--R         x
+--R     + 
+--R              2 2 3                    2  3 2            2             4
+--R       - 16A b d e  + (192A b c + 96B b )d e  + (- 256A c  - 512B b c)d e
+--R     + 
+--R             2 5
+--R       512B c d
+--R  /
+--R         8 2        7       2 6  +-------+
+--R     (15e x  + 30d e x + 15d e )\|e x + d
+--R                                         Type: Union(Expression(Integer),...)
+--E 699
+
+--S 700 of 1457
+m0:=a0-r0
+--R 
+--R
+--R   (4)  0
+--R                                                    Type: Expression(Integer)
+--E 700
+
+--S 701 of 1457
+d0:=D(m0,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 701
+
+)clear all
+
+--S 702 of 1457
+t0:=(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)
+--R 
+--R
+--R   (1)
+--R            3 4       3         2  3          2       2   2        2       3
+--R         B e x  + (A e  + 3B d e )x  + (3A d e  + 3B d e)x  + (3A d e + B d )x
+--R       + 
+--R            3
+--R         A d
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R  /
+--R        2
+--R     c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 702
+
+--S 703 of 1457
+r0:=2/3*(B*(c*d-b*e)^2+A*c*e*(2*c*d-b*e))*(d+e*x)^(3/2)/c^3+2/5*_
+     (B*c*d-b*B*e+A*c*e)*(d+e*x)^(5/2)/c^2+2/7*B*(d+e*x)^(7/2)/c-_
+     2*A*d^(7/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(7/2)*_
+     atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(9/2))+2*(B*(c*d-b*e)^3+_
+     A*c*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/c^4
+--R 
+--R
+--R   (2)
+--R                    3          4  3          2 2         3     2
+--R           (- 210A b c + 210B b )e  + (630A b c  - 630B b c)d e
+--R         + 
+--R                      3         2 2  2           4           3  3
+--R           (- 630A b c  + 630B b c )d e + (210A c  - 210B b c )d
+--R      *
+--R                              +-+ +-------+
+--R          +-----------+      \|c \|e x + d
+--R         \|- b e + c d atanh(--------------)
+--R                              +-----------+
+--R                             \|- b e + c d
+--R     + 
+--R                                 +-------+
+--R               4 3 +-+ +-+      \|e x + d
+--R       - 210A c d \|c \|d atanh(----------)
+--R                                    +-+
+--R                                   \|d
+--R     + 
+--R                  3 3 3            3        2 2  3           3   2  2
+--R           30B b c e x  + ((42A b c  - 42B b c )e  + 132B b c d e )x
+--R         + 
+--R                       2 2        3   3            3         2 2    2
+--R               (- 70A b c  + 70B b c)e  + (224A b c  - 224B b c )d e
+--R             + 
+--R                       3 2
+--R               244B b c d e
+--R          *
+--R             x
+--R         + 
+--R                  3          4  3            2 2         3     2
+--R           (210A b c - 210B b )e  + (- 700A b c  + 700B b c)d e
+--R         + 
+--R                    3         2 2  2            3 3
+--R           (812A b c  - 812B b c )d e + 352B b c d
+--R      *
+--R          +-+ +-------+
+--R         \|c \|e x + d
+--R  /
+--R           4 +-+
+--R     105b c \|c
+--R                                                    Type: Expression(Integer)
+--E 703
+
+--S 704 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                      3          4  3          2 2         3     2
+--R             (- 105A b c + 105B b )e  + (315A b c  - 315B b c)d e
+--R           + 
+--R                        3         2 2  2           4           3  3
+--R             (- 315A b c  + 315B b c )d e + (105A c  - 105B b c )d
+--R        *
+--R                                +-----------+
+--R                                |- b e + c d  +-------+
+--R            +-----------+    2c |----------- \|e x + d  + c e x - b e + 2c d
+--R            |- b e + c d       \|     c
+--R            |----------- log(-----------------------------------------------)
+--R           \|     c                              c x + b
+--R       + 
+--R                              +-+ +-------+
+--R               4 3 +-+    - 2\|d \|e x + d  + e x + 2d
+--R         105A c d \|d log(----------------------------)
+--R                                        x
+--R       + 
+--R                    3 3 3            3        2 2  3           3   2  2
+--R             30B b c e x  + ((42A b c  - 42B b c )e  + 132B b c d e )x
+--R           + 
+--R                         2 2        3   3            3         2 2    2
+--R                 (- 70A b c  + 70B b c)e  + (224A b c  - 224B b c )d e
+--R               + 
+--R                         3 2
+--R                 244B b c d e
+--R            *
+--R               x
+--R           + 
+--R                    3          4  3            2 2         3     2
+--R             (210A b c - 210B b )e  + (- 700A b c  + 700B b c)d e
+--R           + 
+--R                      3         2 2  2            3 3
+--R             (812A b c  - 812B b c )d e + 352B b c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R    /
+--R             4
+--R       105b c
+--R     ,
+--R
+--R                              +-+ +-------+
+--R               4 3 +-+    - 2\|d \|e x + d  + e x + 2d
+--R         105A c d \|d log(----------------------------)
+--R                                        x
+--R       + 
+--R                      3          4  3          2 2         3     2
+--R             (- 210A b c + 210B b )e  + (630A b c  - 630B b c)d e
+--R           + 
+--R                        3         2 2  2           4           3  3
+--R             (- 630A b c  + 630B b c )d e + (210A c  - 210B b c )d
+--R        *
+--R            +---------+       +-------+
+--R            |b e - c d       \|e x + d
+--R            |--------- atan(------------)
+--R           \|    c           +---------+
+--R                             |b e - c d
+--R                             |---------
+--R                            \|    c
+--R       + 
+--R                    3 3 3            3        2 2  3           3   2  2
+--R             30B b c e x  + ((42A b c  - 42B b c )e  + 132B b c d e )x
+--R           + 
+--R                         2 2        3   3            3         2 2    2
+--R                 (- 70A b c  + 70B b c)e  + (224A b c  - 224B b c )d e
+--R               + 
+--R                         3 2
+--R                 244B b c d e
+--R            *
+--R               x
+--R           + 
+--R                    3          4  3            2 2         3     2
+--R             (210A b c - 210B b )e  + (- 700A b c  + 700B b c)d e
+--R           + 
+--R                      3         2 2  2            3 3
+--R             (812A b c  - 812B b c )d e + 352B b c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R    /
+--R             4
+--R       105b c
+--R     ,
+--R
+--R                      3          4  3          2 2         3     2
+--R             (- 105A b c + 105B b )e  + (315A b c  - 315B b c)d e
+--R           + 
+--R                        3         2 2  2           4           3  3
+--R             (- 315A b c  + 315B b c )d e + (105A c  - 105B b c )d
+--R        *
+--R                                +-----------+
+--R                                |- b e + c d  +-------+
+--R            +-----------+    2c |----------- \|e x + d  + c e x - b e + 2c d
+--R            |- b e + c d       \|     c
+--R            |----------- log(-----------------------------------------------)
+--R           \|     c                              c x + b
+--R       + 
+--R                                +-------+
+--R                 4 3 +---+     \|e x + d
+--R         - 210A c d \|- d atan(----------)
+--R                                  +---+
+--R                                 \|- d
+--R       + 
+--R                    3 3 3            3        2 2  3           3   2  2
+--R             30B b c e x  + ((42A b c  - 42B b c )e  + 132B b c d e )x
+--R           + 
+--R                         2 2        3   3            3         2 2    2
+--R                 (- 70A b c  + 70B b c)e  + (224A b c  - 224B b c )d e
+--R               + 
+--R                         3 2
+--R                 244B b c d e
+--R            *
+--R               x
+--R           + 
+--R                    3          4  3            2 2         3     2
+--R             (210A b c - 210B b )e  + (- 700A b c  + 700B b c)d e
+--R           + 
+--R                      3         2 2  2            3 3
+--R             (812A b c  - 812B b c )d e + 352B b c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R    /
+--R             4
+--R       105b c
+--R     ,
+--R
+--R                                +-------+
+--R                 4 3 +---+     \|e x + d
+--R         - 210A c d \|- d atan(----------)
+--R                                  +---+
+--R                                 \|- d
+--R       + 
+--R                      3          4  3          2 2         3     2
+--R             (- 210A b c + 210B b )e  + (630A b c  - 630B b c)d e
+--R           + 
+--R                        3         2 2  2           4           3  3
+--R             (- 630A b c  + 630B b c )d e + (210A c  - 210B b c )d
+--R        *
+--R            +---------+       +-------+
+--R            |b e - c d       \|e x + d
+--R            |--------- atan(------------)
+--R           \|    c           +---------+
+--R                             |b e - c d
+--R                             |---------
+--R                            \|    c
+--R       + 
+--R                    3 3 3            3        2 2  3           3   2  2
+--R             30B b c e x  + ((42A b c  - 42B b c )e  + 132B b c d e )x
+--R           + 
+--R                         2 2        3   3            3         2 2    2
+--R                 (- 70A b c  + 70B b c)e  + (224A b c  - 224B b c )d e
+--R               + 
+--R                         3 2
+--R                 244B b c d e
+--R            *
+--R               x
+--R           + 
+--R                    3          4  3            2 2         3     2
+--R             (210A b c - 210B b )e  + (- 700A b c  + 700B b c)d e
+--R           + 
+--R                      3         2 2  2            3 3
+--R             (812A b c  - 812B b c )d e + 352B b c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R    /
+--R             4
+--R       105b c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 704
+
+--S 705 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                 3       4  3        2 2       3     2
+--R           (- A b c + B b )e  + (3A b c  - 3B b c)d e
+--R         + 
+--R                    3       2 2  2        4        3  3
+--R           (- 3A b c  + 3B b c )d e + (A c  - B b c )d
+--R      *
+--R                                  +-----------+
+--R                                  |- b e + c d  +-------+
+--R          +-----------+        2c |----------- \|e x + d  + c e x - b e + 2c d
+--R          |- b e + c d  +-+      \|     c
+--R          |----------- \|c log(-----------------------------------------------)
+--R         \|     c                                  c x + b
+--R     + 
+--R                             +-+ +-------+
+--R          4 3 +-+ +-+    - 2\|d \|e x + d  + e x + 2d
+--R       A c d \|c \|d log(----------------------------)
+--R                                       x
+--R     + 
+--R                3        4  3          2 2       3     2
+--R           (2A b c - 2B b )e  + (- 6A b c  + 6B b c)d e
+--R         + 
+--R                  3       2 2  2           4         3  3
+--R           (6A b c  - 6B b c )d e + (- 2A c  + 2B b c )d
+--R      *
+--R                              +-+ +-------+
+--R          +-----------+      \|c \|e x + d
+--R         \|- b e + c d atanh(--------------)
+--R                              +-----------+
+--R                             \|- b e + c d
+--R     + 
+--R                             +-------+
+--R           4 3 +-+ +-+      \|e x + d
+--R       2A c d \|c \|d atanh(----------)
+--R                                +-+
+--R                               \|d
+--R  /
+--R        4 +-+
+--R     b c \|c
+--R                                                    Type: Expression(Integer)
+--E 705
+
+--S 706 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 706
+
+--S 707 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                             +-+ +-------+
+--R          4 3 +-+ +-+    - 2\|d \|e x + d  + e x + 2d
+--R       A c d \|c \|d log(----------------------------)
+--R                                       x
+--R     + 
+--R                3        4  3          2 2       3     2
+--R           (2A b c - 2B b )e  + (- 6A b c  + 6B b c)d e
+--R         + 
+--R                  3       2 2  2           4         3  3
+--R           (6A b c  - 6B b c )d e + (- 2A c  + 2B b c )d
+--R      *
+--R                              +-+ +-------+
+--R          +-----------+      \|c \|e x + d
+--R         \|- b e + c d atanh(--------------)
+--R                              +-----------+
+--R                             \|- b e + c d
+--R     + 
+--R                             +-------+
+--R           4 3 +-+ +-+      \|e x + d
+--R       2A c d \|c \|d atanh(----------)
+--R                                +-+
+--R                               \|d
+--R     + 
+--R                  3        4  3        2 2       3     2
+--R           (- 2A b c + 2B b )e  + (6A b c  - 6B b c)d e
+--R         + 
+--R                    3       2 2  2         4         3  3
+--R           (- 6A b c  + 6B b c )d e + (2A c  - 2B b c )d
+--R      *
+--R              +---------+       +-------+
+--R          +-+ |b e - c d       \|e x + d
+--R         \|c  |--------- atan(------------)
+--R             \|    c           +---------+
+--R                               |b e - c d
+--R                               |---------
+--R                              \|    c
+--R  /
+--R        4 +-+
+--R     b c \|c
+--R                                                    Type: Expression(Integer)
+--E 707
+
+--S 708 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 708
+
+)clear all
+
+--S 709 of 1457
+t0:=(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)
+--R 
+--R
+--R            2 3       2           2                2        2  +-------+
+--R        (B e x  + (A e  + 2B d e)x  + (2A d e + B d )x + A d )\|e x + d
+--R   (1)  ----------------------------------------------------------------
+--R                                      2
+--R                                   c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 709
+
+--S 710 of 1457
+r0:=2/3*(B*c*d-b*B*e+A*c*e)*(d+e*x)^(3/2)/c^2+2/5*B*(d+e*x)^(5/2)/c-_
+     2*A*d^(5/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(5/2)*_
+     atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(7/2))+2*(B*(c*d-b*e)^2+_
+     A*c*e*(2*c*d-b*e))*sqrt(d+e*x)/c^3
+--R 
+--R
+--R   (2)
+--R                 2         3  2             2        2
+--R           (30A b c - 30B b )e  + (- 60A b c  + 60B b c)d e
+--R         + 
+--R                 3          2  2
+--R           (30A c  - 30B b c )d
+--R      *
+--R                              +-+ +-------+
+--R          +-----------+      \|c \|e x + d
+--R         \|- b e + c d atanh(--------------)
+--R                              +-----------+
+--R                             \|- b e + c d
+--R     + 
+--R                                +-------+
+--R              3 2 +-+ +-+      \|e x + d
+--R       - 30A c d \|c \|d atanh(----------)
+--R                                   +-+
+--R                                  \|d
+--R     + 
+--R                 2 2 2            2        2   2          2
+--R           6B b c e x  + ((10A b c  - 10B b c)e  + 22B b c d e)x
+--R         + 
+--R                   2         3  2           2        2               2 2
+--R           (- 30A b c + 30B b )e  + (70A b c  - 70B b c)d e + 46B b c d
+--R      *
+--R          +-+ +-------+
+--R         \|c \|e x + d
+--R  /
+--R          3 +-+
+--R     15b c \|c
+--R                                                    Type: Expression(Integer)
+--E 710
+
+--S 711 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                     2         3  2           2        2
+--R             (- 15A b c + 15B b )e  + (30A b c  - 30B b c)d e
+--R           + 
+--R                     3          2  2
+--R             (- 15A c  + 15B b c )d
+--R        *
+--R                                  +-----------+
+--R                                  |- b e + c d  +-------+
+--R            +-----------+    - 2c |----------- \|e x + d  + c e x - b e + 2c d
+--R            |- b e + c d         \|     c
+--R            |----------- log(-------------------------------------------------)
+--R           \|     c                               c x + b
+--R       + 
+--R                             +-+ +-------+
+--R              3 2 +-+    - 2\|d \|e x + d  + e x + 2d
+--R         15A c d \|d log(----------------------------)
+--R                                       x
+--R       + 
+--R                   2 2 2            2        2   2          2
+--R             6B b c e x  + ((10A b c  - 10B b c)e  + 22B b c d e)x
+--R           + 
+--R                     2         3  2           2        2               2 2
+--R             (- 30A b c + 30B b )e  + (70A b c  - 70B b c)d e + 46B b c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R    /
+--R            3
+--R       15b c
+--R     ,
+--R
+--R                             +-+ +-------+
+--R              3 2 +-+    - 2\|d \|e x + d  + e x + 2d
+--R         15A c d \|d log(----------------------------)
+--R                                       x
+--R       + 
+--R                   2         3  2             2        2
+--R             (30A b c - 30B b )e  + (- 60A b c  + 60B b c)d e
+--R           + 
+--R                   3          2  2
+--R             (30A c  - 30B b c )d
+--R        *
+--R            +---------+       +-------+
+--R            |b e - c d       \|e x + d
+--R            |--------- atan(------------)
+--R           \|    c           +---------+
+--R                             |b e - c d
+--R                             |---------
+--R                            \|    c
+--R       + 
+--R                   2 2 2            2        2   2          2
+--R             6B b c e x  + ((10A b c  - 10B b c)e  + 22B b c d e)x
+--R           + 
+--R                     2         3  2           2        2               2 2
+--R             (- 30A b c + 30B b )e  + (70A b c  - 70B b c)d e + 46B b c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R    /
+--R            3
+--R       15b c
+--R     ,
+--R
+--R                     2         3  2           2        2
+--R             (- 15A b c + 15B b )e  + (30A b c  - 30B b c)d e
+--R           + 
+--R                     3          2  2
+--R             (- 15A c  + 15B b c )d
+--R        *
+--R                                  +-----------+
+--R                                  |- b e + c d  +-------+
+--R            +-----------+    - 2c |----------- \|e x + d  + c e x - b e + 2c d
+--R            |- b e + c d         \|     c
+--R            |----------- log(-------------------------------------------------)
+--R           \|     c                               c x + b
+--R       + 
+--R                               +-------+
+--R                3 2 +---+     \|e x + d
+--R         - 30A c d \|- d atan(----------)
+--R                                 +---+
+--R                                \|- d
+--R       + 
+--R                   2 2 2            2        2   2          2
+--R             6B b c e x  + ((10A b c  - 10B b c)e  + 22B b c d e)x
+--R           + 
+--R                     2         3  2           2        2               2 2
+--R             (- 30A b c + 30B b )e  + (70A b c  - 70B b c)d e + 46B b c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R    /
+--R            3
+--R       15b c
+--R     ,
+--R
+--R                               +-------+
+--R                3 2 +---+     \|e x + d
+--R         - 30A c d \|- d atan(----------)
+--R                                 +---+
+--R                                \|- d
+--R       + 
+--R                   2         3  2             2        2
+--R             (30A b c - 30B b )e  + (- 60A b c  + 60B b c)d e
+--R           + 
+--R                   3          2  2
+--R             (30A c  - 30B b c )d
+--R        *
+--R            +---------+       +-------+
+--R            |b e - c d       \|e x + d
+--R            |--------- atan(------------)
+--R           \|    c           +---------+
+--R                             |b e - c d
+--R                             |---------
+--R                            \|    c
+--R       + 
+--R                   2 2 2            2        2   2          2
+--R             6B b c e x  + ((10A b c  - 10B b c)e  + 22B b c d e)x
+--R           + 
+--R                     2         3  2           2        2               2 2
+--R             (- 30A b c + 30B b )e  + (70A b c  - 70B b c)d e + 46B b c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R    /
+--R            3
+--R       15b c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 711
+
+--S 712 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                2       3  2          2       2              3        2  2
+--R         ((- A b c + B b )e  + (2A b c  - 2B b c)d e + (- A c  + B b c )d )
+--R      *
+--R                                  +-----------+
+--R                                  |- b e + c d  +-------+
+--R        +-----------+        - 2c |----------- \|e x + d  + c e x - b e + 2c d
+--R        |- b e + c d  +-+        \|     c
+--R        |----------- \|c log(-------------------------------------------------)
+--R       \|     c                                   c x + b
+--R     + 
+--R                             +-+ +-------+
+--R          3 2 +-+ +-+    - 2\|d \|e x + d  + e x + 2d
+--R       A c d \|c \|d log(----------------------------)
+--R                                       x
+--R     + 
+--R                 2        3  2          2       2               3         2  2
+--R         ((- 2A b c + 2B b )e  + (4A b c  - 4B b c)d e + (- 2A c  + 2B b c )d )
+--R      *
+--R                              +-+ +-------+
+--R          +-----------+      \|c \|e x + d
+--R         \|- b e + c d atanh(--------------)
+--R                              +-----------+
+--R                             \|- b e + c d
+--R     + 
+--R                             +-------+
+--R           3 2 +-+ +-+      \|e x + d
+--R       2A c d \|c \|d atanh(----------)
+--R                                +-+
+--R                               \|d
+--R  /
+--R        3 +-+
+--R     b c \|c
+--R                                                    Type: Expression(Integer)
+--E 712
+
+--S 713 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 713
+
+--S 714 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                             +-+ +-------+
+--R          3 2 +-+ +-+    - 2\|d \|e x + d  + e x + 2d
+--R       A c d \|c \|d log(----------------------------)
+--R                                       x
+--R     + 
+--R                 2        3  2          2       2               3         2  2
+--R         ((- 2A b c + 2B b )e  + (4A b c  - 4B b c)d e + (- 2A c  + 2B b c )d )
+--R      *
+--R                              +-+ +-------+
+--R          +-----------+      \|c \|e x + d
+--R         \|- b e + c d atanh(--------------)
+--R                              +-----------+
+--R                             \|- b e + c d
+--R     + 
+--R                             +-------+
+--R           3 2 +-+ +-+      \|e x + d
+--R       2A c d \|c \|d atanh(----------)
+--R                                +-+
+--R                               \|d
+--R     + 
+--R               2        3  2            2       2             3         2  2
+--R         ((2A b c - 2B b )e  + (- 4A b c  + 4B b c)d e + (2A c  - 2B b c )d )
+--R      *
+--R              +---------+       +-------+
+--R          +-+ |b e - c d       \|e x + d
+--R         \|c  |--------- atan(------------)
+--R             \|    c           +---------+
+--R                               |b e - c d
+--R                               |---------
+--R                              \|    c
+--R  /
+--R        3 +-+
+--R     b c \|c
+--R                                                    Type: Expression(Integer)
+--E 714
+
+--S 715 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 715
+
+)clear all
+
+--S 716 of 1457
+t0:=(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)
+--R 
+--R
+--R              2                       +-------+
+--R        (B e x  + (A e + B d)x + A d)\|e x + d
+--R   (1)  ---------------------------------------
+--R                          2
+--R                       c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 716
+
+--S 717 of 1457
+r0:=2/3*B*(d+e*x)^(3/2)/c-2*A*d^(3/2)*atanh(sqrt(d+e*x)/sqrt(d))/b-_
+     2*(b*B-A*c)*(c*d-b*e)^(3/2)*atanh(sqrt(c)*sqrt(d+e*x)/_
+     sqrt(c*d-b*e))/(b*c^(5/2))+2*(B*c*d-b*B*e+A*c*e)*sqrt(d+e*x)/c^2
+--R 
+--R
+--R   (2)
+--R                          2          2             +-----------+
+--R         ((- 6A b c + 6B b )e + (6A c  - 6B b c)d)\|- b e + c d
+--R      *
+--R                +-+ +-------+
+--R               \|c \|e x + d
+--R         atanh(--------------)
+--R                +-----------+
+--R               \|- b e + c d
+--R     + 
+--R                              +-------+
+--R             2  +-+ +-+      \|e x + d
+--R       - 6A c d\|c \|d atanh(----------)
+--R                                 +-+
+--R                                \|d
+--R     + 
+--R                                   2               +-+ +-------+
+--R       (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|c \|e x + d
+--R  /
+--R         2 +-+
+--R     3b c \|c
+--R                                                    Type: Expression(Integer)
+--E 717
+
+--S 718 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                                                     +-----------+
+--R                            2          2             |- b e + c d
+--R           ((- 3A b c + 3B b )e + (3A c  - 3B b c)d) |-----------
+--R                                                    \|     c
+--R        *
+--R                  +-----------+
+--R                  |- b e + c d  +-------+
+--R               2c |----------- \|e x + d  + c e x - b e + 2c d
+--R                 \|     c
+--R           log(-----------------------------------------------)
+--R                                   c x + b
+--R       + 
+--R                           +-+ +-------+
+--R             2  +-+    - 2\|d \|e x + d  + e x + 2d
+--R         3A c d\|d log(----------------------------)
+--R                                     x
+--R       + 
+--R                                     2               +-------+
+--R         (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d
+--R    /
+--R           2
+--R       3b c
+--R     ,
+--R
+--R                           +-+ +-------+
+--R             2  +-+    - 2\|d \|e x + d  + e x + 2d
+--R         3A c d\|d log(----------------------------)
+--R                                     x
+--R       + 
+--R                                                   +---------+       +-------+
+--R                          2          2             |b e - c d       \|e x + d
+--R         ((- 6A b c + 6B b )e + (6A c  - 6B b c)d) |--------- atan(------------)
+--R                                                  \|    c           +---------+
+--R                                                                    |b e - c d
+--R                                                                    |---------
+--R                                                                   \|    c
+--R       + 
+--R                                     2               +-------+
+--R         (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d
+--R    /
+--R           2
+--R       3b c
+--R     ,
+--R
+--R                                                     +-----------+
+--R                            2          2             |- b e + c d
+--R           ((- 3A b c + 3B b )e + (3A c  - 3B b c)d) |-----------
+--R                                                    \|     c
+--R        *
+--R                  +-----------+
+--R                  |- b e + c d  +-------+
+--R               2c |----------- \|e x + d  + c e x - b e + 2c d
+--R                 \|     c
+--R           log(-----------------------------------------------)
+--R                                   c x + b
+--R       + 
+--R                             +-------+
+--R               2  +---+     \|e x + d
+--R         - 6A c d\|- d atan(----------)
+--R                               +---+
+--R                              \|- d
+--R       + 
+--R                                     2               +-------+
+--R         (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d
+--R    /
+--R           2
+--R       3b c
+--R     ,
+--R
+--R                             +-------+
+--R               2  +---+     \|e x + d
+--R         - 6A c d\|- d atan(----------)
+--R                               +---+
+--R                              \|- d
+--R       + 
+--R                                                   +---------+       +-------+
+--R                          2          2             |b e - c d       \|e x + d
+--R         ((- 6A b c + 6B b )e + (6A c  - 6B b c)d) |--------- atan(------------)
+--R                                                  \|    c           +---------+
+--R                                                                    |b e - c d
+--R                                                                    |---------
+--R                                                                   \|    c
+--R       + 
+--R                                     2               +-------+
+--R         (2B b c e x + (6A b c - 6B b )e + 8B b c d)\|e x + d
+--R    /
+--R           2
+--R       3b c
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 718
+
+--S 719 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                               +-----------+
+--R                        2         2            |- b e + c d  +-+
+--R         ((- A b c + B b )e + (A c  - B b c)d) |----------- \|c
+--R                                              \|     c
+--R      *
+--R                +-----------+
+--R                |- b e + c d  +-------+
+--R             2c |----------- \|e x + d  + c e x - b e + 2c d
+--R               \|     c
+--R         log(-----------------------------------------------)
+--R                                 c x + b
+--R     + 
+--R                            +-+ +-------+
+--R          2  +-+ +-+    - 2\|d \|e x + d  + e x + 2d
+--R       A c d\|c \|d log(----------------------------)
+--R                                      x
+--R     + 
+--R                        2            2             +-----------+
+--R         ((2A b c - 2B b )e + (- 2A c  + 2B b c)d)\|- b e + c d
+--R      *
+--R                +-+ +-------+
+--R               \|c \|e x + d
+--R         atanh(--------------)
+--R                +-----------+
+--R               \|- b e + c d
+--R     + 
+--R                            +-------+
+--R           2  +-+ +-+      \|e x + d
+--R       2A c d\|c \|d atanh(----------)
+--R                               +-+
+--R                              \|d
+--R  /
+--R        2 +-+
+--R     b c \|c
+--R                                                    Type: Expression(Integer)
+--E 719
+
+--S 720 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 720
+
+--S 721 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                            +-+ +-------+
+--R          2  +-+ +-+    - 2\|d \|e x + d  + e x + 2d
+--R       A c d\|c \|d log(----------------------------)
+--R                                      x
+--R     + 
+--R                        2            2             +-----------+
+--R         ((2A b c - 2B b )e + (- 2A c  + 2B b c)d)\|- b e + c d
+--R      *
+--R                +-+ +-------+
+--R               \|c \|e x + d
+--R         atanh(--------------)
+--R                +-----------+
+--R               \|- b e + c d
+--R     + 
+--R                            +-------+
+--R           2  +-+ +-+      \|e x + d
+--R       2A c d\|c \|d atanh(----------)
+--R                               +-+
+--R                              \|d
+--R     + 
+--R                                                   +---------+       +-------+
+--R                      2          2             +-+ |b e - c d       \|e x + d
+--R     ((- 2A b c + 2B b )e + (2A c  - 2B b c)d)\|c  |--------- atan(------------)
+--R                                                  \|    c           +---------+
+--R                                                                    |b e - c d
+--R                                                                    |---------
+--R                                                                   \|    c
+--R  /
+--R        2 +-+
+--R     b c \|c
+--R                                                    Type: Expression(Integer)
+--E 721
+
+--S 722 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 722
+
+)clear all
+
+--S 723 of 1457
+t0:=(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)
+--R 
+--R
+--R                  +-------+
+--R        (B x + A)\|e x + d
+--R   (1)  -------------------
+--R                2
+--R             c x  + b x
+--R                                                    Type: Expression(Integer)
+--E 723
+
+--S 724 of 1457
+r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b-2*(b*B-A*c)*atanh(sqrt(c)*_
+     sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b*c^(3/2))+2*B*sqrt(d+e*x)/c
+--R 
+--R
+--R   (2)
+--R                                         +-+ +-------+
+--R                     +-----------+      \|c \|e x + d
+--R       (2A c - 2B b)\|- b e + c d atanh(--------------)
+--R                                         +-----------+
+--R                                        \|- b e + c d
+--R     + 
+--R                            +-------+
+--R              +-+ +-+      \|e x + d          +-+ +-------+
+--R       - 2A c\|c \|d atanh(----------) + 2B b\|c \|e x + d
+--R                               +-+
+--R                              \|d
+--R  /
+--R         +-+
+--R     b c\|c
+--R                                                    Type: Expression(Integer)
+--E 724
+
+--S 725 of 1457
+--a0:=integrate(t0,x)
+--E 725
+
+--S 726 of 1457
+--m0a:=a0.1-r0
+--E 726
+
+--S 727 of 1457
+--d0a:=D(m0a,x)
+--E 727
+
+--S 728 of 1457
+--m0b:=a0.2-r0
+--E 728
+
+--S 729 of 1457
+--d0b:=D(m0b,x)
+--E 729
+
+)clear all
+
+--S 730 of 1457
+t0:=(A+B*x)/((b*x+c*x^2)*sqrt(d+e*x))
+--R 
+--R
+--R                B x + A
+--R   (1)  ----------------------
+--R            2        +-------+
+--R        (c x  + b x)\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 730
+
+--S 731 of 1457
+r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*sqrt(d))-2*(b*B-A*c)*atanh(sqrt(c)*_
+     sqrt(d+e*x)/sqrt(c*d-b*e))/(b*sqrt(c)*sqrt(c*d-b*e))
+--R 
+--R
+--R   (2)
+--R                               +-+ +-------+
+--R                     +-+      \|c \|e x + d
+--R       (2A c - 2B b)\|d atanh(--------------)
+--R                               +-----------+
+--R                              \|- b e + c d
+--R     + 
+--R                                    +-------+
+--R            +-----------+ +-+      \|e x + d
+--R       - 2A\|- b e + c d \|c atanh(----------)
+--R                                       +-+
+--R                                      \|d
+--R  /
+--R       +-----------+ +-+ +-+
+--R     b\|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 731
+
+--S 732 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R           +-------------+         +-------+              +-+
+--R           |           2      - 2d\|e x + d  + (e x + 2d)\|d
+--R         A\|- b c e + c d log(-------------------------------)
+--R                                             x
+--R       + 
+--R                       +-+
+--R           (A c - B b)\|d
+--R        *
+--R                                                                +-------------+
+--R                           2   +-------+                        |           2
+--R             (- 2b c e + 2c d)\|e x + d  + (c e x - b e + 2c d)\|- b c e + c d
+--R         log(------------------------------------------------------------------)
+--R                                           c x + b
+--R    /
+--R         +-------------+
+--R         |           2   +-+
+--R       b\|- b c e + c d \|d
+--R     ,
+--R
+--R           +-----------+         +-------+              +-+
+--R           |         2      - 2d\|e x + d  + (e x + 2d)\|d
+--R         A\|b c e - c d log(-------------------------------)
+--R                                           x
+--R       + 
+--R                                  +-----------+
+--R                                  |         2   +-------+
+--R                         +-+     \|b c e - c d \|e x + d
+--R         (- 2A c + 2B b)\|d atan(------------------------)
+--R                                         b e - c d
+--R    /
+--R             +-----------+
+--R         +-+ |         2
+--R       b\|d \|b c e - c d
+--R     ,
+--R
+--R                       +---+
+--R           (A c - B b)\|- d
+--R        *
+--R                                                                +-------------+
+--R                           2   +-------+                        |           2
+--R             (- 2b c e + 2c d)\|e x + d  + (c e x - b e + 2c d)\|- b c e + c d
+--R         log(------------------------------------------------------------------)
+--R                                           c x + b
+--R       + 
+--R              +-------------+      +---+ +-------+
+--R              |           2       \|- d \|e x + d
+--R         - 2A\|- b c e + c d atan(----------------)
+--R                                          d
+--R    /
+--R         +-------------+
+--R         |           2   +---+
+--R       b\|- b c e + c d \|- d
+--R     ,
+--R
+--R                                    +-----------+
+--R                                    |         2   +-------+
+--R                         +---+     \|b c e - c d \|e x + d
+--R         (- 2A c + 2B b)\|- d atan(------------------------)
+--R                                           b e - c d
+--R       + 
+--R              +-----------+      +---+ +-------+
+--R              |         2       \|- d \|e x + d
+--R         - 2A\|b c e - c d atan(----------------)
+--R                                        d
+--R    /
+--R               +-----------+
+--R         +---+ |         2
+--R       b\|- d \|b c e - c d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 732
+
+--S 733 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R         +-------------+                           +-------+              +-+
+--R         |           2   +-----------+ +-+    - 2d\|e x + d  + (e x + 2d)\|d
+--R       A\|- b c e + c d \|- b e + c d \|c log(-------------------------------)
+--R                                                             x
+--R     + 
+--R                     +-----------+ +-+ +-+
+--R         (A c - B b)\|- b e + c d \|c \|d
+--R      *
+--R                                                              +-------------+
+--R                         2   +-------+                        |           2
+--R           (- 2b c e + 2c d)\|e x + d  + (c e x - b e + 2c d)\|- b c e + c d
+--R       log(------------------------------------------------------------------)
+--R                                         c x + b
+--R     + 
+--R                       +-------------+           +-+ +-------+
+--R                       |           2   +-+      \|c \|e x + d
+--R       (- 2A c + 2B b)\|- b c e + c d \|d atanh(--------------)
+--R                                                 +-----------+
+--R                                                \|- b e + c d
+--R     + 
+--R          +-------------+                         +-------+
+--R          |           2   +-----------+ +-+      \|e x + d
+--R       2A\|- b c e + c d \|- b e + c d \|c atanh(----------)
+--R                                                     +-+
+--R                                                    \|d
+--R  /
+--R       +-------------+
+--R       |           2   +-----------+ +-+ +-+
+--R     b\|- b c e + c d \|- b e + c d \|c \|d
+--R                                                    Type: Expression(Integer)
+--E 733
+
+--S 734 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 734
+
+--S 735 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                           +-----------+         +-------+              +-+
+--R         +-----------+ +-+ |         2      - 2d\|e x + d  + (e x + 2d)\|d
+--R       A\|- b e + c d \|c \|b c e - c d log(-------------------------------)
+--R                                                           x
+--R     + 
+--R                           +-----------+       +-+ +-------+
+--R                       +-+ |         2        \|c \|e x + d
+--R       (- 2A c + 2B b)\|d \|b c e - c d atanh(--------------)
+--R                                               +-----------+
+--R                                              \|- b e + c d
+--R     + 
+--R                            +-----------+       +-------+
+--R          +-----------+ +-+ |         2        \|e x + d
+--R       2A\|- b e + c d \|c \|b c e - c d atanh(----------)
+--R                                                   +-+
+--R                                                  \|d
+--R     + 
+--R                                                  +-----------+
+--R                                                  |         2   +-------+
+--R                       +-----------+ +-+ +-+     \|b c e - c d \|e x + d
+--R       (- 2A c + 2B b)\|- b e + c d \|c \|d atan(------------------------)
+--R                                                         b e - c d
+--R  /
+--R                             +-----------+
+--R       +-----------+ +-+ +-+ |         2
+--R     b\|- b e + c d \|c \|d \|b c e - c d
+--R                                                    Type: Expression(Integer)
+--E 735
+
+--S 736 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 736
+
+)clear all
+
+--S 737 of 1457
+t0:=(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2))
+--R 
+--R
+--R                          B x + A
+--R   (1)  ------------------------------------------
+--R              3               2          +-------+
+--R        (c e x  + (b e + c d)x  + b d x)\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 737
+
+--S 738 of 1457
+r0:=-2*A*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(3/2))-2*(b*B-A*c)*atanh(sqrt(c)*_
+     sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b*(c*d-b*e)^(3/2))+_
+     2*(B*d-A*e)/(d*(c*d-b*e)*sqrt(d+e*x))
+--R 
+--R
+--R   (2)
+--R                                                +-+ +-------+
+--R                        +-+ +-+ +-------+      \|c \|e x + d
+--R       (- 2A c + 2B b)d\|c \|d \|e x + d atanh(--------------)
+--R                                                +-----------+
+--R                                               \|- b e + c d
+--R     + 
+--R                                                         +-------+
+--R                           +-----------+ +-------+      \|e x + d
+--R       (- 2A b e + 2A c d)\|- b e + c d \|e x + d atanh(----------)
+--R                                                            +-+
+--R                                                           \|d
+--R     + 
+--R                         +-----------+ +-+
+--R       (2A b e - 2B b d)\|- b e + c d \|d
+--R  /
+--R       2           2  +-----------+ +-+ +-------+
+--R     (b d e - b c d )\|- b e + c d \|d \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 738
+
+--S 739 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                        +-----------+
+--R                        |      c      +-+ +-------+
+--R           (A c - B b)d |- --------- \|d \|e x + d
+--R                       \|  b e - c d
+--R        *
+--R                             +-----------+
+--R                             |      c      +-------+
+--R               (2b e - 2c d) |- --------- \|e x + d  + c e x - b e + 2c d
+--R                            \|  b e - c d
+--R           log(----------------------------------------------------------)
+--R                                         c x + b
+--R       + 
+--R                                           +-------+              +-+
+--R                         +-------+    - 2d\|e x + d  + (e x + 2d)\|d
+--R         (A b e - A c d)\|e x + d log(-------------------------------)
+--R                                                     x
+--R       + 
+--R                           +-+
+--R         (2A b e - 2B b d)\|d
+--R    /
+--R         2           2  +-+ +-------+
+--R       (b d e - b c d )\|d \|e x + d
+--R     ,
+--R
+--R                                           +-------+              +-+
+--R                         +-------+    - 2d\|e x + d  + (e x + 2d)\|d
+--R         (A b e - A c d)\|e x + d log(-------------------------------)
+--R                                                     x
+--R       + 
+--R                        +---------+                           +-------+
+--R                        |    c      +-+ +-------+           c\|e x + d
+--R         (2A c - 2B b)d |--------- \|d \|e x + d atan(-----------------------)
+--R                       \|b e - c d                                +---------+
+--R                                                                  |    c
+--R                                                      (b e - c d) |---------
+--R                                                                 \|b e - c d
+--R       + 
+--R                           +-+
+--R         (2A b e - 2B b d)\|d
+--R    /
+--R         2           2  +-+ +-------+
+--R       (b d e - b c d )\|d \|e x + d
+--R     ,
+--R
+--R                              +-----------+
+--R                        +---+ |      c      +-------+
+--R           (A c - B b)d\|- d  |- --------- \|e x + d
+--R                             \|  b e - c d
+--R        *
+--R                             +-----------+
+--R                             |      c      +-------+
+--R               (2b e - 2c d) |- --------- \|e x + d  + c e x - b e + 2c d
+--R                            \|  b e - c d
+--R           log(----------------------------------------------------------)
+--R                                         c x + b
+--R       + 
+--R                                            +---+ +-------+
+--R                             +-------+     \|- d \|e x + d
+--R         (- 2A b e + 2A c d)\|e x + d atan(----------------)
+--R                                                   d
+--R       + 
+--R                           +---+
+--R         (2A b e - 2B b d)\|- d
+--R    /
+--R         2           2  +---+ +-------+
+--R       (b d e - b c d )\|- d \|e x + d
+--R     ,
+--R
+--R                                            +---+ +-------+
+--R                             +-------+     \|- d \|e x + d
+--R         (- 2A b e + 2A c d)\|e x + d atan(----------------)
+--R                                                   d
+--R       + 
+--R                              +---------+                       +-------+
+--R                        +---+ |    c      +-------+           c\|e x + d
+--R         (2A c - 2B b)d\|- d  |--------- \|e x + d atan(-----------------------)
+--R                             \|b e - c d                            +---------+
+--R                                                                    |    c
+--R                                                        (b e - c d) |---------
+--R                                                                   \|b e - c d
+--R       + 
+--R                           +---+
+--R         (2A b e - 2B b d)\|- d
+--R    /
+--R         2           2  +---+ +-------+
+--R       (b d e - b c d )\|- d \|e x + d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 739
+
+--S 740 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R                                    +-----------+
+--R                      +-----------+ |      c      +-+
+--R         (A c - B b)d\|- b e + c d  |- --------- \|d
+--R                                   \|  b e - c d
+--R      *
+--R                           +-----------+
+--R                           |      c      +-------+
+--R             (2b e - 2c d) |- --------- \|e x + d  + c e x - b e + 2c d
+--R                          \|  b e - c d
+--R         log(----------------------------------------------------------)
+--R                                       c x + b
+--R     + 
+--R                                             +-------+              +-+
+--R                       +-----------+    - 2d\|e x + d  + (e x + 2d)\|d
+--R       (A b e - A c d)\|- b e + c d log(-------------------------------)
+--R                                                       x
+--R     + 
+--R                                    +-+ +-------+
+--R                      +-+ +-+      \|c \|e x + d
+--R       (2A c - 2B b)d\|c \|d atanh(--------------)
+--R                                    +-----------+
+--R                                   \|- b e + c d
+--R     + 
+--R                                             +-------+
+--R                         +-----------+      \|e x + d
+--R       (2A b e - 2A c d)\|- b e + c d atanh(----------)
+--R                                                +-+
+--R                                               \|d
+--R  /
+--R       2           2  +-----------+ +-+
+--R     (b d e - b c d )\|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 740
+
+--S 741 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 741
+
+--S 742 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R                                             +-------+              +-+
+--R                       +-----------+    - 2d\|e x + d  + (e x + 2d)\|d
+--R       (A b e - A c d)\|- b e + c d log(-------------------------------)
+--R                                                       x
+--R     + 
+--R                                    +-+ +-------+
+--R                      +-+ +-+      \|c \|e x + d
+--R       (2A c - 2B b)d\|c \|d atanh(--------------)
+--R                                    +-----------+
+--R                                   \|- b e + c d
+--R     + 
+--R                                             +-------+
+--R                         +-----------+      \|e x + d
+--R       (2A b e - 2A c d)\|- b e + c d atanh(----------)
+--R                                                +-+
+--R                                               \|d
+--R     + 
+--R                                  +---------+                 +-------+
+--R                    +-----------+ |    c      +-+           c\|e x + d
+--R     (2A c - 2B b)d\|- b e + c d  |--------- \|d atan(-----------------------)
+--R                                 \|b e - c d                      +---------+
+--R                                                                  |    c
+--R                                                      (b e - c d) |---------
+--R                                                                 \|b e - c d
+--R  /
+--R       2           2  +-----------+ +-+
+--R     (b d e - b c d )\|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 742
+
+--S 743 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 743
+
+)clear all
+
+--S 744 of 1457
+t0:=(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2))
+--R 
+--R
+--R                                      B x + A
+--R   (1)  ------------------------------------------------------------------
+--R            2 4       2           3                2  2      2   +-------+
+--R        (c e x  + (b e  + 2c d e)x  + (2b d e + c d )x  + b d x)\|e x + d
+--R                                                    Type: Expression(Integer)
+--E 744
+
+--S 745 of 1457
+r0:=2/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_
+     sqrt(d))/(b*d^(5/2))-2*c^(3/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_
+     sqrt(c*d-b*e))/(b*(c*d-b*e)^(5/2))+2*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*_
+     (c*d-b*e)^2*sqrt(d+e*x))
+--R 
+--R
+--R   (2)
+--R               2           2           2           3  +-+ +-+ +-------+
+--R         ((6A c  - 6B b c)d e x + (6A c  - 6B b c)d )\|c \|d \|e x + d
+--R      *
+--R                +-+ +-------+
+--R               \|c \|e x + d
+--R         atanh(--------------)
+--R                +-----------+
+--R               \|- b e + c d
+--R     + 
+--R                  2 3              2       2 2          2   2            2
+--R           (- 6A b e  + 12A b c d e  - 6A c d e)x - 6A b d e  + 12A b c d e
+--R         + 
+--R                 2 3
+--R           - 6A c d
+--R      *
+--R                                        +-------+
+--R          +-----------+ +-------+      \|e x + d
+--R         \|- b e + c d \|e x + d atanh(----------)
+--R                                           +-+
+--R                                          \|d
+--R     + 
+--R                2 3              2           2          2   2
+--R           (6A b e  - 12A b c d e  + 6B b c d e)x + 8A b d e
+--R         + 
+--R                            2  2            3
+--R           (- 14A b c - 2B b )d e + 8B b c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R  /
+--R           3 2 3     2   3 2       2 4        3 3 2     2   4        2 5
+--R       ((3b d e  - 6b c d e  + 3b c d e)x + 3b d e  - 6b c d e + 3b c d )
+--R    *
+--R        +-----------+ +-+ +-------+
+--R       \|- b e + c d \|d \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 745
+
+--S 746 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                  2 3             2       2 2          2   2           2
+--R             (3A b e  - 6A b c d e  + 3A c d e)x + 3A b d e  - 6A b c d e
+--R           + 
+--R                 2 3
+--R             3A c d
+--R        *
+--R                              +-------+              +-+
+--R            +-------+    - 2d\|e x + d  + (e x + 2d)\|d
+--R           \|e x + d log(-------------------------------)
+--R                                        x
+--R       + 
+--R                                                        +-----------+
+--R                 2           2           2           3  |      c      +-+
+--R           ((3A c  - 3B b c)d e x + (3A c  - 3B b c)d ) |- --------- \|d
+--R                                                       \|  b e - c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R        *
+--R                               +-----------+
+--R                               |      c      +-------+
+--R               (- 2b e + 2c d) |- --------- \|e x + d  + c e x - b e + 2c d
+--R                              \|  b e - c d
+--R           log(------------------------------------------------------------)
+--R                                          c x + b
+--R       + 
+--R                  2 3              2           2          2   2
+--R             (6A b e  - 12A b c d e  + 6B b c d e)x + 8A b d e
+--R           + 
+--R                              2  2            3
+--R             (- 14A b c - 2B b )d e + 8B b c d
+--R        *
+--R            +-+
+--R           \|d
+--R    /
+--R             3 2 3     2   3 2       2 4        3 3 2     2   4        2 5  +-+
+--R         ((3b d e  - 6b c d e  + 3b c d e)x + 3b d e  - 6b c d e + 3b c d )\|d
+--R      *
+--R          +-------+
+--R         \|e x + d
+--R     ,
+--R
+--R                  2 3             2       2 2          2   2           2
+--R             (3A b e  - 6A b c d e  + 3A c d e)x + 3A b d e  - 6A b c d e
+--R           + 
+--R                 2 3
+--R             3A c d
+--R        *
+--R                              +-------+              +-+
+--R            +-------+    - 2d\|e x + d  + (e x + 2d)\|d
+--R           \|e x + d log(-------------------------------)
+--R                                        x
+--R       + 
+--R                                                            +---------+
+--R                   2           2             2           3  |    c      +-+
+--R           ((- 6A c  + 6B b c)d e x + (- 6A c  + 6B b c)d ) |--------- \|d
+--R                                                           \|b e - c d
+--R        *
+--R                                  +-------+
+--R            +-------+           c\|e x + d
+--R           \|e x + d atan(-----------------------)
+--R                                      +---------+
+--R                                      |    c
+--R                          (b e - c d) |---------
+--R                                     \|b e - c d
+--R       + 
+--R                  2 3              2           2          2   2
+--R             (6A b e  - 12A b c d e  + 6B b c d e)x + 8A b d e
+--R           + 
+--R                              2  2            3
+--R             (- 14A b c - 2B b )d e + 8B b c d
+--R        *
+--R            +-+
+--R           \|d
+--R    /
+--R             3 2 3     2   3 2       2 4        3 3 2     2   4        2 5  +-+
+--R         ((3b d e  - 6b c d e  + 3b c d e)x + 3b d e  - 6b c d e + 3b c d )\|d
+--R      *
+--R          +-------+
+--R         \|e x + d
+--R     ,
+--R
+--R                                                              +-----------+
+--R                 2           2           2           3  +---+ |      c
+--R           ((3A c  - 3B b c)d e x + (3A c  - 3B b c)d )\|- d  |- ---------
+--R                                                             \|  b e - c d
+--R        *
+--R            +-------+
+--R           \|e x + d
+--R        *
+--R                               +-----------+
+--R                               |      c      +-------+
+--R               (- 2b e + 2c d) |- --------- \|e x + d  + c e x - b e + 2c d
+--R                              \|  b e - c d
+--R           log(------------------------------------------------------------)
+--R                                          c x + b
+--R       + 
+--R                    2 3              2       2 2          2   2            2
+--R             (- 6A b e  + 12A b c d e  - 6A c d e)x - 6A b d e  + 12A b c d e
+--R           + 
+--R                   2 3
+--R             - 6A c d
+--R        *
+--R                           +---+ +-------+
+--R            +-------+     \|- d \|e x + d
+--R           \|e x + d atan(----------------)
+--R                                  d
+--R       + 
+--R                  2 3              2           2          2   2
+--R             (6A b e  - 12A b c d e  + 6B b c d e)x + 8A b d e
+--R           + 
+--R                              2  2            3
+--R             (- 14A b c - 2B b )d e + 8B b c d
+--R        *
+--R            +---+
+--R           \|- d
+--R    /
+--R             3 2 3     2   3 2       2 4        3 3 2     2   4        2 5
+--R         ((3b d e  - 6b c d e  + 3b c d e)x + 3b d e  - 6b c d e + 3b c d )
+--R      *
+--R          +---+ +-------+
+--R         \|- d \|e x + d
+--R     ,
+--R
+--R                    2 3              2       2 2          2   2            2
+--R             (- 6A b e  + 12A b c d e  - 6A c d e)x - 6A b d e  + 12A b c d e
+--R           + 
+--R                   2 3
+--R             - 6A c d
+--R        *
+--R                           +---+ +-------+
+--R            +-------+     \|- d \|e x + d
+--R           \|e x + d atan(----------------)
+--R                                  d
+--R       + 
+--R                                                                  +---------+
+--R                   2           2             2           3  +---+ |    c
+--R           ((- 6A c  + 6B b c)d e x + (- 6A c  + 6B b c)d )\|- d  |---------
+--R                                                                 \|b e - c d
+--R        *
+--R                                  +-------+
+--R            +-------+           c\|e x + d
+--R           \|e x + d atan(-----------------------)
+--R                                      +---------+
+--R                                      |    c
+--R                          (b e - c d) |---------
+--R                                     \|b e - c d
+--R       + 
+--R                  2 3              2           2          2   2
+--R             (6A b e  - 12A b c d e  + 6B b c d e)x + 8A b d e
+--R           + 
+--R                              2  2            3
+--R             (- 14A b c - 2B b )d e + 8B b c d
+--R        *
+--R            +---+
+--R           \|- d
+--R    /
+--R             3 2 3     2   3 2       2 4        3 3 2     2   4        2 5
+--R         ((3b d e  - 6b c d e  + 3b c d e)x + 3b d e  - 6b c d e + 3b c d )
+--R      *
+--R          +---+ +-------+
+--R         \|- d \|e x + d
+--R     ]
+--R                                   Type: Union(List(Expression(Integer)),...)
+--E 746
+
+--S 747 of 1457
+m0a:=a0.1-r0
+--R 
+--R
+--R   (4)
+--R             2 2                   2 2  +-----------+
+--R         (A b e  - 2A b c d e + A c d )\|- b e + c d
+--R      *
+--R                  +-------+              +-+
+--R             - 2d\|e x + d  + (e x + 2d)\|d
+--R         log(-------------------------------)
+--R                            x
+--R     + 
+--R                                        +-----------+
+--R             2          2 +-----------+ |      c      +-+
+--R         (A c  - B b c)d \|- b e + c d  |- --------- \|d
+--R                                       \|  b e - c d
+--R      *
+--R                             +-----------+
+--R                             |      c      +-------+
+--R             (- 2b e + 2c d) |- --------- \|e x + d  + c e x - b e + 2c d
+--R                            \|  b e - c d
+--R         log(------------------------------------------------------------)
+--R                                        c x + b
+--R     + 
+--R                                          +-+ +-------+
+--R              2           2 +-+ +-+      \|c \|e x + d
+--R       (- 2A c  + 2B b c)d \|c \|d atanh(--------------)
+--R                                          +-----------+
+--R                                         \|- b e + c d
+--R     + 
+--R                                                            +-------+
+--R            2 2                    2 2  +-----------+      \|e x + d
+--R       (2A b e  - 4A b c d e + 2A c d )\|- b e + c d atanh(----------)
+--R                                                               +-+
+--R                                                              \|d
+--R  /
+--R       3 2 2     2   3       2 4  +-----------+ +-+
+--R     (b d e  - 2b c d e + b c d )\|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 747
+
+--S 748 of 1457
+d0a:=D(m0a,x)
+--R 
+--R
+--R   (5)  0
+--R                                                    Type: Expression(Integer)
+--E 748
+
+--S 749 of 1457
+m0b:=a0.2-r0
+--R 
+--R
+--R   (6)
+--R             2 2                   2 2  +-----------+
+--R         (A b e  - 2A b c d e + A c d )\|- b e + c d
+--R      *
+--R                  +-------+              +-+
+--R             - 2d\|e x + d  + (e x + 2d)\|d
+--R         log(-------------------------------)
+--R                            x
+--R     + 
+--R                                          +-+ +-------+
+--R              2           2 +-+ +-+      \|c \|e x + d
+--R       (- 2A c  + 2B b c)d \|c \|d atanh(--------------)
+--R                                          +-----------+
+--R                                         \|- b e + c d
+--R     + 
+--R                                                            +-------+
+--R            2 2                    2 2  +-----------+      \|e x + d
+--R       (2A b e  - 4A b c d e + 2A c d )\|- b e + c d atanh(----------)
+--R                                                               +-+
+--R                                                              \|d
+--R     + 
+--R                                            +---------+
+--R                2           2 +-----------+ |    c      +-+
+--R         (- 2A c  + 2B b c)d \|- b e + c d  |--------- \|d
+--R                                           \|b e - c d
+--R      *
+--R                      +-------+
+--R                    c\|e x + d
+--R         atan(-----------------------)
+--R                          +---------+
+--R                          |    c
+--R              (b e - c d) |---------
+--R                         \|b e - c d
+--R  /
+--R       3 2 2     2   3       2 4  +-----------+ +-+
+--R     (b d e  - 2b c d e + b c d )\|- b e + c d \|d
+--R                                                    Type: Expression(Integer)
+--E 749
+
+--S 750 of 1457
+d0b:=D(m0b,x)
+--R 
+--R
+--R   (7)  0
+--R                                                    Type: Expression(Integer)
+--E 750
+
+)clear all
+
+--S 751 of 1457
+t0:=(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2))
+--R 
+--R
+--R   (1)
+--R     B x + A
+--R  /
+--R            3 5       3         2  4          2       2   3        2       3  2
+--R         c e x  + (b e  + 3c d e )x  + (3b d e  + 3c d e)x  + (3b d e + c d )x
+--R       + 
+--R            3
+--R         b d x
+--R    *
+--R        +-------+
+--R       \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 751
+
+--S 752 of 1457
+r0:=2/5*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(5/2))+2/3*(B*c*d^2-A*e*(2*c*d-_
+     b*e))/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-2*A*atanh(sqrt(d+e*x)/_
+     sqrt(d))/(b*d^(7/2))-2*c^(5/2)*(b*B-A*c)*atanh(sqrt(c)*sqrt(d+e*x)/_
+     sqrt(c*d-b*e))/(b*(c*d-b*e)^(7/2))+2*(B*c^2*d^3-A*e*(3*c^2*d^2-_
+     3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*sqrt(d+e*x))
+--R 
+--R
+--R   (2)
+--R                   3          2  3 2 2           3          2  4
+--R           (- 30A c  + 30B b c )d e x  + (- 60A c  + 60B b c )d e x
+--R         + 
+--R                   3          2  5
+--R           (- 30A c  + 30B b c )d
+--R      *
+--R                                  +-+ +-------+
+--R          +-+ +-+ +-------+      \|c \|e x + d
+--R         \|c \|d \|e x + d atanh(--------------)
+--R                                  +-----------+
+--R                                 \|- b e + c d
+--R     + 
+--R                   3 5        2     4          2 2 3        3 3 2  2
+--R           (- 30A b e  + 90A b c d e  - 90A b c d e  + 30A c d e )x
+--R         + 
+--R                   3   4         2   2 3           2 3 2        3 4
+--R           (- 60A b d e  + 180A b c d e  - 180A b c d e  + 60A c d e)x
+--R         + 
+--R                  3 2 3        2   3 2          2 4         3 5
+--R           - 30A b d e  + 90A b c d e  - 90A b c d e + 30A c d
+--R      *
+--R                                        +-------+
+--R          +-----------+ +-------+      \|e x + d
+--R         \|- b e + c d \|e x + d atanh(----------)
+--R                                           +-+
+--R                                          \|d
+--R     + 
+--R                 3 5        2     4          2 2 3          2 3 2  2
+--R           (30A b e  - 90A b c d e  + 90A b c d e  - 30B b c d e )x
+--R         + 
+--R                    3   4         2   2 3            2        2   3 2
+--R               70A b d e  - 210A b c d e  + (200A b c  + 10B b c)d e
+--R             + 
+--R                        2 4
+--R               - 70B b c d e
+--R          *
+--R             x
+--R         + 
+--R                3 2 3            2        3  3 2            2        2   4
+--R           46A b d e  + (- 132A b c - 6B b )d e  + (116A b c  + 22B b c)d e
+--R         + 
+--R                    2 5
+--R           - 46B b c d
+--R      *
+--R          +-----------+ +-+
+--R         \|- b e + c d \|d
+--R  /
+--R             4 3 5      3   4 4      2 2 5 3        3 6 2  2
+--R         (15b d e  - 45b c d e  + 45b c d e  - 15b c d e )x
+--R       + 
+--R             4 4 4      3   5 3      2 2 6 2        3 7         4 5 3
+--R         (30b d e  - 90b c d e  + 90b c d e  - 30b c d e)x + 15b d e
+--R       + 
+--R              3   6 2      2 2 7         3 8
+--R         - 45b c d e  + 45b c d e - 15b c d
+--R    *
+--R        +-----------+ +-+ +-------+
+--R       \|- b e + c d \|d \|e x + d
+--R                                                    Type: Expression(Integer)
+--E 752
+
+--S 753 of 1457
+a0:=integrate(t0,x)
+--R 
+--R
+--R   (3)
+--R   [
+--R                   3          2  3 2 2         3          2  4
+--R             (15A c  - 15B b c )d e x  + (30A c  - 30B b c )d e x
+--R           + 
+--R                   3          2  5
+--R             (15A c  - 15B b c )d
+--R        *
+--R            +-----------+
+--R            |      c      +-+ +-------+
+--R            |- --------- \|d \|e x + d
+--R           \|  b e - c d
+--R        *
+--R                             +-----------+
+--R                             |      c      +-------+
+--R               (2b e - 2c d) |- --------- \|e x + d  + c e x - b e + 2c d
+--R                            \|  b e - c d
+--R           log(--------------------------------------------------