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 source
pdf
+
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 1)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 2)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 3)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 4)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 5)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 6)
+ source
+ pdf
Rich Derivatives
@@ -587,6 +606,25 @@ Mathematica. This test suite shows Axiom's results.
source
pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 1)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 2)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 3)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 4)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 5)
+ source
+ pdf
+ (d+e x)^m (f+g x)^n (a+b x+c x^2)^p (part 6)
+ source
+ pdf
+
Rich
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
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+--R +
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+--R (- A c - B b)d e - B c d
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+--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x
+--R +
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+--R 60d e
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 1457
+m0:=a0-r0
+--R
+--R
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+--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
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+--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
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+--R +
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+--R 1044A b d e + (- 2088A b c - 1044B b )d e
+--R +
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+--R +
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+--R *
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+--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 +
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+--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 +
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+--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 *
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+--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 +
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+--R ((34A b c + 17B b )e + (12A c + 24B b c)d e - 5B c d e )m
+--R +
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+--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 +
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+--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 +
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+--R 240A b e
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+--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 +
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+--R 194A b d e + (- 246A b c - 123B b )d e
+--R +
+--R 2 3 3 2 4 2
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+--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
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+--R +
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+--R (- 24A c - 48B b c)d e
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+--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
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+--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
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+--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
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+--R x
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+--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 +
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+--R ((792A b c + 396B b )e + (36A c + 72B b c)d e - 30B c d e )m
+--R +
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+--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 +
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+--R ((- A c - 2B b c)e + 5B c d)m + ((- 16A c - 32B b c)e + 80B c d)m
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+--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
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+--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
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+--R 3 2 3 3 4
+--R (20A c + 60B b c )d e - 35B c d
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+--R +
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+--R +
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+--R +
+--R 3 4
+--R - 1120B c d
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+--R +
+--R 3 4 2 3 3
+--R - 418A b e + (5016A b c + 1672B b )d e
+--R +
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+--R (- 12540A b c - 12540B b c)d e + (8360A c + 25080B b c )d e
+--R +
+--R 3 4
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+--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
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+--R +
+--R 3 4 2 3 3
+--R - 10993A b e + (131916A b c + 43972B b )d e
+--R +
+--R 2 2 2 2
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+--R 3 2 3 3 4
+--R (219860A c + 659580B b c )d e - 384755B c d
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+--R - 23312A b e + (279744A b c + 93248B b )d e
+--R +
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+--R 3 2 3 3 4
+--R (466240A c + 1398720B b c )d e - 815920B c d
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+--R +
+--R 3 4 2 3 3
+--R - 24876A b e + (298512A b c + 99504B b )d e
+--R +
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+--R +
+--R 3 2 3 3 4
+--R (497520A c + 1492560B b c )d e - 870660B c d
+--R *
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+--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 *
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+--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
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+--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
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+--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
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+--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 [
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+--R *
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+--R \|- b d e + c d \|c
+--R *
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+--R 768B c e x + ((960A c + 2016B b c )e - 1152B c d e )x
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+--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
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+--R (150A b c - 45B b )d e + (2400A b c - 300B b c)d e
+--R +
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+--R (- 21600A b c - 3600B b c )d e + (38400A b c + 28800B b c )d e
+--R +
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+--R (- 19200A c - 48000B b c )d e + 23040B c d
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+--R +
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+--R +
+--R 4 3 4 4 5
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+--R +-+ | 2 d\|c x + b x
+--R \|c \|b d e - c d atan(----------------)
+--R +------------+
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+--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
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+--R +
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+--R \|c \|c x + b x
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+--R 2 8 2 7 +-+
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+--R ,
+--R
+--R 2 2 4 3 2 2 2 3
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+--R (9600A c + 18240B b c )d e - 11520B c d
+--R *
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+--R | 2 +---+
+--R \|- b d e + c d \|- c
+--R *
+--R +--------------+ +----------+
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+--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d
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+--R (- 150A b c + 45B b )e + (- 2400A b c + 300B b c)d e
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+--R 2 3 3 2 2 4
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+--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 +
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+--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 *
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+--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 +
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+--R (1360A b c + 744B b c )e + (- 800A c - 1712B b c )d e
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+--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
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+--R 4 3 2 4 4 3 3
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+--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 +
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+--R 11520B c d e
+--R *
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+--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
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+--R +
+--R 4 2 3 3 3
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+--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
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+--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 +
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+--R 384B c e x + ((480A c + 1008B b c )e - 576B c d e )x
+--R +
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+--R +
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+--R 960B c d e
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+--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
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+--R +
+--R 3 4 5 2 2 3 2 4
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+--R +
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+--R +
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+--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
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+--R +
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+--R *
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+--R 2 2 3 3 2 2 2 2
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+--R +
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+--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
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+--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
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+--R +
+--R 5 4 4 5 5
+--R (- 1280A c - 3200B b c )d e + 1536B c d
+--R *
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+--R log(- 2c\|c x + b x + (2c x + b)\|c )
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+--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
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+--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(--------------------------------------------------