diff --git a/changelog b/changelog index e88dbba..30d4e06 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,8 @@ +20130718 tpd src/axiom-website/patches.html 20130718.01.tpd.patch +20130718 tpd src/input/rich1b.input +20130718 tpd src/input/rich1a.input +20130718 tpd src/input/Makefile +20130718 tpd src/interp/Makefile 20130715 tpd src/axiom-website/patches.html 20130715.01.tpd.patch 20130715 tpd buglist add kamke4, kamke6 missing bug 20130715 tpd src/axiom-website/CATS/index.html updated diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 4f4d7eb..1c5dfb2 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4234,6 +4234,8 @@ add rich integral set to CATS test suite src/input/charlwood.input added 20130715.01.tpd.patch CATS updated with txt, charlwood +20130718.01.tpd.patch +CATS rich1a, rich1b diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 790ea9e..0a5cccd 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -432,6 +432,8 @@ CATSTESTS= \ These long-running tests have been split into a different group so we can run them in parallel. <>= +NEWRICHTESTS = rich1a.regress rich1b.regress + RICHTESTS= \ richalgebraic000-099.regress \ richalgebraic100-199.regress \ @@ -472,7 +474,6 @@ RICHTESTS= \ richtrig800-899.regress \ richtrig900-920.regress - IN= ${SRC}/input MID= ${INT}/input TMPFN:=$(shell echo $$RANDOM) @@ -489,6 +490,11 @@ algebratests: ${OUTS} ${MAKE} -f Makefile.algebra ) @ echo si14 finished ${INT}/input +newrichtests: ${NEWRICHTESTS} ${OUTS} + @ echo ====================================== + @ echo src/input RUNNING NEW RICH TESTS + @ echo ====================================== + richtests: ${RICHTESTS} ${OUTS} @ echo ====================================== @ echo src/input RUNNING RICH TESTS @@ -504,7 +510,7 @@ regresstests: ${REGRESSTESTS} ${OUTS} @ echo src/input RUNNING REGRESSION TESTS @ echo ====================================== -alltests: regresstests catstests richtests algebratests ${OUTS} +alltests: regresstests catstests newrichtests richtests algebratests ${OUTS} @ echo ====================================== @ echo src/input RUNNING ALL TESTS @ echo ====================================== @@ -779,7 +785,9 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/pmint.input ${OUT}/polycoer.input \ ${OUT}/poly1.input ${OUT}/psgenfcn.input \ ${OUT}/quat.input ${OUT}/quat1.input ${OUT}/ribbon.input \ - ${OUT}/ribbons.input ${OUT}/ribbonsnew.input ${OUT}/rk4draw.input \ + ${OUT}/ribbons.input ${OUT}/ribbonsnew.input \ + ${OUT}/rich1a.input ${OUT}/rich1b.input \ + ${OUT}/rk4draw.input \ ${OUT}/r20abugs.input \ ${OUT}/r20bugs.input ${OUT}/r21bugsbig.input \ ${OUT}/r21bugs.input \ @@ -863,6 +871,8 @@ FILES2=${OUT}/arith.input ${OUT}/bugs.input \ ${OUT}/spadprof.input \ ${OUT}/synonym2.input ${OUT}/torus.input +NEWRICHINPUT= ${OUT}/rich1a.input ${OUT}/rich1b.input + RICHINPUT= \ ${OUT}/richalgebraic000-099.input \ ${OUT}/richalgebraic100-199.input \ @@ -1180,6 +1190,8 @@ DOCFILES= \ ${DOC}/regset.input.dvi ${DOC}/repa6.input.dvi \ ${DOC}/ribbon.input.dvi ${DOC}/ribbons.input.dvi \ ${DOC}/ribbonsnew.input.dvi \ + ${DOC}/rich1a.input.dvi \ + ${DOC}/rich1b.input.dvi \ ${DOC}/richalgebraic000-099.input.dvi \ ${DOC}/richalgebraic100-199.input.dvi \ ${DOC}/richalgebraic200-299.input.dvi \ diff --git a/src/input/rich1a.input.pamphlet b/src/input/rich1a.input.pamphlet new file mode 100644 index 0000000..4ae6691 --- /dev/null +++ b/src/input/rich1a.input.pamphlet @@ -0,0 +1,41096 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich1a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +\begin{chunk}{license} +--Copyright The Numerical Algorithms Group Limited 1991. +\end{chunk} +\section{Integrands of the form $x^m (a+b x)^n$} +\subsection{Integrands of the form $x^m$} +\subsubsection{Integrands of the form $a$} + +\begin{chunk}{*} +)set break resume +)sys rm -f rich1a.output +)spool rich1a.output +)set message test on +)set message auto off +)clear all + +--S 1 of 3330 +t0000:=0 +--R +--R +--R (1) 0 +--R Type: NonNegativeInteger +--E 1 + +--S 2 of 3330 +r0000:=0 +--R +--R +--R (2) 0 +--R Type: NonNegativeInteger +--E 2 + +--S 3 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 3 + +--S 4 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 4 + +--S 5 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 5 + +)clear all + +--S 6 of 3330 +t0000:=1 +--R +--R +--R (1) 1 +--R Type: PositiveInteger +--E 6 + +--S 7 of 3330 +r0000:=x +--R +--R +--R (2) x +--R Type: Variable(x) +--E 7 + +--S 8 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) x +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 9 + +--S 10 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 10 + +)clear all + +--S 11 of 3330 +t0000:=5 +--R +--R +--R (1) 5 +--R Type: PositiveInteger +--E 11 + +--S 12 of 3330 +r0000:=5*x +--R +--R +--R (2) 5x +--R Type: Polynomial(Integer) +--E 12 + +--S 13 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) 5x +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +)clear all + +--S 16 of 3330 +t0000:=-2 +--R +--R +--R (1) - 2 +--R Type: Integer +--E 16 + +--S 17 of 3330 +r0000:=-2*x +--R +--R +--R (2) - 2x +--R Type: Polynomial(Integer) +--E 17 + +--S 18 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) - 2x +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 3330 +t0000:=-3/2 +--R +--R +--R 3 +--R (1) - - +--R 2 +--R Type: Fraction(Integer) +--E 21 + +--S 22 of 3330 +r0000:=-3/2*x +--R +--R +--R 3 +--R (2) - - x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3x +--R (3) - -- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 3330 +t0000:=%pi +--R +--R +--R (1) %pi +--R Type: Pi +--E 26 + +--S 27 of 3330 +r0000:=%pi*x +--R +--R +--R (2) %pi x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) %pi x +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 3330 +t0000:=a +--R +--R +--R (1) a +--R Type: Variable(a) +--E 31 + +--S 32 of 3330 +r0000:=a*x +--R +--R +--R (2) a x +--R Type: Polynomial(Integer) +--E 32 + +--S 33 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) a x +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 3330 +t0000:=3*a +--R +--R +--R (1) 3a +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 3330 +r0000:=3*a*x +--R +--R +--R (2) 3a x +--R Type: Polynomial(Integer) +--E 37 + +--S 38 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) 3a x +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +)clear all + +--S 41 of 3330 +t0000:=%pi/sqrt(16-%e^2) +--R +--R +--R %pi +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- %e + 16 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 3330 +r0000:=%pi*x/sqrt(16-%e^2) +--R +--R +--R %pi x +--R (2) ------------- +--R +----------+ +--R | 2 +--R \|- %e + 16 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R %pi x +--R (3) ------------- +--R +----------+ +--R | 2 +--R \|- %e + 16 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 3330 +t0000:=x^m +--R +--R +--R m +--R (1) x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 3330 +r0000:=x^(1+m)/(1+m) +--R +--R +--R m + 1 +--R x +--R (2) ------ +--R m + 1 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R m log(x) +--R x %e +--R (3) ------------ +--R m + 1 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R m log(x) m + 1 +--R x %e - x +--R (4) --------------------- +--R m + 1 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 3330 +t0000:=x^100 +--R +--R +--R 100 +--R (1) x +--R Type: Polynomial(Integer) +--E 51 + +--S 52 of 3330 +r0000:=1/101*x^101 +--R +--R +--R 1 101 +--R (2) --- x +--R 101 +--R Type: Polynomial(Fraction(Integer)) +--E 52 + +--S 53 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 101 +--R (3) --- x +--R 101 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 54 + +--S 55 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 55 + +)clear all + +--S 56 of 3330 +t0000:=x^3 +--R +--R +--R 3 +--R (1) x +--R Type: Polynomial(Integer) +--E 56 + +--S 57 of 3330 +r0000:=1/4*x^4 +--R +--R +--R 1 4 +--R (2) - x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 57 + +--S 58 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 4 +--R (3) - x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 58 + +--S 59 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 60 + +)clear all + +--S 61 of 3330 +t0000:=x^2 +--R +--R +--R 2 +--R (1) x +--R Type: Polynomial(Integer) +--E 61 + +--S 62 of 3330 +r0000:=1/3*x^3 +--R +--R +--R 1 3 +--R (2) - x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 62 + +--S 63 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 +--R (3) - x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 63 + +--S 64 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 64 + +--S 65 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 65 + +)clear all + +--S 66 of 3330 +t0000:=x +--R +--R +--R (1) x +--R Type: Variable(x) +--E 66 + +--S 67 of 3330 +r0000:=1/2*x^2 +--R +--R +--R 1 2 +--R (2) - x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 67 + +--S 68 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 +--R (3) - x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 68 + +--S 69 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 69 + +--S 70 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 70 + +)clear all + +--S 71 of 3330 +t0000:=1 +--R +--R +--R (1) 1 +--R Type: PositiveInteger +--E 71 + +--S 72 of 3330 +r0000:=x +--R +--R +--R (2) x +--R Type: Variable(x) +--E 72 + +--S 73 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) x +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +)clear all + +--S 76 of 3330 +t0000:=1/x +--R +--R +--R 1 +--R (1) - +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 3330 +r0000:=log(x) +--R +--R +--R (2) log(x) +--R Type: Expression(Integer) +--E 77 + +--S 78 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) log(x) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 3330 +t0000:=1/x^2 +--R +--R +--R 1 +--R (1) -- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 3330 +r0000:=(-1)/x +--R +--R +--R 1 +--R (2) - - +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 82 + +--S 83 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - - +--R x +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 3330 +t0000:=1/x^3 +--R +--R +--R 1 +--R (1) -- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 3330 +r0000:=(-1/2)/x^2 +--R +--R +--R 1 +--R - +--R 2 +--R (2) - --- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 3330 +t0000:=1/x^4 +--R +--R +--R 1 +--R (1) -- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 3330 +r0000:=(-1/3)/x^3 +--R +--R +--R 1 +--R - +--R 3 +--R (2) - --- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 3330 +t0000:=1/x^100 +--R +--R +--R 1 +--R (1) ---- +--R 100 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 3330 +r0000:=(-1/99)/x^99 +--R +--R +--R 1 +--R -- +--R 99 +--R (2) - ---- +--R 99 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 97 + +--S 98 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - ----- +--R 99 +--R 99x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 3330 +t0000:=1/(a*x^n+b*x^n) +--R +--R +--R 1 +--R (1) --------- +--R n +--R (b + a)x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 3330 +r0000:=x^(1-n)/((a+b)*(1-n)) +--R +--R +--R - n + 1 +--R x +--R (2) - ---------------- +--R (b + a)n - b - a +--R Type: Expression(Integer) +--E 102 + +--S 103 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R (3) - ---------------------------- +--R n log(x) +--R ((b + a)n - b - a)%e +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R - n + 1 n log(x) +--R x %e - x +--R (4) ---------------------------- +--R n log(x) +--R ((b + a)n - b - a)%e +--R Type: Expression(Integer) +--E 104 + +--S 105 of 3330 +d0000:=D(m0000,x) +--R +--R +--R - n n log(x) +--R - x %e + 1 +--R (5) -------------------- +--R n log(x) +--R (b + a)%e +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 3330 +t0000:=x^(5/2) +--R +--R +--R 2 +-+ +--R (1) x \|x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 3330 +r0000:=2/7*x^(7/2) +--R +--R +--R 3 +-+ +--R 2x \|x +--R (2) ------- +--R 7 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +-+ +--R 2x \|x +--R (3) ------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 3330 +t0000:=x^(3/2) +--R +--R +--R +-+ +--R (1) x\|x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 3330 +r0000:=2/5*x^(5/2) +--R +--R +--R 2 +-+ +--R 2x \|x +--R (2) ------- +--R 5 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-+ +--R 2x \|x +--R (3) ------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 3330 +t0000:=x^(1/2) +--R +--R +--R +-+ +--R (1) \|x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 3330 +r0000:=2/3*x^(3/2) +--R +--R +--R +-+ +--R 2x\|x +--R (2) ------ +--R 3 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R 2x\|x +--R (3) ------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 3330 +t0000:=1/x^(1/2) +--R +--R +--R 1 +--R (1) ---- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 3330 +r0000:=2*sqrt(x) +--R +--R +--R +-+ +--R (2) 2\|x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R (3) 2\|x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 3330 +t0000:=1/x^(3/2) +--R +--R +--R 1 +--R (1) ----- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 3330 +r0000:=(-2)/sqrt(x) +--R +--R +--R 2 +--R (2) - ---- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ---- +--R +-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 3330 +t0000:=1/x^(5/2) +--R +--R +--R 1 +--R (1) ------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 3330 +r0000:=(-2/3)/x^(3/2) +--R +--R +--R 2 +--R (2) - ------ +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 132 + +--S 133 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ------ +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 3330 +t0000:=x^(5/3) +--R +--R +--R 3+-+2 +--R (1) x \|x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 3330 +r0000:=3/8*x^(8/3) +--R +--R +--R 2 3+-+2 +--R 3x \|x +--R (2) -------- +--R 8 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3+-+2 +--R 3x \|x +--R (3) -------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 3330 +t0000:=x^(4/3) +--R +--R +--R 3+-+ +--R (1) x\|x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 3330 +r0000:=3/7*x^(7/3) +--R +--R +--R 2 3+-+ +--R 3x \|x +--R (2) ------- +--R 7 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3+-+ +--R 3x \|x +--R (3) ------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 3330 +t0000:=x^(2/3) +--R +--R +--R 3+-+2 +--R (1) \|x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 3330 +r0000:=3/5*x^(5/3) +--R +--R +--R 3+-+2 +--R 3x \|x +--R (2) -------- +--R 5 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+2 +--R 3x \|x +--R (3) -------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 3330 +t0000:=x^(1/3) +--R +--R +--R 3+-+ +--R (1) \|x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 3330 +r0000:=3/4*x^(4/3) +--R +--R +--R 3+-+ +--R 3x\|x +--R (2) ------ +--R 4 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+ +--R 3x\|x +--R (3) ------ +--R 4 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 3330 +t0000:=1/x^(1/3) +--R +--R +--R 1 +--R (1) ---- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 156 + +--S 157 of 3330 +r0000:=3/2*x^(2/3) +--R +--R +--R 3+-+2 +--R 3\|x +--R (2) ------ +--R 2 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+2 +--R 3\|x +--R (3) ------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 3330 +t0000:=1/x^(2/3) +--R +--R +--R 1 +--R (1) ----- +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 161 + +--S 162 of 3330 +r0000:=3*x^(1/3) +--R +--R +--R 3+-+ +--R (2) 3\|x +--R Type: Expression(Integer) +--E 162 + +--S 163 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+ +--R (3) 3\|x +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 3330 +t0000:=1/x^(4/3) +--R +--R +--R 1 +--R (1) ----- +--R 3+-+ +--R x\|x +--R Type: Expression(Integer) +--E 166 + +--S 167 of 3330 +r0000:=(-3)/x^(1/3) +--R +--R +--R 3 +--R (2) - ---- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R (3) - ---- +--R 3+-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 3330 +t0000:=1/x^(5/3) +--R +--R +--R 1 +--R (1) ------- +--R 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 3330 +r0000:=(-3/2)/x^(2/3) +--R +--R +--R 3 +--R (2) - ------ +--R 3+-+2 +--R 2\|x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R (3) - ------ +--R 3+-+2 +--R 2\|x +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 3330 +t0000:=x^m*(a+b*x) +--R +--R +--R m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 3330 +r0000:=a*x^(1+m)/(1+m)+b*x^(2+m)/(2+m) +--R +--R +--R m + 2 m + 1 +--R (b m + b)x + (a m + 2a)x +--R (2) ---------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 m log(x) +--R ((b m + b)x + (a m + 2a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 m log(x) m + 2 +--R ((b m + b)x + (a m + 2a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 2a)x +--R / +--R 2 +--R m + 3m + 2 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 3330 +t0000:=x^3*(a+b*x) +--R +--R +--R 4 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 181 + +--S 182 of 3330 +r0000:=1/4*a*x^4+1/5*b*x^5 +--R +--R +--R 1 5 1 4 +--R (2) - b x + - a x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 182 + +--S 183 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 5 1 4 +--R (3) - b x + - a x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 183 + +--S 184 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 184 + +--S 185 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 185 + +)clear all + +--S 186 of 3330 +t0000:=x^2*(a+b*x) +--R +--R +--R 3 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 3330 +r0000:=1/3*a*x^3+1/4*b*x^4 +--R +--R +--R 1 4 1 3 +--R (2) - b x + - a x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 187 + +--S 188 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 4 1 3 +--R (3) - b x + - a x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 189 + +--S 190 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +)clear all + +--S 191 of 3330 +t0000:=x*(a+b*x) +--R +--R +--R 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 3330 +r0000:=1/2*a*x^2+1/3*b*x^3 +--R +--R +--R 1 3 1 2 +--R (2) - b x + - a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 1 2 +--R (3) - b x + - a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 194 + +--S 195 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +)clear all + +--S 196 of 3330 +t0000:=a+b*x +--R +--R +--R (1) b x + a +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 3330 +r0000:=a*x+1/2*b*x^2 +--R +--R +--R 1 2 +--R (2) - b x + a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 +--R (3) - b x + a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 199 + +--S 200 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +)clear all + +--S 201 of 3330 +t0000:=(a+b*x)/x +--R +--R +--R b x + a +--R (1) ------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 3330 +r0000:=b*x+a*log(x) +--R +--R +--R (2) a log(x) + b x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) a log(x) + b x +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 3330 +t0000:=(a+b*x)/x^2 +--R +--R +--R b x + a +--R (1) ------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 3330 +r0000:=-a/x+b*log(x) +--R +--R +--R b x log(x) - a +--R (2) -------------- +--R x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(x) - a +--R (3) -------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 3330 +t0000:=(a+b*x)/x^3 +--R +--R +--R b x + a +--R (1) ------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 3330 +r0000:=-1/2*a/x^2-b/x +--R +--R +--R 1 +--R - b x - - a +--R 2 +--R (2) ----------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 2b x - a +--R (3) ---------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 3330 +t0000:=(a+b*x)/x^4 +--R +--R +--R b x + a +--R (1) ------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 3330 +r0000:=-1/3*a/x^3-1/2*b/x^2 +--R +--R +--R 1 1 +--R - - b x - - a +--R 2 3 +--R (2) ------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 3b x - 2a +--R (3) ----------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 3330 +t0000:=(a+b*x)/x^5 +--R +--R +--R b x + a +--R (1) ------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 3330 +r0000:=-1/4*a/x^4-1/3*b/x^3 +--R +--R +--R 1 1 +--R - - b x - - a +--R 3 4 +--R (2) ------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 222 + +--S 223 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 4b x - 3a +--R (3) ----------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 3330 +t0000:=x^m*(a+b*x)^2 +--R +--R +--R 2 2 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 3330 +r0000:=a^2*x^(1+m)/(1+m)+2*a*b*x^(2+m)/(2+m)+b^2*x^(3+m)/(3+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 3 2 m + 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 5a m + 6a )x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 3 2 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 +--R (a m + 5a m + 6a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 2 2 3 2 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 +--R (a m + 5a m + 6a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 3 2 m + 2 +--R (- b m - 3b m - 2b )x + (- 2a b m - 8a b m - 6a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 5a m - 6a )x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 3330 +t0000:=x^3*(a+b*x)^2 +--R +--R +--R 2 5 4 2 3 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 3330 +r0000:=1/4*a^2*x^4+2/5*a*b*x^5+1/6*b^2*x^6 +--R +--R +--R 1 2 6 2 5 1 2 4 +--R (2) - b x + - a b x + - a x +--R 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 232 + +--S 233 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 6 2 5 1 2 4 +--R (3) - b x + - a b x + - a x +--R 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 234 + +--S 235 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 235 + +)clear all + +--S 236 of 3330 +t0000:=x^2*(a+b*x)^2 +--R +--R +--R 2 4 3 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 236 + +--S 237 of 3330 +r0000:=1/3*a^2*x^3+1/2*a*b*x^4+1/5*b^2*x^5 +--R +--R +--R 1 2 5 1 4 1 2 3 +--R (2) - b x + - a b x + - a x +--R 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 237 + +--S 238 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 5 1 4 1 2 3 +--R (3) - b x + - a b x + - a x +--R 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 238 + +--S 239 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 239 + +--S 240 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 240 + +)clear all + +--S 241 of 3330 +t0000:=x*(a+b*x)^2 +--R +--R +--R 2 3 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 241 + +--S 242 of 3330 +r0000:=1/2*a^2*x^2+2/3*a*b*x^3+1/4*b^2*x^4 +--R +--R +--R 1 2 4 2 3 1 2 2 +--R (2) - b x + - a b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 242 + +--S 243 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 4 2 3 1 2 2 +--R (3) - b x + - a b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 243 + +--S 244 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 244 + +--S 245 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 245 + +)clear all + +--S 246 of 3330 +t0000:=(a+b*x)^2 +--R +--R +--R 2 2 2 +--R (1) b x + 2a b x + a +--R Type: Polynomial(Integer) +--E 246 + +--S 247 of 3330 +r0000:=1/3*(a+b*x)^3/b +--R +--R +--R 1 3 3 2 2 2 1 3 +--R - b x + a b x + a b x + - a +--R 3 3 +--R (2) ------------------------------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 247 + +--S 248 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 3 2 2 +--R (3) - b x + a b x + a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 248 + +--S 249 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 3 +--R - a +--R 3 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 249 + +--S 250 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 250 + +)clear all + +--S 251 of 3330 +t0000:=(a+b*x)^2/x +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 3330 +r0000:=2*a*b*x+1/2*b^2*x^2+a^2*log(x) +--R +--R +--R 2 2 2 +--R 2a log(x) + b x + 4a b x +--R (2) ------------------------- +--R 2 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2a log(x) + b x + 4a b x +--R (3) ------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 3330 +t0000:=(a+b*x)^2/x^2 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 3330 +r0000:=-a^2/x+b^2*x+2*a*b*log(x) +--R +--R +--R 2 2 2 +--R 2a b x log(x) + b x - a +--R (2) ------------------------- +--R x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2a b x log(x) + b x - a +--R (3) ------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 3330 +t0000:=(a+b*x)^2/x^3 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 3330 +r0000:=-1/2*a^2/x^2-2*a*b/x+b^2*log(x) +--R +--R +--R 2 2 2 +--R 2b x log(x) - 4a b x - a +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2b x log(x) - 4a b x - a +--R (3) ------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 3330 +t0000:=(a+b*x)^2/x^4 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 3330 +r0000:=-1/3*(a+b*x)^3/(a*x^3) +--R +--R +--R 1 3 3 2 2 2 1 3 +--R - - b x - a b x - a b x - - a +--R 3 3 +--R (2) -------------------------------- +--R 3 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 3b x - 3a b x - a +--R (3) --------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 3 +--R b +--R (4) -- +--R 3a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 3330 +t0000:=(a+b*x)^2/x^5 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 3330 +r0000:=-1/4*a^2/x^4-2/3*a*b/x^3-1/2*b^2/x^2 +--R +--R +--R 1 2 2 2 1 2 +--R - - b x - - a b x - - a +--R 2 3 4 +--R (2) ------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 272 + +--S 273 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 6b x - 8a b x - 3a +--R (3) ---------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 3330 +t0000:=(a+b*x)^2/x^6 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 3330 +r0000:=-1/5*a^2/x^5-1/2*a*b/x^4-1/3*b^2/x^3 +--R +--R +--R 1 2 2 1 1 2 +--R - - b x - - a b x - - a +--R 3 2 5 +--R (2) ------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 277 + +--S 278 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 10b x - 15a b x - 6a +--R (3) ------------------------ +--R 5 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 3330 +t0000:=(a+b*x)^2/x^7 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 3330 +r0000:=-1/6*a^2/x^6-2/5*a*b/x^5-1/4*b^2/x^4 +--R +--R +--R 1 2 2 2 1 2 +--R - - b x - - a b x - - a +--R 4 5 6 +--R (2) ------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 282 + +--S 283 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 15b x - 24a b x - 10a +--R (3) ------------------------- +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 3330 +t0000:=(a+b*x)^2/x^8 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 3330 +r0000:=-1/7*a^2/x^7-1/3*a*b/x^6-1/5*b^2/x^5 +--R +--R +--R 1 2 2 1 1 2 +--R - - b x - - a b x - - a +--R 5 3 7 +--R (2) ------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 287 + +--S 288 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 21b x - 35a b x - 15a +--R (3) ------------------------- +--R 7 +--R 105x +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 3330 +t0000:=x^m*(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 291 + +--S 292 of 3330 +r0000:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(2+m)/(2+m)+3*a*b^2*x^(3+m)/_ + (3+m)+b^3*x^(4+m)/(4+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (3a b m + 24a b m + 57a b m + 36a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 9a m + 26a m + 24a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 3 3 +--R (3a b m + 24a b m + 57a b m + 36a b)x + (a m + 9a m + 26a m + 24a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 3 3 2 3 3 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 2 +--R (3a b m + 24a b m + 57a b m + 36a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 9a m + 26a m + 24a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 4 +--R (- b m - 6b m - 11b m - 6b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (- 3a b m - 21a b m - 42a b m - 24a b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (- 3a b m - 24a b m - 57a b m - 36a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 9a m - 26a m - 24a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 3330 +t0000:=x^3*(a+b*x)^3 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 296 + +--S 297 of 3330 +r0000:=1/4*a^3*x^4+3/5*a^2*b*x^5+1/2*a*b^2*x^6+1/7*b^3*x^7 +--R +--R +--R 1 3 7 1 2 6 3 2 5 1 3 4 +--R (2) - b x + - a b x + - a b x + - a x +--R 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 297 + +--S 298 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 7 1 2 6 3 2 5 1 3 4 +--R (3) - b x + - a b x + - a b x + - a x +--R 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 298 + +--S 299 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 299 + +--S 300 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 300 + +)clear all + +--S 301 of 3330 +t0000:=x^2*(a+b*x)^3 +--R +--R +--R 3 5 2 4 2 3 3 2 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 301 + +--S 302 of 3330 +r0000:=1/3*a^3*x^3+3/4*a^2*b*x^4+3/5*a*b^2*x^5+1/6*b^3*x^6 +--R +--R +--R 1 3 6 3 2 5 3 2 4 1 3 3 +--R (2) - b x + - a b x + - a b x + - a x +--R 6 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 302 + +--S 303 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 6 3 2 5 3 2 4 1 3 3 +--R (3) - b x + - a b x + - a b x + - a x +--R 6 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 303 + +--S 304 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 304 + +--S 305 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 305 + +)clear all + +--S 306 of 3330 +t0000:=x*(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 306 + +--S 307 of 3330 +r0000:=-1/4*a*(a+b*x)^4/b^2+1/5*(a+b*x)^5/b^2 +--R +--R +--R 1 5 5 3 4 4 2 3 3 1 3 2 2 1 5 +--R - b x + - a b x + a b x + - a b x - -- a +--R 5 4 2 20 +--R (2) --------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 307 + +--S 308 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 5 3 2 4 2 3 1 3 2 +--R (3) - b x + - a b x + a b x + - a x +--R 5 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 308 + +--S 309 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 5 +--R -- a +--R 20 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 309 + +--S 310 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 310 + +)clear all + +--S 311 of 3330 +t0000:=(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 311 + +--S 312 of 3330 +r0000:=1/4*(a+b*x)^4/b +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - b x + a b x + - a b x + a b x + - a +--R 4 2 4 +--R (2) ----------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 312 + +--S 313 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 4 2 3 3 2 2 3 +--R (3) - b x + a b x + - a b x + a x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 313 + +--S 314 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 4 +--R - a +--R 4 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 314 + +--S 315 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 315 + +)clear all + +--S 316 of 3330 +t0000:=(a+b*x)^3/x +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 3330 +r0000:=3*a^2*b*x+3/2*a*b^2*x^2+1/3*b^3*x^3+a^3*log(x) +--R +--R +--R 3 3 3 2 2 2 +--R 6a log(x) + 2b x + 9a b x + 18a b x +--R (2) ------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 3 2 2 2 +--R 6a log(x) + 2b x + 9a b x + 18a b x +--R (3) ------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 3330 +t0000:=(a+b*x)^3/x^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 3330 +r0000:=-a^3/x+3*a*b^2*x+1/2*b^3*x^2+3*a^2*b*log(x) +--R +--R +--R 2 3 3 2 2 3 +--R 6a b x log(x) + b x + 6a b x - 2a +--R (2) ------------------------------------ +--R 2x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 3 2 2 3 +--R 6a b x log(x) + b x + 6a b x - 2a +--R (3) ------------------------------------ +--R 2x +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 3330 +t0000:=(a+b*x)^3/x^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 3330 +r0000:=-1/2*a^3/x^2-3*a^2*b/x+b^3*x+3*a*b^2*log(x) +--R +--R +--R 2 2 3 3 2 3 +--R 6a b x log(x) + 2b x - 6a b x - a +--R (2) ----------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 3 3 2 3 +--R 6a b x log(x) + 2b x - 6a b x - a +--R (3) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 3330 +t0000:=(a+b*x)^3/x^4 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 3330 +r0000:=-1/3*a^3/x^3-3/2*a^2*b/x^2-3*a*b^2/x+b^3*log(x) +--R +--R +--R 3 3 2 2 2 3 +--R 6b x log(x) - 18a b x - 9a b x - 2a +--R (2) ------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 332 + +--S 333 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 6b x log(x) - 18a b x - 9a b x - 2a +--R (3) ------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 3330 +t0000:=(a+b*x)^3/x^5 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 3330 +r0000:=-1/4*(a+b*x)^4/(a*x^4) +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - - b x - a b x - - a b x - a b x - - a +--R 4 2 4 +--R (2) ------------------------------------------- +--R 4 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 337 + +--S 338 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 4b x - 6a b x - 4a b x - a +--R (3) ------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 4 +--R b +--R (4) -- +--R 4a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 3330 +t0000:=(a+b*x)^3/x^6 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 3330 +r0000:=-1/5*a^3/x^5-3/4*a^2*b/x^4-a*b^2/x^3-1/2*b^3/x^2 +--R +--R +--R 1 3 3 2 2 3 2 1 3 +--R - - b x - a b x - - a b x - - a +--R 2 4 5 +--R (2) ---------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 342 + +--S 343 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 10b x - 20a b x - 15a b x - 4a +--R (3) ----------------------------------- +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 3330 +t0000:=(a+b*x)^3/x^7 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 3330 +r0000:=-1/6*a^3/x^6-3/5*a^2*b/x^5-3/4*a*b^2/x^4-1/3*b^3/x^3 +--R +--R +--R 1 3 3 3 2 2 3 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 3 4 5 6 +--R (2) ------------------------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 347 + +--S 348 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 20b x - 45a b x - 36a b x - 10a +--R (3) ------------------------------------ +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 3330 +t0000:=(a+b*x)^3/x^8 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 3330 +r0000:=-1/7*a^3/x^7-1/2*a^2*b/x^6-3/5*a*b^2/x^5-1/4*b^3/x^4 +--R +--R +--R 1 3 3 3 2 2 1 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 4 5 2 7 +--R (2) ------------------------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 352 + +--S 353 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 35b x - 84a b x - 70a b x - 20a +--R (3) ------------------------------------ +--R 7 +--R 140x +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 3330 +t0000:=x^m*(a+b*x)^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 m +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a )x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 3330 +r0000:=a^7*x^(1+m)/(1+m)+7*a^6*b*x^(2+m)/(2+m)+_ + 21*a^5*b^2*x^(3+m)/(3+m)+35*a^4*b^3*x^(4+m)/(4+m)+_ + 35*a^3*b^4*x^(5+m)/(5+m)+21*a^2*b^5*x^(6+m)/(6+m)+_ + 7*a*b^6*x^(7+m)/(7+m)+b^7*x^(8+m)/(8+m) +--R +--R +--R (2) +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m + 13068b m +--R + +--R 7 +--R 5040b +--R * +--R m + 8 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 203a b m + 2401a b m + 14945a b m + 52528a b m +--R + +--R 6 2 6 6 +--R 103292a b m + 103824a b m + 40320a b +--R * +--R m + 7 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R 21a b m + 630a b m + 7686a b m + 49140a b m + 176589a b m +--R + +--R 2 5 2 2 5 2 5 +--R 353430a b m + 360024a b m + 141120a b +--R * +--R m + 6 +--R x +--R + +--R 3 4 7 3 4 6 3 4 5 3 4 4 3 4 3 +--R 35a b m + 1085a b m + 13685a b m + 90335a b m + 334040a b m +--R + +--R 3 4 2 3 4 3 4 +--R 684740a b m + 710640a b m + 282240a b +--R * +--R m + 5 +--R x +--R + +--R 4 3 7 4 3 6 4 3 5 4 3 4 4 3 3 +--R 35a b m + 1120a b m + 14630a b m + 100240a b m + 384755a b m +--R + +--R 4 3 2 4 3 4 3 +--R 815920a b m + 870660a b m + 352800a b +--R * +--R m + 4 +--R x +--R + +--R 5 2 7 5 2 6 5 2 5 5 2 4 5 2 3 +--R 21a b m + 693a b m + 9387a b m + 67095a b m + 270144a b m +--R + +--R 5 2 2 5 2 5 2 +--R 602532a b m + 673008a b m + 282240a b +--R * +--R m + 3 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 238a b m + 3346a b m + 25060a b m + 107023a b m +--R + +--R 6 2 6 6 +--R 256942a b m + 312984a b m + 141120a b +--R * +--R m + 2 +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R a m + 35a m + 511a m + 4025a m + 18424a m + 48860a m + 69264a m +--R + +--R 7 +--R 40320a +--R * +--R m + 1 +--R x +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m +--R + +--R 7 7 +--R 13068b m + 5040b +--R * +--R 8 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 203a b m + 2401a b m + 14945a b m + 52528a b m +--R + +--R 6 2 6 6 +--R 103292a b m + 103824a b m + 40320a b +--R * +--R 7 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R 21a b m + 630a b m + 7686a b m + 49140a b m + 176589a b m +--R + +--R 2 5 2 2 5 2 5 +--R 353430a b m + 360024a b m + 141120a b +--R * +--R 6 +--R x +--R + +--R 3 4 7 3 4 6 3 4 5 3 4 4 3 4 3 +--R 35a b m + 1085a b m + 13685a b m + 90335a b m + 334040a b m +--R + +--R 3 4 2 3 4 3 4 +--R 684740a b m + 710640a b m + 282240a b +--R * +--R 5 +--R x +--R + +--R 4 3 7 4 3 6 4 3 5 4 3 4 4 3 3 +--R 35a b m + 1120a b m + 14630a b m + 100240a b m + 384755a b m +--R + +--R 4 3 2 4 3 4 3 +--R 815920a b m + 870660a b m + 352800a b +--R * +--R 4 +--R x +--R + +--R 5 2 7 5 2 6 5 2 5 5 2 4 5 2 3 +--R 21a b m + 693a b m + 9387a b m + 67095a b m + 270144a b m +--R + +--R 5 2 2 5 2 5 2 +--R 602532a b m + 673008a b m + 282240a b +--R * +--R 3 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 238a b m + 3346a b m + 25060a b m + 107023a b m +--R + +--R 6 2 6 6 +--R 256942a b m + 312984a b m + 141120a b +--R * +--R 2 +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a m + 35a m + 511a m + 4025a m + 18424a m + 48860a m +--R + +--R 7 7 +--R 69264a m + 40320a +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m +--R + +--R 7 7 +--R 13068b m + 5040b +--R * +--R 8 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 203a b m + 2401a b m + 14945a b m + 52528a b m +--R + +--R 6 2 6 6 +--R 103292a b m + 103824a b m + 40320a b +--R * +--R 7 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R 21a b m + 630a b m + 7686a b m + 49140a b m + 176589a b m +--R + +--R 2 5 2 2 5 2 5 +--R 353430a b m + 360024a b m + 141120a b +--R * +--R 6 +--R x +--R + +--R 3 4 7 3 4 6 3 4 5 3 4 4 3 4 3 +--R 35a b m + 1085a b m + 13685a b m + 90335a b m + 334040a b m +--R + +--R 3 4 2 3 4 3 4 +--R 684740a b m + 710640a b m + 282240a b +--R * +--R 5 +--R x +--R + +--R 4 3 7 4 3 6 4 3 5 4 3 4 4 3 3 +--R 35a b m + 1120a b m + 14630a b m + 100240a b m + 384755a b m +--R + +--R 4 3 2 4 3 4 3 +--R 815920a b m + 870660a b m + 352800a b +--R * +--R 4 +--R x +--R + +--R 5 2 7 5 2 6 5 2 5 5 2 4 5 2 3 +--R 21a b m + 693a b m + 9387a b m + 67095a b m + 270144a b m +--R + +--R 5 2 2 5 2 5 2 +--R 602532a b m + 673008a b m + 282240a b +--R * +--R 3 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 238a b m + 3346a b m + 25060a b m + 107023a b m +--R + +--R 6 2 6 6 +--R 256942a b m + 312984a b m + 141120a b +--R * +--R 2 +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a m + 35a m + 511a m + 4025a m + 18424a m + 48860a m +--R + +--R 7 7 +--R 69264a m + 40320a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R - b m - 28b m - 322b m - 1960b m - 6769b m - 13132b m +--R + +--R 7 7 +--R - 13068b m - 5040b +--R * +--R m + 8 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R - 7a b m - 203a b m - 2401a b m - 14945a b m - 52528a b m +--R + +--R 6 2 6 6 +--R - 103292a b m - 103824a b m - 40320a b +--R * +--R m + 7 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R - 21a b m - 630a b m - 7686a b m - 49140a b m - 176589a b m +--R + +--R 2 5 2 2 5 2 5 +--R - 353430a b m - 360024a b m - 141120a b +--R * +--R m + 6 +--R x +--R + +--R 3 4 7 3 4 6 3 4 5 3 4 4 3 4 3 +--R - 35a b m - 1085a b m - 13685a b m - 90335a b m - 334040a b m +--R + +--R 3 4 2 3 4 3 4 +--R - 684740a b m - 710640a b m - 282240a b +--R * +--R m + 5 +--R x +--R + +--R 4 3 7 4 3 6 4 3 5 4 3 4 4 3 3 +--R - 35a b m - 1120a b m - 14630a b m - 100240a b m - 384755a b m +--R + +--R 4 3 2 4 3 4 3 +--R - 815920a b m - 870660a b m - 352800a b +--R * +--R m + 4 +--R x +--R + +--R 5 2 7 5 2 6 5 2 5 5 2 4 5 2 3 +--R - 21a b m - 693a b m - 9387a b m - 67095a b m - 270144a b m +--R + +--R 5 2 2 5 2 5 2 +--R - 602532a b m - 673008a b m - 282240a b +--R * +--R m + 3 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R - 7a b m - 238a b m - 3346a b m - 25060a b m - 107023a b m +--R + +--R 6 2 6 6 +--R - 256942a b m - 312984a b m - 141120a b +--R * +--R m + 2 +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R - a m - 35a m - 511a m - 4025a m - 18424a m - 48860a m +--R + +--R 7 7 +--R - 69264a m - 40320a +--R * +--R m + 1 +--R x +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 3330 +t0000:=x^7*(a+b*x)^7 +--R +--R +--R (1) +--R 7 14 6 13 2 5 12 3 4 11 4 3 10 5 2 9 6 8 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 7 +--R a x +--R Type: Polynomial(Integer) +--E 361 + +--S 362 of 3330 +r0000:=1/8*a^7*x^8+7/9*a^6*b*x^9+21/10*a^5*b^2*x^10+35/11*a^4*b^3*x^11+_ + 35/12*a^3*b^4*x^12+21/13*a^2*b^5*x^13+1/2*a*b^6*x^14+1/15*b^7*x^15 +--R +--R +--R (2) +--R 1 7 15 1 6 14 21 2 5 13 35 3 4 12 35 4 3 11 21 5 2 10 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 15 2 13 12 11 10 +--R + +--R 7 6 9 1 7 8 +--R - a b x + - a x +--R 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 362 + +--S 363 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 15 1 6 14 21 2 5 13 35 3 4 12 35 4 3 11 21 5 2 10 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 15 2 13 12 11 10 +--R + +--R 7 6 9 1 7 8 +--R - a b x + - a x +--R 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 363 + +--S 364 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 364 + +--S 365 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 365 + +)clear all + +--S 366 of 3330 +t0000:=x^6*(a+b*x)^7 +--R +--R +--R (1) +--R 7 13 6 12 2 5 11 3 4 10 4 3 9 5 2 8 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 6 +--R a x +--R Type: Polynomial(Integer) +--E 366 + +--S 367 of 3330 +r0000:=1/7*a^7*x^7+7/8*a^6*b*x^8+7/3*a^5*b^2*x^9+7/2*a^4*b^3*x^10+_ + 35/11*a^3*b^4*x^11+7/4*a^2*b^5*x^12+7/13*a*b^6*x^13+1/14*b^7*x^14 +--R +--R +--R (2) +--R 1 7 14 7 6 13 7 2 5 12 35 3 4 11 7 4 3 10 7 5 2 9 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x + - a b x +--R 14 13 4 11 2 3 +--R + +--R 7 6 8 1 7 7 +--R - a b x + - a x +--R 8 7 +--R Type: Polynomial(Fraction(Integer)) +--E 367 + +--S 368 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 14 7 6 13 7 2 5 12 35 3 4 11 7 4 3 10 7 5 2 9 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x + - a b x +--R 14 13 4 11 2 3 +--R + +--R 7 6 8 1 7 7 +--R - a b x + - a x +--R 8 7 +--R Type: Polynomial(Fraction(Integer)) +--E 368 + +--S 369 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 369 + +--S 370 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 370 + +)clear all + +--S 371 of 3330 +t0000:=x^5*(a+b*x)^7 +--R +--R +--R (1) +--R 7 12 6 11 2 5 10 3 4 9 4 3 8 5 2 7 6 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 5 +--R a x +--R Type: Polynomial(Integer) +--E 371 + +--S 372 of 3330 +r0000:=1/6*a^7*x^6+a^6*b*x^7+21/8*a^5*b^2*x^8+35/9*a^4*b^3*x^9+_ + 7/2*a^3*b^4*x^10+21/11*a^2*b^5*x^11+7/12*a*b^6*x^12+1/13*b^7*x^13 +--R +--R +--R (2) +--R 1 7 13 7 6 12 21 2 5 11 7 3 4 10 35 4 3 9 21 5 2 8 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 13 12 11 2 9 8 +--R + +--R 6 7 1 7 6 +--R a b x + - a x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 372 + +--S 373 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 13 7 6 12 21 2 5 11 7 3 4 10 35 4 3 9 21 5 2 8 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 13 12 11 2 9 8 +--R + +--R 6 7 1 7 6 +--R a b x + - a x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 373 + +--S 374 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 374 + +--S 375 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 375 + +)clear all + +--S 376 of 3330 +t0000:=x^4*(a+b*x)^7 +--R +--R +--R (1) +--R 7 11 6 10 2 5 9 3 4 8 4 3 7 5 2 6 6 5 7 4 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 376 + +--S 377 of 3330 +r0000:=1/8*a^4*(a+b*x)^8/b^5-4/9*a^3*(a+b*x)^9/b^5+_ + 3/5*a^2*(a+b*x)^10/b^5-4/11*a*(a+b*x)^11/b^5+1/12*(a+b*x)^12/b^5 +--R +--R +--R (2) +--R 1 12 12 7 11 11 21 2 10 10 35 3 9 9 35 4 8 8 5 7 7 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 3a b x +--R 12 11 10 9 8 +--R + +--R 7 6 6 6 1 7 5 5 1 12 +--R - a b x + - a b x + ---- a +--R 6 5 3960 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 377 + +--S 378 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 12 7 6 11 21 2 5 10 35 3 4 9 35 4 3 8 5 2 7 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 3a b x +--R 12 11 10 9 8 +--R + +--R 7 6 6 1 7 5 +--R - a b x + - a x +--R 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 378 + +--S 379 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 12 +--R ---- a +--R 3960 +--R (4) - -------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 379 + +--S 380 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 380 + +)clear all + +--S 381 of 3330 +t0000:=x^3*(a+b*x)^7 +--R +--R +--R (1) +--R 7 10 6 9 2 5 8 3 4 7 4 3 6 5 2 5 6 4 7 3 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 381 + +--S 382 of 3330 +r0000:=-1/8*a^3*(a+b*x)^8/b^4+1/3*a^2*(a+b*x)^9/b^4-_ + 3/10*a*(a+b*x)^10/b^4+1/11*(a+b*x)^11/b^4 +--R +--R +--R (2) +--R 1 11 11 7 10 10 7 2 9 9 35 3 8 8 4 7 7 7 5 6 6 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + - a b x +--R 11 10 3 8 2 +--R + +--R 7 6 5 5 1 7 4 4 1 11 +--R - a b x + - a b x - ---- a +--R 5 4 1320 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 382 + +--S 383 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 11 7 6 10 7 2 5 9 35 3 4 8 4 3 7 7 5 2 6 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + - a b x +--R 11 10 3 8 2 +--R + +--R 7 6 5 1 7 4 +--R - a b x + - a x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 383 + +--S 384 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 11 +--R ---- a +--R 1320 +--R (4) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 384 + +--S 385 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 385 + +)clear all + +--S 386 of 3330 +t0000:=x^2*(a+b*x)^7 +--R +--R +--R (1) +--R 7 9 6 8 2 5 7 3 4 6 4 3 5 5 2 4 6 3 7 2 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 386 + +--S 387 of 3330 +r0000:=1/8*a^2*(a+b*x)^8/b^3-2/9*a*(a+b*x)^9/b^3+1/10*(a+b*x)^10/b^3 +--R +--R +--R (2) +--R 1 10 10 7 9 9 21 2 8 8 3 7 7 35 4 6 6 21 5 5 5 +--R -- b x + - a b x + -- a b x + 5a b x + -- a b x + -- a b x +--R 10 9 8 6 5 +--R + +--R 7 6 4 4 1 7 3 3 1 10 +--R - a b x + - a b x + --- a +--R 4 3 360 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 387 + +--S 388 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 10 7 6 9 21 2 5 8 3 4 7 35 4 3 6 21 5 2 5 +--R -- b x + - a b x + -- a b x + 5a b x + -- a b x + -- a b x +--R 10 9 8 6 5 +--R + +--R 7 6 4 1 7 3 +--R - a b x + - a x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 388 + +--S 389 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 10 +--R --- a +--R 360 +--R (4) - ------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 389 + +--S 390 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 390 + +)clear all + +--S 391 of 3330 +t0000:=x*(a+b*x)^7 +--R +--R +--R (1) +--R 7 8 6 7 2 5 6 3 4 5 4 3 4 5 2 3 6 2 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 391 + +--S 392 of 3330 +r0000:=-1/8*a*(a+b*x)^8/b^2+1/9*(a+b*x)^9/b^2 +--R +--R +--R (2) +--R 1 9 9 7 8 8 2 7 7 35 3 6 6 4 5 5 21 5 4 4 7 6 3 3 +--R - b x + - a b x + 3a b x + -- a b x + 7a b x + -- a b x + - a b x +--R 9 8 6 4 3 +--R + +--R 1 7 2 2 1 9 +--R - a b x - -- a +--R 2 72 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 392 + +--S 393 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 9 7 6 8 2 5 7 35 3 4 6 4 3 5 21 5 2 4 7 6 3 +--R - b x + - a b x + 3a b x + -- a b x + 7a b x + -- a b x + - a b x +--R 9 8 6 4 3 +--R + +--R 1 7 2 +--R - a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 393 + +--S 394 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 9 +--R -- a +--R 72 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 394 + +--S 395 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 395 + +)clear all + +--S 396 of 3330 +t0000:=(a+b*x)^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Polynomial(Integer) +--E 396 + +--S 397 of 3330 +r0000:=1/8*(a+b*x)^8/b +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R a b x + - a +--R 8 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 397 + +--S 398 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 3 4 5 2 3 7 6 2 7 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x + a x +--R 8 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 398 + +--S 399 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 8 +--R - a +--R 8 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 399 + +--S 400 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 400 + +)clear all + +--S 401 of 3330 +t0000:=(a+b*x)^7/x +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 3330 +r0000:=7*a^6*b*x+21/2*a^5*b^2*x^2+35/3*a^4*b^3*x^3+35/4*a^3*b^4*x^4+_ + 21/5*a^2*b^5*x^5+7/6*a*b^6*x^6+1/7*b^7*x^7+a^7*log(x) +--R +--R +--R (2) +--R 7 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a log(x) + 60b x + 490a b x + 1764a b x + 3675a b x + 4900a b x +--R + +--R 5 2 2 6 +--R 4410a b x + 2940a b x +--R / +--R 420 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a log(x) + 60b x + 490a b x + 1764a b x + 3675a b x + 4900a b x +--R + +--R 5 2 2 6 +--R 4410a b x + 2940a b x +--R / +--R 420 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 3330 +t0000:=(a+b*x)^7/x^2 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 3330 +r0000:=-a^7/x+21*a^5*b^2*x+35/2*a^4*b^3*x^2+35/3*a^3*b^4*x^3+_ + 21/4*a^2*b^5*x^4+7/5*a*b^6*x^5+1/6*b^7*x^6+7*a^6*b*log(x) +--R +--R +--R (2) +--R 6 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 10b x + 84a b x + 315a b x + 700a b x + 1050a b x +--R + +--R 5 2 2 7 +--R 1260a b x - 60a +--R / +--R 60x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 10b x + 84a b x + 315a b x + 700a b x + 1050a b x +--R + +--R 5 2 2 7 +--R 1260a b x - 60a +--R / +--R 60x +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 3330 +t0000:=(a+b*x)^7/x^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 3330 +r0000:=-1/2*a^7/x^2-7*a^6*b/x+35*a^4*b^3*x+35/2*a^3*b^4*x^2+7*a^2*b^5*x^3+_ + 7/4*a*b^6*x^4+1/5*b^7*x^5+21*a^5*b^2*log(x) +--R +--R +--R (2) +--R 5 2 2 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 4b x + 35a b x + 140a b x + 350a b x + 700a b x +--R + +--R 6 7 +--R - 140a b x - 10a +--R / +--R 2 +--R 20x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 2 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 4b x + 35a b x + 140a b x + 350a b x + 700a b x +--R + +--R 6 7 +--R - 140a b x - 10a +--R / +--R 2 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 3330 +t0000:=(a+b*x)^7/x^4 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 3330 +r0000:=-1/3*a^7/x^3-7/2*a^6*b/x^2-21*a^5*b^2/x+35*a^3*b^4*x+21/2*a^2*b^5*x^2+_ + 7/3*a*b^6*x^3+1/4*b^7*x^4+35*a^4*b^3*log(x) +--R +--R +--R (2) +--R 4 3 3 7 7 6 6 2 5 5 3 4 4 5 2 2 +--R 420a b x log(x) + 3b x + 28a b x + 126a b x + 420a b x - 252a b x +--R + +--R 6 7 +--R - 42a b x - 4a +--R / +--R 3 +--R 12x +--R Type: Expression(Integer) +--E 417 + +--S 418 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 7 7 6 6 2 5 5 3 4 4 5 2 2 +--R 420a b x log(x) + 3b x + 28a b x + 126a b x + 420a b x - 252a b x +--R + +--R 6 7 +--R - 42a b x - 4a +--R / +--R 3 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 3330 +t0000:=(a+b*x)^7/x^5 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 3330 +r0000:=-1/4*a^7/x^4-7/3*a^6*b/x^3-21/2*a^5*b^2/x^2-35*a^4*b^3/x+_ + 21*a^2*b^5*x+7/2*a*b^6*x^2+1/3*b^7*x^3+35*a^3*b^4*log(x) +--R +--R +--R (2) +--R 3 4 4 7 7 6 6 2 5 5 4 3 3 5 2 2 +--R 420a b x log(x) + 4b x + 42a b x + 252a b x - 420a b x - 126a b x +--R + +--R 6 7 +--R - 28a b x - 3a +--R / +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 4 7 7 6 6 2 5 5 4 3 3 5 2 2 +--R 420a b x log(x) + 4b x + 42a b x + 252a b x - 420a b x - 126a b x +--R + +--R 6 7 +--R - 28a b x - 3a +--R / +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 3330 +t0000:=(a+b*x)^7/x^6 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 3330 +r0000:=-1/5*a^7/x^5-7/4*a^6*b/x^4-7*a^5*b^2/x^3-35/2*a^4*b^3/x^2-_ + 35*a^3*b^4/x+7*a*b^6*x+1/2*b^7*x^2+21*a^2*b^5*log(x) +--R +--R +--R (2) +--R 2 5 5 7 7 6 6 3 4 4 4 3 3 5 2 2 +--R 420a b x log(x) + 10b x + 140a b x - 700a b x - 350a b x - 140a b x +--R + +--R 6 7 +--R - 35a b x - 4a +--R / +--R 5 +--R 20x +--R Type: Expression(Integer) +--E 427 + +--S 428 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 5 5 7 7 6 6 3 4 4 4 3 3 5 2 2 +--R 420a b x log(x) + 10b x + 140a b x - 700a b x - 350a b x - 140a b x +--R + +--R 6 7 +--R - 35a b x - 4a +--R / +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 3330 +t0000:=(a+b*x)^7/x^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 3330 +r0000:=-1/6*a^7/x^6-7/5*a^6*b/x^5-21/4*a^5*b^2/x^4-35/3*a^4*b^3/x^3-_ + 35/2*a^3*b^4/x^2-21*a^2*b^5/x+b^7*x+7*a*b^6*log(x) +--R +--R +--R (2) +--R 6 6 7 7 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 60b x - 1260a b x - 1050a b x - 700a b x +--R + +--R 5 2 2 6 7 +--R - 315a b x - 84a b x - 10a +--R / +--R 6 +--R 60x +--R Type: Expression(Integer) +--E 432 + +--S 433 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 7 7 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 60b x - 1260a b x - 1050a b x - 700a b x +--R + +--R 5 2 2 6 7 +--R - 315a b x - 84a b x - 10a +--R / +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 3330 +t0000:=(a+b*x)^7/x^8 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 3330 +r0000:=-1/7*a^7/x^7-7/6*a^6*b/x^6-21/5*a^5*b^2/x^5-35/4*a^4*b^3/x^4-_ + 35/3*a^3*b^4/x^3-21/2*a^2*b^5/x^2-7*a*b^6/x+b^7*log(x) +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420b x log(x) - 2940a b x - 4410a b x - 4900a b x - 3675a b x +--R + +--R 5 2 2 6 7 +--R - 1764a b x - 490a b x - 60a +--R / +--R 7 +--R 420x +--R Type: Expression(Integer) +--E 437 + +--S 438 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420b x log(x) - 2940a b x - 4410a b x - 4900a b x - 3675a b x +--R + +--R 5 2 2 6 7 +--R - 1764a b x - 490a b x - 60a +--R / +--R 7 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 3330 +t0000:=(a+b*x)^7/x^9 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 3330 +r0000:=-1/8*(a+b*x)^8/(a*x^8) +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - - b x - a b x - - a b x - 7a b x - -- a b x - 7a b x - - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R - a b x - - a +--R 8 +--R / +--R 8 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 442 + +--S 443 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - 8b x - 28a b x - 56a b x - 70a b x - 56a b x - 28a b x - 8a b x - a +--R ---------------------------------------------------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 8 +--R b +--R (4) -- +--R 8a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 3330 +t0000:=(a+b*x)^7/x^10 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 3330 +r0000:=-1/9*(a+b*x)^8/(a*x^9)+1/72*b*(a+b*x)^8/(a^2*x^8) +--R +--R +--R (2) +--R 1 9 9 1 2 7 7 7 3 6 6 21 4 5 5 5 4 4 35 6 3 3 7 2 2 +--R -- b x - - a b x - - a b x - -- a b x - 7a b x - -- a b x - 3a b x +--R 72 2 3 4 6 +--R + +--R 7 8 1 9 +--R - - a b x - - a +--R 8 9 +--R / +--R 2 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 447 + +--S 448 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 36b x - 168a b x - 378a b x - 504a b x - 420a b x - 216a b x +--R + +--R 6 7 +--R - 63a b x - 8a +--R / +--R 9 +--R 72x +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R b +--R (4) - ---- +--R 2 +--R 72a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 3330 +t0000:=(a+b*x)^7/x^11 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 3330 +r0000:=-1/10*(a+b*x)^8/(a*x^10)+1/45*b*(a+b*x)^8/(a^2*x^9)-_ + 1/360*b^2*(a+b*x)^8/(a^3*x^8) +--R +--R +--R (2) +--R 1 10 10 1 3 7 7 7 4 6 6 21 5 5 5 35 6 4 4 7 3 3 +--R - --- b x - - a b x - - a b x - -- a b x - -- a b x - 5a b x +--R 360 3 4 5 6 +--R + +--R 21 8 2 2 7 9 1 10 +--R - -- a b x - - a b x - -- a +--R 8 9 10 +--R / +--R 3 10 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 452 + +--S 453 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 120b x - 630a b x - 1512a b x - 2100a b x - 1800a b x - 945a b x +--R + +--R 6 7 +--R - 280a b x - 36a +--R / +--R 10 +--R 360x +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 10 +--R b +--R (4) ----- +--R 3 +--R 360a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 3330 +t0000:=(a+b*x)^7/x^12 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 3330 +r0000:=-1/11*(a+b*x)^8/(a*x^11)+3/110*b*(a+b*x)^8/(a^2*x^10)-_ + 1/165*b^2*(a+b*x)^8/(a^3*x^9)+1/1320*b^3*(a+b*x)^8/(a^4*x^8) +--R +--R +--R (2) +--R 1 11 11 1 4 7 7 7 5 6 6 7 6 5 5 7 4 4 35 8 3 3 +--R ---- b x - - a b x - - a b x - - a b x - 5a b x - -- a b x +--R 1320 4 5 2 8 +--R + +--R 7 9 2 2 7 10 1 11 +--R - - a b x - -- a b x - -- a +--R 3 10 11 +--R / +--R 4 11 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 457 + +--S 458 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 330b x - 1848a b x - 4620a b x - 6600a b x - 5775a b x +--R + +--R 5 2 2 6 7 +--R - 3080a b x - 924a b x - 120a +--R / +--R 11 +--R 1320x +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 11 +--R b +--R (4) - ------ +--R 4 +--R 1320a +--R Type: Expression(Integer) +--E 459 + +--S 460 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 3330 +t0000:=(a+b*x)^7/x^13 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 3330 +r0000:=-1/12*a^7/x^12-7/11*a^6*b/x^11-21/10*a^5*b^2/x^10-35/9*a^4*b^3/x^9-_ + 35/8*a^3*b^4/x^8-3*a^2*b^5/x^7-7/6*a*b^6/x^6-1/5*b^7/x^5 +--R +--R +--R (2) +--R 1 7 7 7 6 6 2 5 5 35 3 4 4 35 4 3 3 21 5 2 2 +--R - - b x - - a b x - 3a b x - -- a b x - -- a b x - -- a b x +--R 5 6 8 9 10 +--R + +--R 7 6 1 7 +--R - -- a b x - -- a +--R 11 12 +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 462 + +--S 463 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 792b x - 4620a b x - 11880a b x - 17325a b x - 15400a b x +--R + +--R 5 2 2 6 7 +--R - 8316a b x - 2520a b x - 330a +--R / +--R 12 +--R 3960x +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 3330 +t0000:=(a+b*x)^7/x^14 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 3330 +r0000:=-1/13*a^7/x^13-7/12*a^6*b/x^12-21/11*a^5*b^2/x^11-7/2*a^4*b^3/x^10-_ + 35/9*a^3*b^4/x^9-21/8*a^2*b^5/x^8-a*b^6/x^7-1/6*b^7/x^6 +--R +--R +--R (2) +--R 1 7 7 6 6 21 2 5 5 35 3 4 4 7 4 3 3 21 5 2 2 +--R - - b x - a b x - -- a b x - -- a b x - - a b x - -- a b x +--R 6 8 9 2 11 +--R + +--R 7 6 1 7 +--R - -- a b x - -- a +--R 12 13 +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 467 + +--S 468 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 1716b x - 10296a b x - 27027a b x - 40040a b x - 36036a b x +--R + +--R 5 2 2 6 7 +--R - 19656a b x - 6006a b x - 792a +--R / +--R 13 +--R 10296x +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 3330 +t0000:=(a+b*x)^7/x^15 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 3330 +r0000:=-1/14*a^7/x^14-7/13*a^6*b/x^13-7/4*a^5*b^2/x^12-35/11*a^4*b^3/x^11-_ + 7/2*a^3*b^4/x^10-7/3*a^2*b^5/x^9-7/8*a*b^6/x^8-1/7*b^7/x^7 +--R +--R +--R (2) +--R 1 7 7 7 6 6 7 2 5 5 7 3 4 4 35 4 3 3 7 5 2 2 +--R - - b x - - a b x - - a b x - - a b x - -- a b x - - a b x +--R 7 8 3 2 11 4 +--R + +--R 7 6 1 7 +--R - -- a b x - -- a +--R 13 14 +--R / +--R 14 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 3432b x - 21021a b x - 56056a b x - 84084a b x - 76440a b x +--R + +--R 5 2 2 6 7 +--R - 42042a b x - 12936a b x - 1716a +--R / +--R 14 +--R 24024x +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 3330 +t0000:=(a+b*x)^7/x^16 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 3330 +r0000:=-1/15*a^7/x^15-1/2*a^6*b/x^14-21/13*a^5*b^2/x^13-35/12*a^4*b^3/x^12-_ + 35/11*a^3*b^4/x^11-21/10*a^2*b^5/x^10-7/9*a*b^6/x^9-1/8*b^7/x^8 +--R +--R +--R (2) +--R 1 7 7 7 6 6 21 2 5 5 35 3 4 4 35 4 3 3 21 5 2 2 +--R - - b x - - a b x - -- a b x - -- a b x - -- a b x - -- a b x +--R 8 9 10 11 12 13 +--R + +--R 1 6 1 7 +--R - - a b x - -- a +--R 2 15 +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 477 + +--S 478 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 6435b x - 40040a b x - 108108a b x - 163800a b x - 150150a b x +--R + +--R 5 2 2 6 7 +--R - 83160a b x - 25740a b x - 3432a +--R / +--R 15 +--R 51480x +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 3330 +t0000:=x^m*(a+b*x)^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 481 + +--S 482 of 3330 +r0000:=a^10*x^(1+m)/(1+m)+10*a^9*b*x^(2+m)/(2+m)+45*a^8*b^2*x^(3+m)/(3+m)+_ + 120*a^7*b^3*x^(4+m)/(4+m)+210*a^6*b^4*x^(5+m)/(5+m)+_ + 252*a^5*b^5*x^(6+m)/(6+m)+210*a^4*b^6*x^(7+m)/(7+m)+_ + 120*a^3*b^7*x^(8+m)/(8+m)+45*a^2*b^8*x^(9+m)/(9+m)+_ + 10*a*b^9*x^(10+m)/(10+m)+b^10*x^(11+m)/(11+m) +--R +--R +--R (2) +--R 10 10 10 9 10 8 10 7 10 6 10 5 +--R b m + 55b m + 1320b m + 18150b m + 157773b m + 902055b m +--R + +--R 10 4 10 3 10 2 10 10 +--R 3416930b m + 8409500b m + 12753576b m + 10628640b m + 3628800b +--R * +--R m + 11 +--R x +--R + +--R 9 10 9 9 9 8 9 7 9 6 +--R 10a b m + 560a b m + 13650a b m + 190200a b m + 1672230a b m +--R + +--R 9 5 9 4 9 3 9 2 +--R 9653280a b m + 36862550a b m + 91331800a b m + 139262760a b m +--R + +--R 9 9 +--R 116552160a b m + 39916800a b +--R * +--R m + 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+ 355598730a b m + 1003011660a b m +--R + +--R 8 2 2 8 2 8 2 +--R 1727578440a b m + 1608573600a b m + 598752000a b +--R * +--R m + 3 +--R x +--R + +--R 9 10 9 9 9 8 9 7 9 6 +--R 10a b m + 640a b m + 17970a b m + 290760a b m + 2992710a b m +--R + +--R 9 5 9 4 9 3 9 2 +--R 20390160a b m + 92615030a b m + 274727240a b m + 503126280a b m +--R + +--R 9 9 +--R 502927200a b m + 199584000a b +--R * +--R m + 2 +--R x +--R + +--R 10 10 10 9 10 8 10 7 10 6 +--R a m + 65a m + 1860a m + 30810a m + 326613a m +--R + +--R 10 5 10 4 10 3 10 2 +--R 2310945a m + 11028590a m + 34967140a m + 70290936a m +--R + +--R 10 10 +--R 80627040a m + 39916800a +--R * +--R m + 1 +--R x +--R / +--R 11 10 9 8 7 6 5 +--R m + 66m + 1925m + 32670m + 357423m + 2637558m + 13339535m +--R + +--R 4 3 2 +--R 45995730m + 105258076m + 150917976m + 120543840m + 39916800 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 8 10 7 10 6 +--R b m + 55b m + 1320b m + 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6 2 4 6 +--R - 2581262040a b m - 4035361680a b m - 3445243200a b m +--R + +--R 4 6 +--R - 1197504000a b +--R * +--R m + 7 +--R x +--R + +--R 5 5 10 5 5 9 5 5 8 5 5 7 +--R - 252a b m - 15120a b m - 394380a b m - 5866560a b m +--R + +--R 5 5 6 5 5 5 5 5 4 +--R - 54871236a b m - 335437200a b m - 1348939620a b m +--R + +--R 5 5 3 5 5 2 5 5 +--R - 3497286240a b m - 5541317712a b m - 4783423680a b m +--R + +--R 5 5 +--R - 1676505600a b +--R * +--R m + 6 +--R x +--R + +--R 6 4 10 6 4 9 6 4 8 6 4 7 +--R - 210a b m - 12810a b m - 340200a b m - 5159700a b m +--R + +--R 6 4 6 6 4 5 6 4 4 +--R - 49260330a b m - 307585530a b m - 1263374700a b m +--R + +--R 6 4 3 6 4 2 6 4 +--R - 3342229800a b m - 5393046960a b m - 4727540160a b m +--R + +--R 6 4 +--R - 1676505600a b +--R * +--R m + 5 +--R x +--R + +--R 7 3 10 7 3 9 7 3 8 7 3 7 +--R - 120a b m - 7440a b m - 201240a b m - 3115440a b m +--R + +--R 7 3 6 7 3 5 7 3 4 +--R - 30429000a b m - 194790960a b m - 821580360a b m +--R + +--R 7 3 3 7 3 2 7 3 +--R - 2233166160a b m - 3698304480a b m - 3316939200a b m +--R + +--R 7 3 +--R - 1197504000a b +--R * +--R m + 4 +--R x +--R + +--R 8 2 10 8 2 9 8 2 8 8 2 7 +--R - 45a b m - 2835a b m - 78120a b m - 1235790a b m +--R + +--R 8 2 6 8 2 5 8 2 4 +--R - 12376665a b m - 81560115a b m - 355598730a b m +--R + +--R 8 2 3 8 2 2 8 2 8 2 +--R - 1003011660a b m - 1727578440a b m - 1608573600a b m - 598752000a b +--R * +--R m + 3 +--R x +--R + +--R 9 10 9 9 9 8 9 7 9 6 +--R - 10a b m - 640a b m - 17970a b m - 290760a b m - 2992710a b m +--R + +--R 9 5 9 4 9 3 9 2 +--R - 20390160a b m - 92615030a b m - 274727240a b m - 503126280a b m +--R + +--R 9 9 +--R - 502927200a b m - 199584000a b +--R * +--R m + 2 +--R x +--R + +--R 10 10 10 9 10 8 10 7 10 6 +--R - a m - 65a m - 1860a m - 30810a m - 326613a m +--R + +--R 10 5 10 4 10 3 10 2 +--R - 2310945a m - 11028590a m - 34967140a m - 70290936a m +--R + +--R 10 10 +--R - 80627040a m - 39916800a +--R * +--R m + 1 +--R x +--R / +--R 11 10 9 8 7 6 5 +--R m + 66m + 1925m + 32670m + 357423m + 2637558m + 13339535m +--R + +--R 4 3 2 +--R 45995730m + 105258076m + 150917976m + 120543840m + 39916800 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 3330 +t0000:=x^9*(a+b*x)^10 +--R +--R +--R (1) +--R 10 19 9 18 2 8 17 3 7 16 4 6 15 5 5 14 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 13 7 3 12 8 2 11 9 10 10 9 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 486 + +--S 487 of 3330 +r0000:=1/10*a^10*x^10+10/11*a^9*b*x^11+15/4*a^8*b^2*x^12+_ + 120/13*a^7*b^3*x^13+15*a^6*b^4*x^14+84/5*a^5*b^5*x^15+_ + 105/8*a^4*b^6*x^16+120/17*a^3*b^7*x^17+5/2*a^2*b^8*x^18+_ + 10/19*a*b^9*x^19+1/20*b^10*x^20 +--R +--R +--R (2) +--R 1 10 20 10 9 19 5 2 8 18 120 3 7 17 105 4 6 16 84 5 5 15 +--R -- b x + -- a b x + - a b x + --- a b x + --- a b x + -- a b x +--R 20 19 2 17 8 5 +--R + +--R 6 4 14 120 7 3 13 15 8 2 12 10 9 11 1 10 10 +--R 15a b x + --- a b x + -- a b x + -- a b x + -- a x +--R 13 4 11 10 +--R Type: Polynomial(Fraction(Integer)) +--E 487 + +--S 488 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 20 10 9 19 5 2 8 18 120 3 7 17 105 4 6 16 84 5 5 15 +--R -- b x + -- a b x + - a b x + --- a b x + --- a b x + -- a b x +--R 20 19 2 17 8 5 +--R + +--R 6 4 14 120 7 3 13 15 8 2 12 10 9 11 1 10 10 +--R 15a b x + --- a b x + -- a b x + -- a b x + -- a x +--R 13 4 11 10 +--R Type: Polynomial(Fraction(Integer)) +--E 488 + +--S 489 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 489 + +--S 490 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 490 + +)clear all + +--S 491 of 3330 +t0000:=x^8*(a+b*x)^10 +--R +--R +--R (1) +--R 10 18 9 17 2 8 16 3 7 15 4 6 14 5 5 13 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 12 7 3 11 8 2 10 9 9 10 8 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 491 + +--S 492 of 3330 +r0000:=1/9*a^10*x^9+a^9*b*x^10+45/11*a^8*b^2*x^11+10*a^7*b^3*x^12+_ + 210/13*a^6*b^4*x^13+18*a^5*b^5*x^14+14*a^4*b^6*x^15+_ + 15/2*a^3*b^7*x^16+45/17*a^2*b^8*x^17+5/9*a*b^9*x^18+1/19*b^10*x^19 +--R +--R +--R (2) +--R 1 10 19 5 9 18 45 2 8 17 15 3 7 16 4 6 15 5 5 14 +--R -- b x + - a b x + -- a b x + -- a b x + 14a b x + 18a b x +--R 19 9 17 2 +--R + +--R 210 6 4 13 7 3 12 45 8 2 11 9 10 1 10 9 +--R --- a b x + 10a b x + -- a b x + a b x + - a x +--R 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 492 + +--S 493 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 19 5 9 18 45 2 8 17 15 3 7 16 4 6 15 5 5 14 +--R -- b x + - a b x + -- a b x + -- a b x + 14a b x + 18a b x +--R 19 9 17 2 +--R + +--R 210 6 4 13 7 3 12 45 8 2 11 9 10 1 10 9 +--R --- a b x + 10a b x + -- a b x + a b x + - a x +--R 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 493 + +--S 494 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 494 + +--S 495 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 495 + +)clear all + +--S 496 of 3330 +t0000:=x^7*(a+b*x)^10 +--R +--R +--R (1) +--R 10 17 9 16 2 8 15 3 7 14 4 6 13 5 5 12 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 11 7 3 10 8 2 9 9 8 10 7 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 496 + +--S 497 of 3330 +r0000:=1/8*a^10*x^8+10/9*a^9*b*x^9+9/2*a^8*b^2*x^10+120/11*a^7*b^3*x^11+_ + 35/2*a^6*b^4*x^12+252/13*a^5*b^5*x^13+15*a^4*b^6*x^14+_ + 8*a^3*b^7*x^15+45/16*a^2*b^8*x^16+10/17*a*b^9*x^17+1/18*b^10*x^18 +--R +--R +--R (2) +--R 1 10 18 10 9 17 45 2 8 16 3 7 15 4 6 14 252 5 5 13 +--R -- b x + -- a b x + -- a b x + 8a b x + 15a b x + --- a b x +--R 18 17 16 13 +--R + +--R 35 6 4 12 120 7 3 11 9 8 2 10 10 9 9 1 10 8 +--R -- a b x + --- a b x + - a b x + -- a b x + - a x +--R 2 11 2 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 497 + +--S 498 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 18 10 9 17 45 2 8 16 3 7 15 4 6 14 252 5 5 13 +--R -- b x + -- a b x + -- a b x + 8a b x + 15a b x + --- a b x +--R 18 17 16 13 +--R + +--R 35 6 4 12 120 7 3 11 9 8 2 10 10 9 9 1 10 8 +--R -- a b x + --- a b x + - a b x + -- a b x + - a x +--R 2 11 2 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 498 + +--S 499 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 499 + +--S 500 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 500 + +)clear all + +--S 501 of 3330 +t0000:=x^6*(a+b*x)^10 +--R +--R +--R (1) +--R 10 16 9 15 2 8 14 3 7 13 4 6 12 5 5 11 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 10 7 3 9 8 2 8 9 7 10 6 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 501 + +--S 502 of 3330 +r0000:=1/11*a^6*(a+b*x)^11/b^7-1/2*a^5*(a+b*x)^12/b^7+_ + 15/13*a^4*(a+b*x)^13/b^7-10/7*a^3*(a+b*x)^14/b^7+a^2*(a+b*x)^15/b^7-_ + 3/8*a*(a+b*x)^16/b^7+1/17*(a+b*x)^17/b^7 +--R +--R +--R (2) +--R 1 17 17 5 16 16 2 15 15 60 3 14 14 210 4 13 13 +--R -- b x + - a b x + 3a b x + -- a b x + --- a b x +--R 17 8 7 13 +--R + +--R 5 12 12 210 6 11 11 7 10 10 8 9 9 5 9 8 8 1 10 7 7 +--R 21a b x + --- a b x + 12a b x + 5a b x + - a b x + - a b x +--R 11 4 7 +--R + +--R 1 17 +--R ------ a +--R 136136 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 502 + +--S 503 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 17 5 9 16 2 8 15 60 3 7 14 210 4 6 13 5 5 12 +--R -- b x + - a b x + 3a b x + -- a b x + --- a b x + 21a b x +--R 17 8 7 13 +--R + +--R 210 6 4 11 7 3 10 8 2 9 5 9 8 1 10 7 +--R --- a b x + 12a b x + 5a b x + - a b x + - a x +--R 11 4 7 +--R Type: Polynomial(Fraction(Integer)) +--E 503 + +--S 504 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 17 +--R ------ a +--R 136136 +--R (4) - ---------- +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 504 + +--S 505 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 505 + +)clear all + +--S 506 of 3330 +t0000:=x^5*(a+b*x)^10 +--R +--R +--R (1) +--R 10 15 9 14 2 8 13 3 7 12 4 6 11 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 9 7 3 8 8 2 7 9 6 10 5 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 506 + +--S 507 of 3330 +r0000:=-1/11*a^5*(a+b*x)^11/b^6+5/12*a^4*(a+b*x)^12/b^6-_ + 10/13*a^3*(a+b*x)^13/b^6+5/7*a^2*(a+b*x)^14/b^6-1/3*a*(a+b*x)^15/b^6+_ + 1/16*(a+b*x)^16/b^6 +--R +--R +--R (2) +--R 1 16 16 2 15 15 45 2 14 14 120 3 13 13 35 4 12 12 +--R -- b x + - a b x + -- a b x + --- a b x + -- a b x +--R 16 3 14 13 2 +--R + +--R 252 5 11 11 6 10 10 40 7 9 9 45 8 8 8 10 9 7 7 1 10 6 6 +--R --- a b x + 21a b x + -- a b x + -- a b x + -- a b x + - a b x +--R 11 3 8 7 6 +--R + +--R 1 16 +--R - ----- a +--R 48048 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 507 + +--S 508 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 16 2 9 15 45 2 8 14 120 3 7 13 35 4 6 12 252 5 5 11 +--R -- b x + - a b x + -- a b x + --- a b x + -- a b x + --- a b x +--R 16 3 14 13 2 11 +--R + +--R 6 4 10 40 7 3 9 45 8 2 8 10 9 7 1 10 6 +--R 21a b x + -- a b x + -- a b x + -- a b x + - a x +--R 3 8 7 6 +--R Type: Polynomial(Fraction(Integer)) +--E 508 + +--S 509 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 16 +--R ----- a +--R 48048 +--R (4) --------- +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 509 + +--S 510 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 510 + +)clear all + +--S 511 of 3330 +t0000:=x^4*(a+b*x)^10 +--R +--R +--R (1) +--R 10 14 9 13 2 8 12 3 7 11 4 6 10 5 5 9 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 7 8 2 6 9 5 10 4 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 511 + +--S 512 of 3330 +r0000:=1/11*a^4*(a+b*x)^11/b^5-1/3*a^3*(a+b*x)^12/b^5+_ + 6/13*a^2*(a+b*x)^13/b^5-2/7*a*(a+b*x)^14/b^5+1/15*(a+b*x)^15/b^5 +--R +--R +--R (2) +--R 1 15 15 5 14 14 45 2 13 13 3 12 12 210 4 11 11 +--R -- b x + - a b x + -- a b x + 10a b x + --- a b x +--R 15 7 13 11 +--R + +--R 126 5 10 10 70 6 9 9 7 8 8 45 8 7 7 5 9 6 6 1 10 5 5 +--R --- a b x + -- a b x + 15a b x + -- a b x + - a b x + - a b x +--R 5 3 7 3 5 +--R + +--R 1 15 +--R ----- a +--R 15015 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 512 + +--S 513 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 15 5 9 14 45 2 8 13 3 7 12 210 4 6 11 126 5 5 10 +--R -- b x + - a b x + -- a b x + 10a b x + --- a b x + --- a b x +--R 15 7 13 11 5 +--R + +--R 70 6 4 9 7 3 8 45 8 2 7 5 9 6 1 10 5 +--R -- a b x + 15a b x + -- a b x + - a b x + - a x +--R 3 7 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 513 + +--S 514 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 15 +--R ----- a +--R 15015 +--R (4) - --------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 514 + +--S 515 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 515 + +)clear all + +--S 516 of 3330 +t0000:=x^3*(a+b*x)^10 +--R +--R +--R (1) +--R 10 13 9 12 2 8 11 3 7 10 4 6 9 5 5 8 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 7 7 3 6 8 2 5 9 4 10 3 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 516 + +--S 517 of 3330 +r0000:=-1/11*a^3*(a+b*x)^11/b^4+1/4*a^2*(a+b*x)^12/b^4-_ + 3/13*a*(a+b*x)^13/b^4+1/14*(a+b*x)^14/b^4 +--R +--R +--R (2) +--R 1 14 14 10 13 13 15 2 12 12 120 3 11 11 4 10 10 +--R -- b x + -- a b x + -- a b x + --- a b x + 21a b x +--R 14 13 4 11 +--R + +--R 5 9 9 105 6 8 8 120 7 7 7 15 8 6 6 9 5 5 1 10 4 4 +--R 28a b x + --- a b x + --- a b x + -- a b x + 2a b x + - a b x +--R 4 7 2 4 +--R + +--R 1 14 +--R - ---- a +--R 4004 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 517 + +--S 518 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 14 10 9 13 15 2 8 12 120 3 7 11 4 6 10 5 5 9 +--R -- b x + -- a b x + -- a b x + --- a b x + 21a b x + 28a b x +--R 14 13 4 11 +--R + +--R 105 6 4 8 120 7 3 7 15 8 2 6 9 5 1 10 4 +--R --- a b x + --- a b x + -- a b x + 2a b x + - a x +--R 4 7 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 518 + +--S 519 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 14 +--R ---- a +--R 4004 +--R (4) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 519 + +--S 520 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 520 + +)clear all + +--S 521 of 3330 +t0000:=x^2*(a+b*x)^10 +--R +--R +--R (1) +--R 10 12 9 11 2 8 10 3 7 9 4 6 8 5 5 7 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 6 7 3 5 8 2 4 9 3 10 2 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 521 + +--S 522 of 3330 +r0000:=1/11*a^2*(a+b*x)^11/b^3-1/6*a*(a+b*x)^12/b^3+1/13*(a+b*x)^13/b^3 +--R +--R +--R (2) +--R 1 13 13 5 12 12 45 2 11 11 3 10 10 70 4 9 9 63 5 8 8 +--R -- b x + - a b x + -- a b x + 12a b x + -- a b x + -- a b x +--R 13 6 11 3 2 +--R + +--R 6 7 7 7 6 6 8 5 5 5 9 4 4 1 10 3 3 1 13 +--R 30a b x + 20a b x + 9a b x + - a b x + - a b x + --- a +--R 2 3 858 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 522 + +--S 523 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 13 5 9 12 45 2 8 11 3 7 10 70 4 6 9 63 5 5 8 +--R -- b x + - a b x + -- a b x + 12a b x + -- a b x + -- a b x +--R 13 6 11 3 2 +--R + +--R 6 4 7 7 3 6 8 2 5 5 9 4 1 10 3 +--R 30a b x + 20a b x + 9a b x + - a b x + - a x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 523 + +--S 524 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 13 +--R --- a +--R 858 +--R (4) - ------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 524 + +--S 525 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 525 + +)clear all + +--S 526 of 3330 +t0000:=x*(a+b*x)^10 +--R +--R +--R (1) +--R 10 11 9 10 2 8 9 3 7 8 4 6 7 5 5 6 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 5 7 3 4 8 2 3 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 526 + +--S 527 of 3330 +r0000:=-1/11*a*(a+b*x)^11/b^2+1/12*(a+b*x)^12/b^2 +--R +--R +--R (2) +--R 1 12 12 10 11 11 9 2 10 10 40 3 9 9 105 4 8 8 5 7 7 +--R -- b x + -- a b x + - a b x + -- a b x + --- a b x + 36a b x +--R 12 11 2 3 4 +--R + +--R 6 6 6 7 5 5 45 8 4 4 10 9 3 3 1 10 2 2 1 12 +--R 35a b x + 24a b x + -- a b x + -- a b x + - a b x - --- a +--R 4 3 2 132 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 527 + +--S 528 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 12 10 9 11 9 2 8 10 40 3 7 9 105 4 6 8 5 5 7 +--R -- b x + -- a b x + - a b x + -- a b x + --- a b x + 36a b x +--R 12 11 2 3 4 +--R + +--R 6 4 6 7 3 5 45 8 2 4 10 9 3 1 10 2 +--R 35a b x + 24a b x + -- a b x + -- a b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 528 + +--S 529 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 12 +--R --- a +--R 132 +--R (4) ------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 529 + +--S 530 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 530 + +)clear all + +--S 531 of 3330 +t0000:=(a+b*x)^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Polynomial(Integer) +--E 531 + +--S 532 of 3330 +r0000:=1/11*(a+b*x)^11/b +--R +--R +--R (2) +--R 1 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R -- b x + a b x + 5a b x + 15a b x + 30a b x + 42a b x +--R 11 +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 1 11 +--R 42a b x + 30a b x + 15a b x + 5a b x + a b x + -- a +--R 11 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 532 + +--S 533 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 11 9 10 2 8 9 3 7 8 4 6 7 5 5 6 6 4 5 +--R -- b x + a b x + 5a b x + 15a b x + 30a b x + 42a b x + 42a b x +--R 11 +--R + +--R 7 3 4 8 2 3 9 2 10 +--R 30a b x + 15a b x + 5a b x + a x +--R Type: Polynomial(Fraction(Integer)) +--E 533 + +--S 534 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 11 +--R -- a +--R 11 +--R (4) - ------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 534 + +--S 535 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 535 + +)clear all + +--S 536 of 3330 +t0000:=(a+b*x)^10/x +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 3330 +r0000:=10*a^9*b*x+45/2*a^8*b^2*x^2+40*a^7*b^3*x^3+105/2*a^6*b^4*x^4+_ + 252/5*a^5*b^5*x^5+35*a^4*b^6*x^6+120/7*a^3*b^7*x^7+_ + 45/8*a^2*b^8*x^8+10/9*a*b^9*x^9+1/10*b^10*x^10+a^10*log(x) +--R +--R +--R (2) +--R 10 10 10 9 9 2 8 8 3 7 7 +--R 2520a log(x) + 252b x + 2800a b x + 14175a b x + 43200a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 88200a b x + 127008a b x + 132300a b x + 100800a b x + 56700a b x +--R + +--R 9 +--R 25200a b x +--R / +--R 2520 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 9 2 8 8 3 7 7 +--R 2520a log(x) + 252b x + 2800a b x + 14175a b x + 43200a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 88200a b x + 127008a b x + 132300a b x + 100800a b x + 56700a b x +--R + +--R 9 +--R 25200a b x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 3330 +t0000:=(a+b*x)^10/x^2 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 3330 +r0000:=-a^10/x+45*a^8*b^2*x+60*a^7*b^3*x^2+70*a^6*b^4*x^3+63*a^5*b^5*x^4+_ + 42*a^4*b^6*x^5+20*a^3*b^7*x^6+45/7*a^2*b^8*x^7+5/4*a*b^9*x^8+_ + 1/9*b^10*x^9+10*a^9*b*log(x) +--R +--R +--R (2) +--R 9 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 28b x + 315a b x + 1620a b x + 5040a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 10584a b x + 15876a b x + 17640a b x + 15120a b x + 11340a b x +--R + +--R 10 +--R - 252a +--R / +--R 252x +--R Type: Expression(Integer) +--E 542 + +--S 543 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 28b x + 315a b x + 1620a b x + 5040a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 10584a b x + 15876a b x + 17640a b x + 15120a b x + 11340a b x +--R + +--R 10 +--R - 252a +--R / +--R 252x +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 3330 +t0000:=(a+b*x)^10/x^3 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 3330 +r0000:=-1/2*a^10/x^2-10*a^9*b/x+120*a^7*b^3*x+105*a^6*b^4*x^2+_ + 84*a^5*b^5*x^3+105/2*a^4*b^6*x^4+24*a^3*b^7*x^5+15/2*a^2*b^8*x^6+_ + 10/7*a*b^9*x^7+1/8*b^10*x^8+45*a^8*b^2*log(x) +--R +--R +--R (2) +--R 8 2 2 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 7b x + 80a b x + 420a b x + 1344a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 9 10 +--R 2940a b x + 4704a b x + 5880a b x + 6720a b x - 560a b x - 28a +--R / +--R 2 +--R 56x +--R Type: Expression(Integer) +--E 547 + +--S 548 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 2 2 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 7b x + 80a b x + 420a b x + 1344a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 9 10 +--R 2940a b x + 4704a b x + 5880a b x + 6720a b x - 560a b x - 28a +--R / +--R 2 +--R 56x +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 3330 +t0000:=(a+b*x)^10/x^4 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 3330 +r0000:=-1/3*a^10/x^3-5*a^9*b/x^2-45*a^8*b^2/x+210*a^6*b^4*x+_ + 126*a^5*b^5*x^2+70*a^4*b^6*x^3+30*a^3*b^7*x^4+9*a^2*b^8*x^5+_ + 5/3*a*b^9*x^6+1/7*b^10*x^7+120*a^7*b^3*log(x) +--R +--R +--R (2) +--R 7 3 3 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 3b x + 35a b x + 189a b x + 630a b x +--R + +--R 4 6 6 5 5 5 6 4 4 8 2 2 9 10 +--R 1470a b x + 2646a b x + 4410a b x - 945a b x - 105a b x - 7a +--R / +--R 3 +--R 21x +--R Type: Expression(Integer) +--E 552 + +--S 553 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 3 3 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 3b x + 35a b x + 189a b x + 630a b x +--R + +--R 4 6 6 5 5 5 6 4 4 8 2 2 9 10 +--R 1470a b x + 2646a b x + 4410a b x - 945a b x - 105a b x - 7a +--R / +--R 3 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 3330 +t0000:=(a+b*x)^10/x^5 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 3330 +r0000:=-1/4*a^10/x^4-10/3*a^9*b/x^3-45/2*a^8*b^2/x^2-120*a^7*b^3/x+_ + 252*a^5*b^5*x+105*a^4*b^6*x^2+40*a^3*b^7*x^3+45/4*a^2*b^8*x^4+_ + 2*a*b^9*x^5+1/6*b^10*x^6+210*a^6*b^4*log(x) +--R +--R +--R (2) +--R 6 4 4 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 2b x + 24a b x + 135a b x + 480a b x +--R + +--R 4 6 6 5 5 5 7 3 3 8 2 2 9 10 +--R 1260a b x + 3024a b x - 1440a b x - 270a b x - 40a b x - 3a +--R / +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 557 + +--S 558 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 4 4 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 2b x + 24a b x + 135a b x + 480a b x +--R + +--R 4 6 6 5 5 5 7 3 3 8 2 2 9 10 +--R 1260a b x + 3024a b x - 1440a b x - 270a b x - 40a b x - 3a +--R / +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 3330 +t0000:=(a+b*x)^10/x^6 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 3330 +r0000:=-1/5*a^10/x^5-5/2*a^9*b/x^4-15*a^8*b^2/x^3-60*a^7*b^3/x^2-_ + 210*a^6*b^4/x+210*a^4*b^6*x+60*a^3*b^7*x^2+15*a^2*b^8*x^3+_ + 5/2*a*b^9*x^4+1/5*b^10*x^5+252*a^5*b^5*log(x) +--R +--R +--R (2) +--R 5 5 5 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 2b x + 25a b x + 150a b x + 600a b x +--R + +--R 4 6 6 6 4 4 7 3 3 8 2 2 9 10 +--R 2100a b x - 2100a b x - 600a b x - 150a b x - 25a b x - 2a +--R / +--R 5 +--R 10x +--R Type: Expression(Integer) +--E 562 + +--S 563 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 5 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 2b x + 25a b x + 150a b x + 600a b x +--R + +--R 4 6 6 6 4 4 7 3 3 8 2 2 9 10 +--R 2100a b x - 2100a b x - 600a b x - 150a b x - 25a b x - 2a +--R / +--R 5 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 3330 +t0000:=(a+b*x)^10/x^7 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 3330 +r0000:=-1/6*a^10/x^6-2*a^9*b/x^5-45/4*a^8*b^2/x^4-40*a^7*b^3/x^3-_ + 105*a^6*b^4/x^2-252*a^5*b^5/x+120*a^3*b^7*x+45/2*a^2*b^8*x^2+_ + 10/3*a*b^9*x^3+1/4*b^10*x^4+210*a^4*b^6*log(x) +--R +--R +--R (2) +--R 4 6 6 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 3b x + 40a b x + 270a b x + 1440a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 3024a b x - 1260a b x - 480a b x - 135a b x - 24a b x - 2a +--R / +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 567 + +--S 568 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 6 6 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 3b x + 40a b x + 270a b x + 1440a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 3024a b x - 1260a b x - 480a b x - 135a b x - 24a b x - 2a +--R / +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 3330 +t0000:=(a+b*x)^10/x^8 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 3330 +r0000:=-1/7*a^10/x^7-5/3*a^9*b/x^6-9*a^8*b^2/x^5-30*a^7*b^3/x^4-_ + 70*a^6*b^4/x^3-126*a^5*b^5/x^2-210*a^4*b^6/x+45*a^2*b^8*x+_ + 5*a*b^9*x^2+1/3*b^10*x^3+120*a^3*b^7*log(x) +--R +--R +--R (2) +--R 3 7 7 10 10 9 9 2 8 8 4 6 6 +--R 2520a b x log(x) + 7b x + 105a b x + 945a b x - 4410a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 2646a b x - 1470a b x - 630a b x - 189a b x - 35a b x - 3a +--R / +--R 7 +--R 21x +--R Type: Expression(Integer) +--E 572 + +--S 573 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 7 7 10 10 9 9 2 8 8 4 6 6 +--R 2520a b x log(x) + 7b x + 105a b x + 945a b x - 4410a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 2646a b x - 1470a b x - 630a b x - 189a b x - 35a b x - 3a +--R / +--R 7 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 3330 +t0000:=(a+b*x)^10/x^9 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 3330 +r0000:=-1/8*a^10/x^8-10/7*a^9*b/x^7-15/2*a^8*b^2/x^6-24*a^7*b^3/x^5-_ + 105/2*a^6*b^4/x^4-84*a^5*b^5/x^3-105*a^4*b^6/x^2-120*a^3*b^7/x+_ + 10*a*b^9*x+1/2*b^10*x^2+45*a^2*b^8*log(x) +--R +--R +--R (2) +--R 2 8 8 10 10 9 9 3 7 7 4 6 6 +--R 2520a b x log(x) + 28b x + 560a b x - 6720a b x - 5880a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 4704a b x - 2940a b x - 1344a b x - 420a b x - 80a b x - 7a +--R / +--R 8 +--R 56x +--R Type: Expression(Integer) +--E 577 + +--S 578 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 8 8 10 10 9 9 3 7 7 4 6 6 +--R 2520a b x log(x) + 28b x + 560a b x - 6720a b x - 5880a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 4704a b x - 2940a b x - 1344a b x - 420a b x - 80a b x - 7a +--R / +--R 8 +--R 56x +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 3330 +t0000:=(a+b*x)^10/x^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 3330 +r0000:=-1/9*a^10/x^9-5/4*a^9*b/x^8-45/7*a^8*b^2/x^7-20*a^7*b^3/x^6-_ + 42*a^6*b^4/x^5-63*a^5*b^5/x^4-70*a^4*b^6/x^3-60*a^3*b^7/x^2-_ + 45*a^2*b^8/x+b^10*x+10*a*b^9*log(x) +--R +--R +--R (2) +--R 9 9 10 10 2 8 8 3 7 7 4 6 6 +--R 2520a b x log(x) + 252b x - 11340a b x - 15120a b x - 17640a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 15876a b x - 10584a b x - 5040a b x - 1620a b x - 315a b x - 28a +--R / +--R 9 +--R 252x +--R Type: Expression(Integer) +--E 582 + +--S 583 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 10 10 2 8 8 3 7 7 4 6 6 +--R 2520a b x log(x) + 252b x - 11340a b x - 15120a b x - 17640a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 15876a b x - 10584a b x - 5040a b x - 1620a b x - 315a b x - 28a +--R / +--R 9 +--R 252x +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 3330 +t0000:=(a+b*x)^10/x^11 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 3330 +r0000:=-1/10*a^10/x^10-10/9*a^9*b/x^9-45/8*a^8*b^2/x^8-120/7*a^7*b^3/x^7-_ + 35*a^6*b^4/x^6-252/5*a^5*b^5/x^5-105/2*a^4*b^6/x^4-40*a^3*b^7/x^3-_ + 45/2*a^2*b^8/x^2-10*a*b^9/x+b^10*log(x) +--R +--R +--R (2) +--R 10 10 9 9 2 8 8 3 7 7 +--R 2520b x log(x) - 25200a b x - 56700a b x - 100800a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R - 132300a b x - 127008a b x - 88200a b x - 43200a b x - 14175a b x +--R + +--R 9 10 +--R - 2800a b x - 252a +--R / +--R 10 +--R 2520x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 +--R 2520b x log(x) - 25200a b x - 56700a b x - 100800a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R - 132300a b x - 127008a b x - 88200a b x - 43200a b x - 14175a b x +--R + +--R 9 10 +--R - 2800a b x - 252a +--R / +--R 10 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 3330 +t0000:=(a+b*x)^10/x^12 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 3330 +r0000:=-1/11*(a+b*x)^11/(a*x^11) +--R +--R +--R (2) +--R 1 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R - -- b x - a b x - 5a b x - 15a b x - 30a b x - 42a b x +--R 11 +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 1 11 +--R - 42a b x - 30a b x - 15a b x - 5a b x - a b x - -- a +--R 11 +--R / +--R 11 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 592 + +--S 593 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R - 11b x - 55a b x - 165a b x - 330a b x - 462a b x - 462a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 330a b x - 165a b x - 55a b x - 11a b x - a +--R / +--R 11 +--R 11x +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 11 +--R b +--R (4) --- +--R 11a +--R Type: Expression(Integer) +--E 594 + +--S 595 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 3330 +t0000:=(a+b*x)^10/x^13 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 596 + +--S 597 of 3330 +r0000:=-1/12*(a+b*x)^11/(a*x^12)+1/132*b*(a+b*x)^11/(a^2*x^11) +--R +--R +--R (2) +--R 1 12 12 1 2 10 10 10 3 9 9 45 4 8 8 5 7 7 6 6 6 +--R --- b x - - a b x - -- a b x - -- a b x - 24a b x - 35a b x +--R 132 2 3 4 +--R + +--R 7 5 5 105 8 4 4 40 9 3 3 9 10 2 2 10 11 1 12 +--R - 36a b x - --- a b x - -- a b x - - a b x - -- a b x - -- a +--R 4 3 2 11 12 +--R / +--R 2 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 597 + +--S 598 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 66b x - 440a b x - 1485a b x - 3168a b x - 4620a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 4752a b x - 3465a b x - 1760a b x - 594a b x - 120a b x - 11a +--R / +--R 12 +--R 132x +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 12 +--R b +--R (4) - ----- +--R 2 +--R 132a +--R Type: Expression(Integer) +--E 599 + +--S 600 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 3330 +t0000:=(a+b*x)^10/x^14 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 of 3330 +r0000:=-1/13*(a+b*x)^11/(a*x^13)+1/78*b*(a+b*x)^11/(a^2*x^12)-_ + 1/858*b^2*(a+b*x)^11/(a^3*x^11) +--R +--R +--R (2) +--R 1 13 13 1 3 10 10 5 4 9 9 5 8 8 6 7 7 7 6 6 +--R - --- b x - - a b x - - a b x - 9a b x - 20a b x - 30a b x +--R 858 3 2 +--R + +--R 63 8 5 5 70 9 4 4 10 3 3 45 11 2 2 5 12 1 13 +--R - -- a b x - -- a b x - 12a b x - -- a b x - - a b x - -- a +--R 2 3 11 6 13 +--R / +--R 3 13 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 602 + +--S 603 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 286b x - 2145a b x - 7722a b x - 17160a b x - 25740a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 27027a b x - 20020a b x - 10296a b x - 3510a b x - 715a b x - 66a +--R / +--R 13 +--R 858x +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 13 +--R b +--R (4) ----- +--R 3 +--R 858a +--R Type: Expression(Integer) +--E 604 + +--S 605 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 3330 +t0000:=(a+b*x)^10/x^15 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 606 + +--S 607 of 3330 +r0000:=-1/14*(a+b*x)^11/(a*x^14)+3/182*b*(a+b*x)^11/(a^2*x^13)-_ + 1/364*b^2*(a+b*x)^11/(a^3*x^12)+1/4004*b^3*(a+b*x)^11/(a^4*x^11) +--R +--R +--R (2) +--R 1 14 14 1 4 10 10 5 9 9 15 6 8 8 120 7 7 7 105 8 6 6 +--R ---- b x - - a b x - 2a b x - -- a b x - --- a b x - --- a b x +--R 4004 4 2 7 4 +--R + +--R 9 5 5 10 4 4 120 11 3 3 15 12 2 2 10 13 1 14 +--R - 28a b x - 21a b x - --- a b x - -- a b x - -- a b x - -- a +--R 11 4 13 14 +--R / +--R 4 14 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 607 + +--S 608 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 1001b x - 8008a b x - 30030a b x - 68640a b x - 105105a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 112112a b x - 84084a b x - 43680a b x - 15015a b x - 3080a b x +--R + +--R 10 +--R - 286a +--R / +--R 14 +--R 4004x +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 14 +--R b +--R (4) - ------ +--R 4 +--R 4004a +--R Type: Expression(Integer) +--E 609 + +--S 610 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 3330 +t0000:=(a+b*x)^10/x^16 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 611 + +--S 612 of 3330 +r0000:=-1/15*(a+b*x)^11/(a*x^15)+2/105*b*(a+b*x)^11/(a^2*x^14)-_ + 2/455*b^2*(a+b*x)^11/(a^3*x^13)+1/1365*b^3*(a+b*x)^11/(a^4*x^12)-_ + 1/15015*b^4*(a+b*x)^11/(a^5*x^11) +--R +--R +--R (2) +--R 1 15 15 1 5 10 10 5 6 9 9 45 7 8 8 8 7 7 70 9 6 6 +--R - ----- b x - - a b x - - a b x - -- a b x - 15a b x - -- a b x +--R 15015 5 3 7 3 +--R + +--R 126 10 5 5 210 11 4 4 12 3 3 45 13 2 2 5 14 1 15 +--R - --- a b x - --- a b x - 10a b x - -- a b x - - a b x - -- a +--R 5 11 13 7 15 +--R / +--R 5 15 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 612 + +--S 613 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 3003b x - 25025a b x - 96525a b x - 225225a b x - 350350a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 378378a b x - 286650a b x - 150150a b x - 51975a b x - 10725a b x +--R + +--R 10 +--R - 1001a +--R / +--R 15 +--R 15015x +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 15 +--R b +--R (4) ------- +--R 5 +--R 15015a +--R Type: Expression(Integer) +--E 614 + +--S 615 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 3330 +t0000:=(a+b*x)^10/x^17 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 of 3330 +r0000:=-1/16*(a+b*x)^11/(a*x^16)+1/48*b*(a+b*x)^11/(a^2*x^15)-_ + 1/168*b^2*(a+b*x)^11/(a^3*x^14)+1/728*b^3*(a+b*x)^11/(a^4*x^13)-_ + 1/4368*b^4*(a+b*x)^11/(a^5*x^12)+1/48048*b^5*(a+b*x)^11/(a^6*x^11) +--R +--R +--R (2) +--R 1 16 16 1 6 10 10 10 7 9 9 45 8 8 8 40 9 7 7 10 6 6 +--R ----- b x - - a b x - -- a b x - -- a b x - -- a b x - 21a b x +--R 48048 6 7 8 3 +--R + +--R 252 11 5 5 35 12 4 4 120 13 3 3 45 14 2 2 2 15 1 16 +--R - --- a b x - -- a b x - --- a b x - -- a b x - - a b x - -- a +--R 11 2 13 14 3 16 +--R / +--R 6 16 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 617 + +--S 618 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 8008b x - 68640a b x - 270270a b x - 640640a b x - 1009008a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 1100736a b x - 840840a b x - 443520a b x - 154440a b x - 32032a b x +--R + +--R 10 +--R - 3003a +--R / +--R 16 +--R 48048x +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 16 +--R b +--R (4) - ------- +--R 6 +--R 48048a +--R Type: Expression(Integer) +--E 619 + +--S 620 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 620 + +)clear all + +--S 621 of 3330 +t0000:=(a+b*x)^10/x^18 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 621 + +--S 622 of 3330 +r0000:=-1/17*a^10/x^17-5/8*a^9*b/x^16-3*a^8*b^2/x^15-60/7*a^7*b^3/x^14-_ + 210/13*a^6*b^4/x^13-21*a^5*b^5/x^12-210/11*a^4*b^6/x^11-_ + 12*a^3*b^7/x^10-5*a^2*b^8/x^9-5/4*a*b^9/x^8-1/7*b^10/x^7 +--R +--R +--R (2) +--R 1 10 10 5 9 9 2 8 8 3 7 7 210 4 6 6 5 5 5 +--R - - b x - - a b x - 5a b x - 12a b x - --- a b x - 21a b x +--R 7 4 11 +--R + +--R 210 6 4 4 60 7 3 3 8 2 2 5 9 1 10 +--R - --- a b x - -- a b x - 3a b x - - a b x - -- a +--R 13 7 8 17 +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 622 + +--S 623 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 +--R - 19448b x - 170170a b x - 680680a b x - 1633632a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 2598960a b x - 2858856a b x - 2199120a b x - 1166880a b x +--R + +--R 8 2 2 9 10 +--R - 408408a b x - 85085a b x - 8008a +--R / +--R 17 +--R 136136x +--R Type: Union(Expression(Integer),...) +--E 623 + +--S 624 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 624 + +--S 625 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 625 + +)clear all + +--S 626 of 3330 +t0000:=(a+b*x)^10/x^19 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 626 + +--S 627 of 3330 +r0000:=-1/18*a^10/x^18-10/17*a^9*b/x^17-45/16*a^8*b^2/x^16-8*a^7*b^3/x^15-_ + 15*a^6*b^4/x^14-252/13*a^5*b^5/x^13-35/2*a^4*b^6/x^12-_ + 120/11*a^3*b^7/x^11-9/2*a^2*b^8/x^10-10/9*a*b^9/x^9-1/8*b^10/x^8 +--R +--R +--R (2) +--R 1 10 10 10 9 9 9 2 8 8 120 3 7 7 35 4 6 6 252 5 5 5 +--R - - b x - -- a b x - - a b x - --- a b x - -- a b x - --- a b x +--R 8 9 2 11 2 13 +--R + +--R 6 4 4 7 3 3 45 8 2 2 10 9 1 10 +--R - 15a b x - 8a b x - -- a b x - -- a b x - -- a +--R 16 17 18 +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 627 + +--S 628 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 +--R - 43758b x - 388960a b x - 1575288a b x - 3818880a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 6126120a b x - 6785856a b x - 5250960a b x - 2800512a b x +--R + +--R 8 2 2 9 10 +--R - 984555a b x - 205920a b x - 19448a +--R / +--R 18 +--R 350064x +--R Type: Union(Expression(Integer),...) +--E 628 + +--S 629 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 629 + +--S 630 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 3330 +t0000:=(a+b*x)^10/x^20 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 20 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 631 + +--S 632 of 3330 +r0000:=-1/19*a^10/x^19-5/9*a^9*b/x^18-45/17*a^8*b^2/x^17-15/2*a^7*b^3/x^16-_ + 14*a^6*b^4/x^15-18*a^5*b^5/x^14-210/13*a^4*b^6/x^13-_ + 10*a^3*b^7/x^12-45/11*a^2*b^8/x^11-a*b^9/x^10-1/9*b^10/x^9 +--R +--R +--R (2) +--R 1 10 10 9 9 45 2 8 8 3 7 7 210 4 6 6 5 5 5 +--R - - b x - a b x - -- a b x - 10a b x - --- a b x - 18a b x +--R 9 11 13 +--R + +--R 6 4 4 15 7 3 3 45 8 2 2 5 9 1 10 +--R - 14a b x - -- a b x - -- a b x - - a b x - -- a +--R 2 17 9 19 +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 632 + +--S 633 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 +--R - 92378b x - 831402a b x - 3401190a b x - 8314020a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 13430340a b x - 14965236a b x - 11639628a b x - 6235515a b x +--R + +--R 8 2 2 9 10 +--R - 2200770a b x - 461890a b x - 43758a +--R / +--R 19 +--R 831402x +--R Type: Union(Expression(Integer),...) +--E 633 + +--S 634 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 634 + +--S 635 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 3330 +t0000:=c*(a+b*x) +--R +--R +--R (1) b c x + a c +--R Type: Polynomial(Integer) +--E 636 + +--S 637 of 3330 +r0000:=1/2*c*(a+b*x)^2/b +--R +--R +--R 1 2 2 1 2 +--R - b c x + a b c x + - a c +--R 2 2 +--R (2) -------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 637 + +--S 638 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 +--R (3) - b c x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 638 + +--S 639 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 2 +--R - a c +--R 2 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 639 + +--S 640 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 640 + +)clear all + +--S 641 of 3330 +t0000:=(c+d)*(a+b*x)/e +--R +--R +--R (b d + b c)x + a d + a c +--R (1) ------------------------ +--R e +--R Type: Fraction(Polynomial(Integer)) +--E 641 + +--S 642 of 3330 +r0000:=1/2*(c+d)*(a+b*x)^2/(b*e) +--R +--R +--R 1 2 1 2 2 1 2 1 2 +--R (- b d + - b c)x + (a b d + a b c)x + - a d + - a c +--R 2 2 2 2 +--R (2) ---------------------------------------------------- +--R b e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 642 + +--S 643 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (b d + b c)x + (2a d + 2a c)x +--R (3) ------------------------------ +--R 2e +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R - a d - a c +--R (4) ----------- +--R 2b e +--R Type: Expression(Integer) +--E 644 + +--S 645 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 3330 +t0000:=x^m/(a+b*x) +--R +--R +--R m +--R x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 3330 +--r0000:=x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*(1+m)) +--E 647 + +--S 648 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | -------- d%N +--R ++ %N b + a +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 3330 +--m0000:=a0000 - r0000 +--E 649 + +--S 650 of 3330 +--d0000:=D(m0000,x) +--E 650 + +)clear all + +--S 651 of 3330 +t0000:=x^5/(a+b*x) +--R +--R +--R 5 +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 651 + +--S 652 of 3330 +r0000:=a^4*x/b^5-1/2*a^3*x^2/b^4+1/3*a^2*x^3/b^3-1/4*a*x^4/b^2+1/5*x^5/b-_ + a^5*log(a+b*x)/b^6 +--R +--R +--R 5 5 5 4 4 2 3 3 3 2 2 4 +--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x +--R (2) ---------------------------------------------------------------------- +--R 6 +--R 60b +--R Type: Expression(Integer) +--E 652 + +--S 653 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 5 4 4 2 3 3 3 2 2 4 +--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x +--R (3) ---------------------------------------------------------------------- +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 654 + +--S 655 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 655 + +)clear all + +--S 656 of 3330 +t0000:=x^4/(a+b*x) +--R +--R +--R 4 +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 656 + +--S 657 of 3330 +r0000:=-a^3*x/b^4+1/2*a^2*x^2/b^3-1/3*a*x^3/b^2+1/4*x^4/b+a^4*log(a+b*x)/b^5 +--R +--R +--R 4 4 4 3 3 2 2 2 3 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (2) ------------------------------------------------------ +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 657 + +--S 658 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 4 3 3 2 2 2 3 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (3) ------------------------------------------------------ +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 658 + +--S 659 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 659 + +--S 660 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 3330 +t0000:=x^3/(a+b*x) +--R +--R +--R 3 +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 661 + +--S 662 of 3330 +r0000:=a^2*x/b^3-1/2*a*x^2/b^2+1/3*x^3/b-a^3*log(a+b*x)/b^4 +--R +--R +--R 3 3 3 2 2 2 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) -------------------------------------------- +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 662 + +--S 663 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 3 2 2 2 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (3) -------------------------------------------- +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 664 + +--S 665 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 665 + +)clear all + +--S 666 of 3330 +t0000:=x^2/(a+b*x) +--R +--R +--R 2 +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 666 + +--S 667 of 3330 +r0000:=-a*x/b^2+1/2*x^2/b+a^2*log(a+b*x)/b^3 +--R +--R +--R 2 2 2 +--R 2a log(b x + a) + b x - 2a b x +--R (2) ------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 667 + +--S 668 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2a log(b x + a) + b x - 2a b x +--R (3) ------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 669 + +--S 670 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 670 + +)clear all + +--S 671 of 3330 +t0000:=x/(a+b*x) +--R +--R +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 671 + +--S 672 of 3330 +r0000:=x/b-a*log(a+b*x)/b^2 +--R +--R +--R - a log(b x + a) + b x +--R (2) ---------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 672 + +--S 673 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - a log(b x + a) + b x +--R (3) ---------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 673 + +--S 674 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 3330 +t0000:=1/(a+b*x) +--R +--R +--R 1 +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 676 + +--S 677 of 3330 +r0000:=log(a+b*x)/b +--R +--R +--R log(b x + a) +--R (2) ------------ +--R b +--R Type: Expression(Integer) +--E 677 + +--S 678 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R log(b x + a) +--R (3) ------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 678 + +--S 679 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 679 + +--S 680 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 680 + +)clear all + +--S 681 of 3330 +t0000:=1/(x*(a+b*x)) +--R +--R +--R 1 +--R (1) ---------- +--R 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 681 + +--S 682 of 3330 +r0000:=log(x)/a-log(a+b*x)/a +--R +--R +--R - log(b x + a) + log(x) +--R (2) ----------------------- +--R a +--R Type: Expression(Integer) +--E 682 + +--S 683 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - log(b x + a) + log(x) +--R (3) ----------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 685 + +)clear all + +--S 686 of 3330 +t0000:=1/(x^2*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R 3 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 686 + +--S 687 of 3330 +r0000:=(-1)/(a*x)-b*log(x)/a^2+b*log(a+b*x)/a^2 +--R +--R +--R b x log(b x + a) - b x log(x) - a +--R (2) --------------------------------- +--R 2 +--R a x +--R Type: Expression(Integer) +--E 687 + +--S 688 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(b x + a) - b x log(x) - a +--R (3) --------------------------------- +--R 2 +--R a x +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 3330 +t0000:=1/(x^3*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R 4 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 691 + +--S 692 of 3330 +r0000:=(-1/2)/(a*x^2)+b/(a^2*x)+b^2*log(x)/a^3-b^2*log(a+b*x)/a^3 +--R +--R +--R 2 2 2 2 2 +--R - 2b x log(b x + a) + 2b x log(x) + 2a b x - a +--R (2) ----------------------------------------------- +--R 3 2 +--R 2a x +--R Type: Expression(Integer) +--E 692 + +--S 693 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 +--R - 2b x log(b x + a) + 2b x log(x) + 2a b x - a +--R (3) ----------------------------------------------- +--R 3 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 694 + +--S 695 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 695 + +)clear all + +--S 696 of 3330 +t0000:=1/(x^4*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R 5 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 696 + +--S 697 of 3330 +r0000:=(-1/3)/(a*x^3)+1/2*b/(a^2*x^2)-b^2/(a^3*x)-_ + b^3*log(x)/a^4+b^3*log(a+b*x)/a^4 +--R +--R +--R 3 3 3 3 2 2 2 3 +--R 6b x log(b x + a) - 6b x log(x) - 6a b x + 3a b x - 2a +--R (2) -------------------------------------------------------- +--R 4 3 +--R 6a x +--R Type: Expression(Integer) +--E 697 + +--S 698 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 3 3 2 2 2 3 +--R 6b x log(b x + a) - 6b x log(x) - 6a b x + 3a b x - 2a +--R (3) -------------------------------------------------------- +--R 4 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 699 + +--S 700 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 3330 +t0000:=1/(x^5*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 701 + +--S 702 of 3330 +r0000:=(-1/4)/(a*x^4)+1/3*b/(a^2*x^3)-1/2*b^2/(a^3*x^2)+b^3/(a^4*x)+_ + b^4*log(x)/a^5-b^4*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 4 4 4 4 3 3 2 2 2 3 4 +--R - 12b x log(b x + a) + 12b x log(x) + 12a b x - 6a b x + 4a b x - 3a +--R ----------------------------------------------------------------------- +--R 5 4 +--R 12a x +--R Type: Expression(Integer) +--E 702 + +--S 703 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 4 3 3 2 2 2 3 4 +--R - 12b x log(b x + a) + 12b x log(x) + 12a b x - 6a b x + 4a b x - 3a +--R ----------------------------------------------------------------------- +--R 5 4 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 3330 +t0000:=x^m/(a+b*x)^2 +--R +--R +--R m +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 3330 +--r0000:=x^(1+m)/(a*(a+b*x))-m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a^2*(1+m)) +--E 707 + +--S 708 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | -------------------- d%N +--R ++ 2 2 2 +--R %N b + 2%N a b + a +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 3330 +--m0000:=a0000 - r0000 +--E 709 + +--S 710 of 3330 +--d0000:=D(m0000,x) +--E 710 + +)clear all + +--S 711 of 3330 +t0000:=x^6/(a+b*x)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 711 + +--S 712 of 3330 +r0000:=5*a^4*x/b^6-2*a^3*x^2/b^5+a^2*x^3/b^4-1/2*a*x^4/b^3+1/5*x^5/b^2-_ + a^6/(b^7*(a+b*x))-6*a^5*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 5 6 6 6 5 5 2 4 4 3 3 3 +--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x +--R + +--R 4 2 2 5 6 +--R 30a b x + 50a b x - 10a +--R / +--R 8 7 +--R 10b x + 10a b +--R Type: Expression(Integer) +--E 712 + +--S 713 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 6 6 6 5 5 2 4 4 3 3 3 +--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x +--R + +--R 4 2 2 5 6 +--R 30a b x + 50a b x - 10a +--R / +--R 8 7 +--R 10b x + 10a b +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 3330 +t0000:=x^5/(a+b*x)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 716 + +--S 717 of 3330 +r0000:=-4*a^3*x/b^5+3/2*a^2*x^2/b^4-2/3*a*x^3/b^3+1/4*x^4/b^2+_ + a^5/(b^6*(a+b*x))+5*a^4*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 5 5 5 4 4 2 3 3 3 2 2 +--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x +--R + +--R 4 5 +--R - 48a b x + 12a +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 717 + +--S 718 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 5 5 5 4 4 2 3 3 3 2 2 +--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x +--R + +--R 4 5 +--R - 48a b x + 12a +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 719 + +--S 720 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 3330 +t0000:=x^4/(a+b*x)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 721 + +--S 722 of 3330 +r0000:=3*a^2*x/b^4-a*x^2/b^3+1/3*x^3/b^2-a^4/(b^5*(a+b*x))-4*a^3*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 4 4 4 3 3 2 2 2 3 4 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a +--R ------------------------------------------------------------------------ +--R 6 5 +--R 3b x + 3a b +--R Type: Expression(Integer) +--E 722 + +--S 723 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 4 4 3 3 2 2 2 3 4 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a +--R ------------------------------------------------------------------------ +--R 6 5 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 725 + +)clear all + +--S 726 of 3330 +t0000:=x^3/(a+b*x)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 726 + +--S 727 of 3330 +r0000:=-2*a*x/b^3+1/2*x^2/b^2+a^3/(b^4*(a+b*x))+3*a^2*log(a+b*x)/b^4 +--R +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (2) ---------------------------------------------------------- +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 727 + +--S 728 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (3) ---------------------------------------------------------- +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 729 + +--S 730 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 3330 +t0000:=x^2/(a+b*x)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 731 + +--S 732 of 3330 +r0000:=x/b^2-a^2/(b^3*(a+b*x))-2*a*log(a+b*x)/b^3 +--R +--R +--R 2 2 2 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (2) ------------------------------------------------ +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 732 + +--S 733 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (3) ------------------------------------------------ +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 3330 +t0000:=x/(a+b*x)^2 +--R +--R +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 736 + +--S 737 of 3330 +r0000:=a/(b^2*(a+b*x))+log(a+b*x)/b^2 +--R +--R +--R (b x + a)log(b x + a) + a +--R (2) ------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 737 + +--S 738 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (b x + a)log(b x + a) + a +--R (3) ------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 738 + +--S 739 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 3330 +t0000:=1/(a+b*x)^2 +--R +--R +--R 1 +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 741 + +--S 742 of 3330 +r0000:=(-1)/(b*(a+b*x)) +--R +--R +--R 1 +--R (2) - --------- +--R 2 +--R b x + a b +--R Type: Fraction(Polynomial(Integer)) +--E 742 + +--S 743 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 744 + +--S 745 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 3330 +t0000:=1/(x*(a+b*x)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 746 + +--S 747 of 3330 +r0000:=1/(a*(a+b*x))+log(x)/a^2-log(a+b*x)/a^2 +--R +--R +--R (- b x - a)log(b x + a) + (b x + a)log(x) + a +--R (2) --------------------------------------------- +--R 2 3 +--R a b x + a +--R Type: Expression(Integer) +--E 747 + +--S 748 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (- b x - a)log(b x + a) + (b x + a)log(x) + a +--R (3) --------------------------------------------- +--R 2 3 +--R a b x + a +--R Type: Union(Expression(Integer),...) +--E 748 + +--S 749 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 749 + +--S 750 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 3330 +t0000:=1/(x^2*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 751 + +--S 752 of 3330 +r0000:=(-1)/(a^2*x)-b/(a^2*(a+b*x))-2*b*log(x)/a^3+2*b*log(a+b*x)/a^3 +--R +--R +--R 2 2 2 2 2 +--R (2b x + 2a b x)log(b x + a) + (- 2b x - 2a b x)log(x) - 2a b x - a +--R (2) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + a x +--R Type: Expression(Integer) +--E 752 + +--S 753 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 +--R (2b x + 2a b x)log(b x + a) + (- 2b x - 2a b x)log(x) - 2a b x - a +--R (3) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + a x +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 754 + +--S 755 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 3330 +t0000:=1/(x^3*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 5 4 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 756 + +--S 757 of 3330 +r0000:=(-1/2)/(a^2*x^2)+2*b/(a^3*x)+b^2/(a^3*(a+b*x))+_ + 3*b^2*log(x)/a^4-3*b^2*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6b x - 6a b x )log(b x + a) + (6b x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - a +--R / +--R 4 3 5 2 +--R 2a b x + 2a x +--R Type: Expression(Integer) +--E 757 + +--S 758 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6b x - 6a b x )log(b x + a) + (6b x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - a +--R / +--R 4 3 5 2 +--R 2a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 758 + +--S 759 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 759 + +--S 760 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 760 + +)clear all + +--S 761 of 3330 +t0000:=1/(x^4*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 5 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 761 + +--S 762 of 3330 +r0000:=(-1/3)/(a^2*x^3)+b/(a^3*x^2)-3*b^2/(a^4*x)-b^3/(a^4*(a+b*x))-_ + 4*b^3*log(x)/a^5+4*b^3*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 4 4 3 3 4 4 3 3 3 3 +--R (12b x + 12a b x )log(b x + a) + (- 12b x - 12a b x )log(x) - 12a b x +--R + +--R 2 2 2 3 4 +--R - 6a b x + 2a b x - a +--R / +--R 5 4 6 3 +--R 3a b x + 3a x +--R Type: Expression(Integer) +--E 762 + +--S 763 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 4 4 3 3 3 3 +--R (12b x + 12a b x )log(b x + a) + (- 12b x - 12a b x )log(x) - 12a b x +--R + +--R 2 2 2 3 4 +--R - 6a b x + 2a b x - a +--R / +--R 5 4 6 3 +--R 3a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 763 + +--S 764 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 3330 +t0000:=1/(x^5*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 6 2 5 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 766 + +--S 767 of 3330 +r0000:=(-1/4)/(a^2*x^4)+2/3*b/(a^3*x^3)-3/2*b^2/(a^4*x^2)+4*b^3/(a^5*x)+_ + b^4/(a^5*(a+b*x))+5*b^4*log(x)/a^6-5*b^4*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 5 5 4 4 5 5 4 4 4 4 +--R (- 60b x - 60a b x )log(b x + a) + (60b x + 60a b x )log(x) + 60a b x +--R + +--R 2 3 3 3 2 2 4 5 +--R 30a b x - 10a b x + 5a b x - 3a +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Expression(Integer) +--E 767 + +--S 768 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 5 5 4 4 4 4 +--R (- 60b x - 60a b x )log(b x + a) + (60b x + 60a b x )log(x) + 60a b x +--R + +--R 2 3 3 3 2 2 4 5 +--R 30a b x - 10a b x + 5a b x - 3a +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 768 + +--S 769 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 770 + +)clear all + +--S 771 of 3330 +t0000:=x^m/(a+b*x)^3 +--R +--R +--R m +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 3330 +--r0000:=1/2*x^(1+m)/(a*(a+b*x)^2)+1/2*(1-m)*x^(1+m)/(a^2*(a+b*x))-_ +-- 1/2*(1-m)*m*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a^3*(1+m)) +--E 772 + +--S 773 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | ------------------------------- d%N +--R ++ 3 3 2 2 2 3 +--R %N b + 3%N a b + 3%N a b + a +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 3330 +--m0000:=a0000 - r0000 +--E 774 + +--S 775 of 3330 +--d0000:=D(m0000,x) +--E 775 + +)clear all + +--S 776 of 3330 +t0000:=x^7/(a+b*x)^3 +--R +--R +--R 7 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 776 + +--S 777 of 3330 +r0000:=15*a^4*x/b^7-5*a^3*x^2/b^6+2*a^2*x^3/b^5-3/4*a*x^4/b^4+1/5*x^5/b^3+_ + 1/2*a^7/(b^8*(a+b*x)^2)-7*a^6/(b^8*(a+b*x))-21*a^5*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 5 2 2 6 7 7 7 6 6 2 5 5 +--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x + 14a b x +--R + +--R 3 4 4 4 3 3 5 2 2 6 7 +--R - 35a b x + 140a b x + 500a b x + 160a b x - 130a +--R / +--R 10 2 9 2 8 +--R 20b x + 40a b x + 20a b +--R Type: Expression(Integer) +--E 777 + +--S 778 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 2 6 7 7 7 6 6 2 5 5 +--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x + 14a b x +--R + +--R 3 4 4 4 3 3 5 2 2 6 7 +--R - 35a b x + 140a b x + 500a b x + 160a b x - 130a +--R / +--R 10 2 9 2 8 +--R 20b x + 40a b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 778 + +--S 779 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 779 + +--S 780 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 780 + +)clear all + +--S 781 of 3330 +t0000:=x^6/(a+b*x)^3 +--R +--R +--R 6 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 781 + +--S 782 of 3330 +r0000:=-10*a^3*x/b^6+3*a^2*x^2/b^5-a*x^3/b^4+1/4*x^4/b^3-_ + 1/2*a^6/(b^7*(a+b*x)^2)+6*a^5/(b^7*(a+b*x))+15*a^4*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 4 2 2 5 6 6 6 5 5 2 4 4 +--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x +--R + +--R 3 3 3 4 2 2 5 6 +--R - 20a b x - 68a b x - 16a b x + 22a +--R / +--R 9 2 8 2 7 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 782 + +--S 783 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 2 2 5 6 6 6 5 5 2 4 4 +--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x +--R + +--R 3 3 3 4 2 2 5 6 +--R - 20a b x - 68a b x - 16a b x + 22a +--R / +--R 9 2 8 2 7 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 783 + +--S 784 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 784 + +--S 785 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 3330 +t0000:=x^5/(a+b*x)^3 +--R +--R +--R 5 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 786 + +--S 787 of 3330 +r0000:=6*a^2*x/b^5-3/2*a*x^2/b^4+1/3*x^3/b^3+1/2*a^5/(b^6*(a+b*x)^2)-_ + 5*a^4/(b^6*(a+b*x))-10*a^3*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 2 4 5 5 5 4 4 2 3 3 +--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x + 20a b x +--R + +--R 3 2 2 4 5 +--R 63a b x + 6a b x - 27a +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 787 + +--S 788 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 4 5 5 5 4 4 2 3 3 +--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x + 20a b x +--R + +--R 3 2 2 4 5 +--R 63a b x + 6a b x - 27a +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 788 + +--S 789 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 789 + +--S 790 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 3330 +t0000:=x^4/(a+b*x)^3 +--R +--R +--R 4 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 791 + +--S 792 of 3330 +r0000:=-3*a*x/b^4+1/2*x^2/b^3-1/2*a^4/(b^5*(a+b*x)^2)+4*a^3/(b^5*(a+b*x))+_ + 6*a^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 2 3 4 4 4 3 3 2 2 2 +--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x +--R + +--R 3 4 +--R 2a b x + 7a +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 792 + +--S 793 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 3 4 4 4 3 3 2 2 2 +--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x +--R + +--R 3 4 +--R 2a b x + 7a +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 793 + +--S 794 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 794 + +--S 795 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +)clear all + +--S 796 of 3330 +t0000:=x^3/(a+b*x)^3 +--R +--R +--R 3 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 796 + +--S 797 of 3330 +r0000:=x/b^3+1/2*a^3/(b^4*(a+b*x)^2)-3*a^2/(b^4*(a+b*x))-3*a*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a +--R ------------------------------------------------------------------------ +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 797 + +--S 798 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a +--R ------------------------------------------------------------------------ +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 799 + +--S 800 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 3330 +t0000:=x^2/(a+b*x)^3 +--R +--R +--R 2 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 801 + +--S 802 of 3330 +r0000:=-1/2*a^2/(b^3*(a+b*x)^2)+2*a/(b^3*(a+b*x))+log(a+b*x)/b^3 +--R +--R +--R 2 2 2 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (2) ------------------------------------------------- +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 802 + +--S 803 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (3) ------------------------------------------------- +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 3330 +t0000:=x/(a+b*x)^3 +--R +--R +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 806 + +--S 807 of 3330 +r0000:=1/2*x^2/(a*(a+b*x)^2) +--R +--R +--R 1 2 +--R - x +--R 2 +--R (2) -------------------- +--R 2 2 2 3 +--R a b x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 807 + +--S 808 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 2b x - a +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 808 + +--S 809 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 2a b +--R Type: Expression(Integer) +--E 809 + +--S 810 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 810 + +)clear all + +--S 811 of 3330 +t0000:=1/(a+b*x)^3 +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 811 + +--S 812 of 3330 +r0000:=(-1/2)/(b*(a+b*x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ------------------- +--R 3 2 2 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 812 + +--S 813 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --------------------- +--R 3 2 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 813 + +--S 814 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 814 + +--S 815 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 3330 +t0000:=1/(x*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 4 2 3 2 2 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 816 + +--S 817 of 3330 +r0000:=1/2/(a*(a+b*x)^2)+1/(a^2*(a+b*x))+log(x)/a^3-log(a+b*x)/a^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (2b x + 4a b x + 2a )log(x) +--R + +--R 2 +--R 2a b x + 3a +--R / +--R 3 2 2 4 5 +--R 2a b x + 4a b x + 2a +--R Type: Expression(Integer) +--E 817 + +--S 818 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (2b x + 4a b x + 2a )log(x) +--R + +--R 2 +--R 2a b x + 3a +--R / +--R 3 2 2 4 5 +--R 2a b x + 4a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 818 + +--S 819 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 819 + +--S 820 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 3330 +t0000:=1/(x^2*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 5 2 4 2 3 3 2 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 821 + +--S 822 of 3330 +r0000:=(-1)/(a^3*x)-1/2*b/(a^2*(a+b*x)^2)-2*b/(a^3*(a+b*x))-_ + 3*b*log(x)/a^4+3*b*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 3 3 2 2 2 +--R (6b x + 12a b x + 6a b x)log(b x + a) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6b x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2a +--R / +--R 4 2 3 5 2 6 +--R 2a b x + 4a b x + 2a x +--R Type: Expression(Integer) +--E 822 + +--S 823 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 +--R (6b x + 12a b x + 6a b x)log(b x + a) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6b x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2a +--R / +--R 4 2 3 5 2 6 +--R 2a b x + 4a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 823 + +--S 824 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 824 + +--S 825 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 3330 +t0000:=1/(x^3*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 826 + +--S 827 of 3330 +r0000:=(-1/2)/(a^3*x^2)+3*b/(a^4*x)+1/2*b^2/(a^3*(a+b*x)^2)+_ + 3*b^2/(a^4*(a+b*x))+6*b^2*log(x)/a^5-6*b^2*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 +--R (- 12b x - 24a b x - 12a b x )log(b x + a) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12b x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - a +--R / +--R 5 2 4 6 3 7 2 +--R 2a b x + 4a b x + 2a x +--R Type: Expression(Integer) +--E 827 + +--S 828 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 +--R (- 12b x - 24a b x - 12a b x )log(b x + a) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12b x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - a +--R / +--R 5 2 4 6 3 7 2 +--R 2a b x + 4a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 3330 +t0000:=1/(x^4*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 7 2 6 2 5 3 4 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 831 + +--S 832 of 3330 +r0000:=(-1/3)/(a^3*x^3)+3/2*b/(a^4*x^2)-6*b^2/(a^5*x)-1/2*b^3/(a^4*(a+b*x)^2)-_ + 4*b^3/(a^5*(a+b*x))-10*b^3*log(x)/a^6+10*b^3*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 +--R (60b x + 120a b x + 60a b x )log(b x + a) +--R + +--R 5 5 4 4 2 3 3 4 4 2 3 3 3 2 2 +--R (- 60b x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x +--R + +--R 4 5 +--R 5a b x - 2a +--R / +--R 6 2 5 7 4 8 3 +--R 6a b x + 12a b x + 6a x +--R Type: Expression(Integer) +--E 832 + +--S 833 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 +--R (60b x + 120a b x + 60a b x )log(b x + a) +--R + +--R 5 5 4 4 2 3 3 4 4 2 3 3 3 2 2 +--R (- 60b x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x +--R + +--R 4 5 +--R 5a b x - 2a +--R / +--R 6 2 5 7 4 8 3 +--R 6a b x + 12a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 3330 +t0000:=1/(x^5*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 8 2 7 2 6 3 5 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 836 + +--S 837 of 3330 +r0000:=(-1/4)/(a^3*x^4)+b/(a^4*x^3)-3*b^2/(a^5*x^2)+10*b^3/(a^6*x)+_ + 1/2*b^4/(a^5*(a+b*x)^2)+5*b^4/(a^6*(a+b*x))+_ + 15*b^4*log(x)/a^7-15*b^4*log(a+b*x)/a^7 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 +--R (- 60b x - 120a b x - 60a b x )log(b x + a) +--R + +--R 6 6 5 5 2 4 4 5 5 2 4 4 3 3 3 +--R (60b x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x +--R + +--R 4 2 2 5 6 +--R - 5a b x + 2a b x - a +--R / +--R 7 2 6 8 5 9 4 +--R 4a b x + 8a b x + 4a x +--R Type: Expression(Integer) +--E 837 + +--S 838 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 +--R (- 60b x - 120a b x - 60a b x )log(b x + a) +--R + +--R 6 6 5 5 2 4 4 5 5 2 4 4 3 3 3 +--R (60b x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x +--R + +--R 4 2 2 5 6 +--R - 5a b x + 2a b x - a +--R / +--R 7 2 6 8 5 9 4 +--R 4a b x + 8a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 838 + +--S 839 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 3330 +t0000:=x^8/(a+b*x)^4 +--R +--R +--R 8 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 841 + +--S 842 of 3330 +r0000:=35*a^4*x/b^8-10*a^3*x^2/b^7+10/3*a^2*x^3/b^6-a*x^4/b^5+_ + 1/5*x^5/b^4-1/3*a^8/(b^9*(a+b*x)^3)+4*a^7/(b^9*(a+b*x)^2)-_ + 28*a^6/(b^9*(a+b*x))-56*a^5*log(a+b*x)/b^9 +--R +--R +--R (2) +--R 5 3 3 6 2 2 7 8 8 8 +--R (- 840a b x - 2520a b x - 2520a b x - 840a )log(b x + a) + 3b x +--R + +--R 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R - 6a b x + 14a b x - 42a b x + 210a b x + 1175a b x + 1005a b x +--R + +--R 7 8 +--R - 255a b x - 365a +--R / +--R 12 3 11 2 2 10 3 9 +--R 15b x + 45a b x + 45a b x + 15a b +--R Type: Expression(Integer) +--E 842 + +--S 843 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 3 3 6 2 2 7 8 8 8 +--R (- 840a b x - 2520a b x - 2520a b x - 840a )log(b x + a) + 3b x +--R + +--R 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R - 6a b x + 14a b x - 42a b x + 210a b x + 1175a b x + 1005a b x +--R + +--R 7 8 +--R - 255a b x - 365a +--R / +--R 12 3 11 2 2 10 3 9 +--R 15b x + 45a b x + 45a b x + 15a b +--R Type: Union(Expression(Integer),...) +--E 843 + +--S 844 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)clear all + +--S 846 of 3330 +t0000:=x^7/(a+b*x)^4 +--R +--R +--R 7 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 846 + +--S 847 of 3330 +r0000:=-20*a^3*x/b^7+5*a^2*x^2/b^6-4/3*a*x^3/b^5+1/4*x^4/b^4+_ + 1/3*a^7/(b^8*(a+b*x)^3)-7/2*a^6/(b^8*(a+b*x)^2)+_ + 21*a^5/(b^8*(a+b*x))+35*a^4*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 4 3 3 5 2 2 6 7 7 7 +--R (420a b x + 1260a b x + 1260a b x + 420a )log(b x + a) + 3b x +--R + +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - 7a b x + 21a b x - 105a b x - 556a b x - 408a b x + 222a b x + 214a +--R / +--R 11 3 10 2 2 9 3 8 +--R 12b x + 36a b x + 36a b x + 12a b +--R Type: Expression(Integer) +--E 847 + +--S 848 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 5 2 2 6 7 7 7 +--R (420a b x + 1260a b x + 1260a b x + 420a )log(b x + a) + 3b x +--R + +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - 7a b x + 21a b x - 105a b x - 556a b x - 408a b x + 222a b x + 214a +--R / +--R 11 3 10 2 2 9 3 8 +--R 12b x + 36a b x + 36a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 3330 +t0000:=x^6/(a+b*x)^4 +--R +--R +--R 6 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 851 + +--S 852 of 3330 +r0000:=10*a^2*x/b^6-2*a*x^2/b^5+1/3*x^3/b^4-1/3*a^6/(b^7*(a+b*x)^3)+_ + 3*a^5/(b^7*(a+b*x)^2)-15*a^4/(b^7*(a+b*x))-20*a^3*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 3 3 3 4 2 2 5 6 6 6 5 5 +--R (- 60a b x - 180a b x - 180a b x - 60a )log(b x + a) + b x - 3a b x +--R + +--R 2 4 4 3 3 3 4 2 2 5 6 +--R 15a b x + 73a b x + 39a b x - 51a b x - 37a +--R / +--R 10 3 9 2 2 8 3 7 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Expression(Integer) +--E 852 + +--S 853 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 4 2 2 5 6 6 6 5 5 +--R (- 60a b x - 180a b x - 180a b x - 60a )log(b x + a) + b x - 3a b x +--R + +--R 2 4 4 3 3 3 4 2 2 5 6 +--R 15a b x + 73a b x + 39a b x - 51a b x - 37a +--R / +--R 10 3 9 2 2 8 3 7 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 854 + +--S 855 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +)clear all + +--S 856 of 3330 +t0000:=x^5/(a+b*x)^4 +--R +--R +--R 5 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 856 + +--S 857 of 3330 +r0000:=-4*a*x/b^5+1/2*x^2/b^4+1/3*a^5/(b^6*(a+b*x)^3)-_ + 5/2*a^4/(b^6*(a+b*x)^2)+10*a^3/(b^6*(a+b*x))+10*a^2*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 2 3 3 3 2 2 4 5 5 5 4 4 +--R (60a b x + 180a b x + 180a b x + 60a )log(b x + a) + 3b x - 15a b x +--R + +--R 2 3 3 3 2 2 4 5 +--R - 63a b x - 9a b x + 81a b x + 47a +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 857 + +--S 858 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 4 5 5 5 4 4 +--R (60a b x + 180a b x + 180a b x + 60a )log(b x + a) + 3b x - 15a b x +--R + +--R 2 3 3 3 2 2 4 5 +--R - 63a b x - 9a b x + 81a b x + 47a +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 858 + +--S 859 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 859 + +--S 860 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 3330 +t0000:=x^4/(a+b*x)^4 +--R +--R +--R 4 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 861 + +--S 862 of 3330 +r0000:=x/b^4-1/3*a^4/(b^5*(a+b*x)^3)+2*a^3/(b^5*(a+b*x)^2)-_ + 6*a^2/(b^5*(a+b*x))-4*a*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 4 4 4 3 3 +--R (- 12a b x - 36a b x - 36a b x - 12a )log(b x + a) + 3b x + 9a b x +--R + +--R 2 2 2 3 4 +--R - 9a b x - 27a b x - 13a +--R / +--R 8 3 7 2 2 6 3 5 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Expression(Integer) +--E 862 + +--S 863 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 4 4 4 3 3 +--R (- 12a b x - 36a b x - 36a b x - 12a )log(b x + a) + 3b x + 9a b x +--R + +--R 2 2 2 3 4 +--R - 9a b x - 27a b x - 13a +--R / +--R 8 3 7 2 2 6 3 5 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 863 + +--S 864 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +)clear all + +--S 866 of 3330 +t0000:=x^3/(a+b*x)^4 +--R +--R +--R 3 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 866 + +--S 867 of 3330 +r0000:=1/3*a^3/(b^4*(a+b*x)^3)-3/2*a^2/(b^4*(a+b*x)^2)+_ + 3*a/(b^4*(a+b*x))+log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 2 2 3 +--R (6b x + 18a b x + 18a b x + 6a )log(b x + a) + 18a b x + 27a b x + 11a +--R -------------------------------------------------------------------------- +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 867 + +--S 868 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 2 2 2 3 +--R (6b x + 18a b x + 18a b x + 6a )log(b x + a) + 18a b x + 27a b x + 11a +--R -------------------------------------------------------------------------- +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 868 + +--S 869 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 869 + +--S 870 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 870 + +)clear all + +--S 871 of 3330 +t0000:=x^2/(a+b*x)^4 +--R +--R +--R 2 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 871 + +--S 872 of 3330 +r0000:=1/3*x^3/(a*(a+b*x)^3) +--R +--R +--R 1 3 +--R - x +--R 3 +--R (2) ------------------------------ +--R 3 3 2 2 2 3 4 +--R a b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 872 + +--S 873 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 3b x - 3a b x - a +--R (3) -------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 873 + +--S 874 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ----- +--R 3 +--R 3a b +--R Type: Expression(Integer) +--E 874 + +--S 875 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 875 + +)clear all + +--S 876 of 3330 +t0000:=x/(a+b*x)^4 +--R +--R +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 876 + +--S 877 of 3330 +r0000:=1/3*a/(b^2*(a+b*x)^3)+(-1/2)/(b^2*(a+b*x)^2) +--R +--R +--R 1 1 +--R - - b x - - a +--R 2 6 +--R (2) ------------------------------ +--R 5 3 4 2 2 3 3 2 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 877 + +--S 878 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 3b x - a +--R (3) ---------------------------------- +--R 5 3 4 2 2 3 3 2 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 878 + +--S 879 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 3330 +t0000:=1/(a+b*x)^4 +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 881 + +--S 882 of 3330 +r0000:=(-1/3)/(b*(a+b*x)^3) +--R +--R +--R 1 +--R - +--R 3 +--R (2) - ----------------------------- +--R 4 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 882 + +--S 883 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - ------------------------------- +--R 4 3 3 2 2 2 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 3330 +t0000:=1/(x*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 4 5 3 4 2 2 3 3 2 4 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 886 + +--S 887 of 3330 +r0000:=1/3/(a*(a+b*x)^3)+1/2/(a^2*(a+b*x)^2)+1/(a^3*(a+b*x))+log(x)/a^4-_ + log(a+b*x)/a^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (- 6b x - 18a b x - 18a b x - 6a )log(b x + a) +--R + +--R 3 3 2 2 2 3 2 2 2 3 +--R (6b x + 18a b x + 18a b x + 6a )log(x) + 6a b x + 15a b x + 11a +--R / +--R 4 3 3 5 2 2 6 7 +--R 6a b x + 18a b x + 18a b x + 6a +--R Type: Expression(Integer) +--E 887 + +--S 888 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (- 6b x - 18a b x - 18a b x - 6a )log(b x + a) +--R + +--R 3 3 2 2 2 3 2 2 2 3 +--R (6b x + 18a b x + 18a b x + 6a )log(x) + 6a b x + 15a b x + 11a +--R / +--R 4 3 3 5 2 2 6 7 +--R 6a b x + 18a b x + 18a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 3330 +t0000:=1/(x^2*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 6 3 5 2 2 4 3 3 4 2 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 891 + +--S 892 of 3330 +r0000:=(-1)/(a^4*x)-1/3*b/(a^2*(a+b*x)^3)-b/(a^3*(a+b*x)^2)-_ + 3*b/(a^4*(a+b*x))-4*b*log(x)/a^5+4*b*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 3 +--R (12b x + 36a b x + 36a b x + 12a b x)log(b x + a) +--R + +--R 4 4 3 3 2 2 2 3 3 3 2 2 2 +--R (- 12b x - 36a b x - 36a b x - 12a b x)log(x) - 12a b x - 30a b x +--R + +--R 3 4 +--R - 22a b x - 3a +--R / +--R 5 3 4 6 2 3 7 2 8 +--R 3a b x + 9a b x + 9a b x + 3a x +--R Type: Expression(Integer) +--E 892 + +--S 893 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 +--R (12b x + 36a b x + 36a b x + 12a b x)log(b x + a) +--R + +--R 4 4 3 3 2 2 2 3 3 3 2 2 2 +--R (- 12b x - 36a b x - 36a b x - 12a b x)log(x) - 12a b x - 30a b x +--R + +--R 3 4 +--R - 22a b x - 3a +--R / +--R 5 3 4 6 2 3 7 2 8 +--R 3a b x + 9a b x + 9a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 894 + +--S 895 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 3330 +t0000:=1/(x^3*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 7 3 6 2 2 5 3 4 4 3 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 896 + +--S 897 of 3330 +r0000:=(-1/2)/(a^4*x^2)+4*b/(a^5*x)+1/3*b^2/(a^3*(a+b*x)^3)+_ + 3/2*b^2/(a^4*(a+b*x)^2)+6*b^2/(a^5*(a+b*x))+_ + 10*b^2*log(x)/a^6-10*b^2*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 3 2 2 +--R (- 60b x - 180a b x - 180a b x - 60a b x )log(b x + a) +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 4 2 3 3 +--R (60b x + 180a b x + 180a b x + 60a b x )log(x) + 60a b x + 150a b x +--R + +--R 3 2 2 4 5 +--R 110a b x + 15a b x - 3a +--R / +--R 6 3 5 7 2 4 8 3 9 2 +--R 6a b x + 18a b x + 18a b x + 6a x +--R Type: Expression(Integer) +--E 897 + +--S 898 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 +--R (- 60b x - 180a b x - 180a b x - 60a b x )log(b x + a) +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 4 2 3 3 +--R (60b x + 180a b x + 180a b x + 60a b x )log(x) + 60a b x + 150a b x +--R + +--R 3 2 2 4 5 +--R 110a b x + 15a b x - 3a +--R / +--R 6 3 5 7 2 4 8 3 9 2 +--R 6a b x + 18a b x + 18a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 898 + +--S 899 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 3330 +t0000:=1/(x^4*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 8 3 7 2 2 6 3 5 4 4 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 901 + +--S 902 of 3330 +r0000:=(-1/3)/(a^4*x^3)+2*b/(a^5*x^2)-10*b^2/(a^6*x)-_ + 1/3*b^3/(a^4*(a+b*x)^3)-2*b^3/(a^5*(a+b*x)^2)-_ + 10*b^3/(a^6*(a+b*x))-20*b^3*log(x)/a^7+20*b^3*log(a+b*x)/a^7 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 +--R (60b x + 180a b x + 180a b x + 60a b x )log(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 5 5 +--R (- 60b x - 180a b x - 180a b x - 60a b x )log(x) - 60a b x +--R + +--R 2 4 4 3 3 3 4 2 2 5 6 +--R - 150a b x - 110a b x - 15a b x + 3a b x - a +--R / +--R 7 3 6 8 2 5 9 4 10 3 +--R 3a b x + 9a b x + 9a b x + 3a x +--R Type: Expression(Integer) +--E 902 + +--S 903 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 +--R (60b x + 180a b x + 180a b x + 60a b x )log(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 5 5 +--R (- 60b x - 180a b x - 180a b x - 60a b x )log(x) - 60a b x +--R + +--R 2 4 4 3 3 3 4 2 2 5 6 +--R - 150a b x - 110a b x - 15a b x + 3a b x - a +--R / +--R 7 3 6 8 2 5 9 4 10 3 +--R 3a b x + 9a b x + 9a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 903 + +--S 904 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 904 + +--S 905 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 905 + +)clear all + +--S 906 of 3330 +t0000:=1/(x^5*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 9 3 8 2 2 7 3 6 4 5 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 906 + +--S 907 of 3330 +r0000:=(-1/4)/(a^4*x^4)+4/3*b/(a^5*x^3)-5*b^2/(a^6*x^2)+20*b^3/(a^7*x)+_ + 1/3*b^4/(a^5*(a+b*x)^3)+5/2*b^4/(a^6*(a+b*x)^2)+15*b^4/(a^7*(a+b*x))+_ + 35*b^4*log(x)/a^8-35*b^4*log(a+b*x)/a^8 +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 +--R (- 420b x - 1260a b x - 1260a b x - 420a b x )log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 6 6 +--R (420b x + 1260a b x + 1260a b x + 420a b x )log(x) + 420a b x +--R + +--R 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R 1050a b x + 770a b x + 105a b x - 21a b x + 7a b x - 3a +--R / +--R 8 3 7 9 2 6 10 5 11 4 +--R 12a b x + 36a b x + 36a b x + 12a x +--R Type: Expression(Integer) +--E 907 + +--S 908 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 +--R (- 420b x - 1260a b x - 1260a b x - 420a b x )log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 6 6 +--R (420b x + 1260a b x + 1260a b x + 420a b x )log(x) + 420a b x +--R + +--R 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R 1050a b x + 770a b x + 105a b x - 21a b x + 7a b x - 3a +--R / +--R 8 3 7 9 2 6 10 5 11 4 +--R 12a b x + 36a b x + 36a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 908 + +--S 909 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 909 + +--S 910 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 910 + +)clear all + +--S 911 of 3330 +t0000:=x^10/(a+b*x)^7 +--R +--R +--R (1) +--R 10 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 911 + +--S 912 of 3330 +r0000:=-84*a^3*x/b^10+14*a^2*x^2/b^9-7/3*a*x^3/b^8+1/4*x^4/b^7-_ + 1/6*a^10/(b^11*(a+b*x)^6)+2*a^9/(b^11*(a+b*x)^5)-_ + 45/4*a^8/(b^11*(a+b*x)^4)+40*a^7/(b^11*(a+b*x)^3)-_ + 105*a^6/(b^11*(a+b*x)^2)+252*a^5/(b^11*(a+b*x))+210*a^4*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 2520a b x + 15120a b x + 37800a b x + 50400a b x + 37800a b x +--R + +--R 9 10 +--R 15120a b x + 2520a +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R 3b x - 10a b x + 45a b x - 360a b x - 4043a b x - 9138a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 3945a b x + 11540a b x + 18105a b x + 10266a b x + 2131a +--R / +--R 17 6 16 5 2 15 4 3 14 3 4 13 2 5 12 +--R 12b x + 72a b x + 180a b x + 240a b x + 180a b x + 72a b x +--R + +--R 6 11 +--R 12a b +--R Type: Expression(Integer) +--E 912 + +--S 913 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 2520a b x + 15120a b x + 37800a b x + 50400a b x + 37800a b x +--R + +--R 9 10 +--R 15120a b x + 2520a +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R 3b x - 10a b x + 45a b x - 360a b x - 4043a b x - 9138a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 3945a b x + 11540a b x + 18105a b x + 10266a b x + 2131a +--R / +--R 17 6 16 5 2 15 4 3 14 3 4 13 2 5 12 +--R 12b x + 72a b x + 180a b x + 240a b x + 180a b x + 72a b x +--R + +--R 6 11 +--R 12a b +--R Type: Union(Expression(Integer),...) +--E 913 + +--S 914 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 914 + +--S 915 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 915 + +)clear all + +--S 916 of 3330 +t0000:=x^9/(a+b*x)^7 +--R +--R +--R (1) +--R 9 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 916 + +--S 917 of 3330 +r0000:=28*a^2*x/b^9-7/2*a*x^2/b^8+1/3*x^3/b^7+1/6*a^9/(b^10*(a+b*x)^6)-_ + 9/5*a^8/(b^10*(a+b*x)^5)+9*a^7/(b^10*(a+b*x)^4)-_ + 28*a^6/(b^10*(a+b*x)^3)+63*a^5/(b^10*(a+b*x)^2)-_ + 126*a^4/(b^10*(a+b*x))-84*a^3*log(a+b*x)/b^10 +--R +--R +--R (2) +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 +--R - 2520a b x - 15120a b x - 37800a b x - 50400a b x - 37800a b x +--R + +--R 8 9 +--R - 15120a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 10b x - 45a b x + 360a b x + 3665a b x + 6870a b x - 1725a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R - 19100a b x - 23775a b x - 12534a b x - 2509a +--R / +--R 16 6 15 5 2 14 4 3 13 3 4 12 2 5 11 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 6 10 +--R 30a b +--R Type: Expression(Integer) +--E 917 + +--S 918 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 +--R - 2520a b x - 15120a b x - 37800a b x - 50400a b x - 37800a b x +--R + +--R 8 9 +--R - 15120a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 10b x - 45a b x + 360a b x + 3665a b x + 6870a b x - 1725a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R - 19100a b x - 23775a b x - 12534a b x - 2509a +--R / +--R 16 6 15 5 2 14 4 3 13 3 4 12 2 5 11 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 6 10 +--R 30a b +--R Type: Union(Expression(Integer),...) +--E 918 + +--S 919 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 919 + +--S 920 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 920 + +)clear all + +--S 921 of 3330 +t0000:=x^8/(a+b*x)^7 +--R +--R +--R (1) +--R 8 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 921 + +--S 922 of 3330 +r0000:=-7*a*x/b^8+1/2*x^2/b^7-1/6*a^8/(b^9*(a+b*x)^6)+_ + 8/5*a^7/(b^9*(a+b*x)^5)-7*a^6/(b^9*(a+b*x)^4)+_ + 56/3*a^5/(b^9*(a+b*x)^3)-35*a^4/(b^9*(a+b*x)^2)+_ + 56*a^3/(b^9*(a+b*x))+28*a^2*log(a+b*x)/b^9 +--R +--R +--R (2) +--R 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R 840a b x + 5040a b x + 12600a b x + 16800a b x + 12600a b x +--R + +--R 7 8 +--R 5040a b x + 840a +--R * +--R log(b x + a) +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 15b x - 120a b x - 1035a b x - 1170a b x + 3375a b x + 10100a b x +--R + +--R 6 2 2 7 8 +--R 10725a b x + 5298a b x + 1023a +--R / +--R 15 6 14 5 2 13 4 3 12 3 4 11 2 5 10 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 6 9 +--R 30a b +--R Type: Expression(Integer) +--E 922 + +--S 923 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R 840a b x + 5040a b x + 12600a b x + 16800a b x + 12600a b x +--R + +--R 7 8 +--R 5040a b x + 840a +--R * +--R log(b x + a) +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 15b x - 120a b x - 1035a b x - 1170a b x + 3375a b x + 10100a b x +--R + +--R 6 2 2 7 8 +--R 10725a b x + 5298a b x + 1023a +--R / +--R 15 6 14 5 2 13 4 3 12 3 4 11 2 5 10 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 6 9 +--R 30a b +--R Type: Union(Expression(Integer),...) +--E 923 + +--S 924 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 924 + +--S 925 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 925 + +)clear all + +--S 926 of 3330 +t0000:=x^7/(a+b*x)^7 +--R +--R +--R (1) +--R 7 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 926 + +--S 927 of 3330 +r0000:=x/b^7+1/6*a^7/(b^8*(a+b*x)^6)-7/5*a^6/(b^8*(a+b*x)^5)+_ + 21/4*a^5/(b^8*(a+b*x)^4)-35/3*a^4/(b^8*(a+b*x)^3)+_ + 35/2*a^3/(b^8*(a+b*x)^2)-21*a^2/(b^8*(a+b*x))-7*a*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 420a b x - 2520a b x - 6300a b x - 8400a b x - 6300a b x +--R + +--R 6 7 +--R - 2520a b x - 420a +--R * +--R log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R 60b x + 360a b x - 360a b x - 4050a b x - 8200a b x - 7725a b x +--R + +--R 6 7 +--R - 3594a b x - 669a +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 8 +--R 60a b +--R Type: Expression(Integer) +--E 927 + +--S 928 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 420a b x - 2520a b x - 6300a b x - 8400a b x - 6300a b x +--R + +--R 6 7 +--R - 2520a b x - 420a +--R * +--R log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R 60b x + 360a b x - 360a b x - 4050a b x - 8200a b x - 7725a b x +--R + +--R 6 7 +--R - 3594a b x - 669a +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 8 +--R 60a b +--R Type: Union(Expression(Integer),...) +--E 928 + +--S 929 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 929 + +--S 930 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 930 + +)clear all + +--S 931 of 3330 +t0000:=x^6/(a+b*x)^7 +--R +--R +--R (1) +--R 6 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 931 + +--S 932 of 3330 +r0000:=-1/6*a^6/(b^7*(a+b*x)^6)+6/5*a^5/(b^7*(a+b*x)^5)-_ + 15/4*a^4/(b^7*(a+b*x)^4)+20/3*a^3/(b^7*(a+b*x)^3)-_ + 15/2*a^2/(b^7*(a+b*x)^2)+6*a/(b^7*(a+b*x))+log(a+b*x)/b^7 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 +--R 60a +--R * +--R log(b x + a) +--R + +--R 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R 360a b x + 1350a b x + 2200a b x + 1875a b x + 822a b x + 147a +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 7 +--R 60a b +--R Type: Expression(Integer) +--E 932 + +--S 933 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 +--R 60a +--R * +--R log(b x + a) +--R + +--R 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R 360a b x + 1350a b x + 2200a b x + 1875a b x + 822a b x + 147a +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 7 +--R 60a b +--R Type: Union(Expression(Integer),...) +--E 933 + +--S 934 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 3330 +t0000:=x^5/(a+b*x)^7 +--R +--R +--R (1) +--R 5 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 936 + +--S 937 of 3330 +r0000:=1/6*x^6/(a*(a+b*x)^6) +--R +--R +--R 1 6 +--R - x +--R 6 +--R (2) --------------------------------------------------------------- +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 937 + +--S 938 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R ----------------------------------------------------------------------- +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R 6b x + 36a b x + 90a b x + 120a b x + 90a b x + 36a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 938 + +--S 939 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ----- +--R 6 +--R 6a b +--R Type: Expression(Integer) +--E 939 + +--S 940 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 940 + +)clear all + +--S 941 of 3330 +t0000:=x^4/(a+b*x)^7 +--R +--R +--R (1) +--R 4 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 941 + +--S 942 of 3330 +r0000:=1/6*x^5/(a*(a+b*x)^6)+1/30*x^5/(a^2*(a+b*x)^5) +--R +--R +--R 1 6 1 5 +--R -- b x + - a x +--R 30 5 +--R (2) --------------------------------------------------------------- +--R 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 7 8 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 942 + +--S 943 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 4 +--R - 15b x - 20a b x - 15a b x - 6a b x - a +--R ---------------------------------------------------------------------------- +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 6 5 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x + 30a b +--R Type: Union(Expression(Integer),...) +--E 943 + +--S 944 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------ +--R 2 5 +--R 30a b +--R Type: Expression(Integer) +--E 944 + +--S 945 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 3330 +t0000:=x^3/(a+b*x)^7 +--R +--R +--R (1) +--R 3 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 946 + +--S 947 of 3330 +r0000:=1/6*x^4/(a*(a+b*x)^6)+1/15*x^4/(a^2*(a+b*x)^5)+_ + 1/60*x^4/(a^3*(a+b*x)^4),1/6*a^3/(b^4*(a+b*x)^6)-_ + 3/5*a^2/(b^4*(a+b*x)^5)+3/4*a/(b^4*(a+b*x)^4)+(-1/3)/(b^4*(a+b*x)^3) +--R +--R +--R (2) +--R 1 2 6 1 5 1 2 4 +--R -- b x + -- a b x + - a x +--R 60 10 4 +--R [---------------------------------------------------------------, +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 8 9 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R 1 3 3 1 2 2 1 2 1 3 +--R - - b x - - a b x - -- a b x - -- a +--R 3 4 10 60 +--R ----------------------------------------------------------------] +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Tuple(Fraction(Polynomial(Fraction(Integer)))) +--E 947 + +--S 948 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R - 20b x - 15a b x - 6a b x - a +--R ---------------------------------------------------------------------------- +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 948 + +--S 949 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------ +--R 3 4 +--R 60a b +--R Type: Expression(Integer) +--E 949 + +--S 950 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 950 + +)clear all + +--S 951 of 3330 +t0000:=x^2/(a+b*x)^7 +--R +--R +--R (1) +--R 2 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 951 + +--S 952 of 3330 +r0000:=-1/6*a^2/(b^3*(a+b*x)^6)+2/5*a/(b^3*(a+b*x)^5)+(-1/4)/(b^3*(a+b*x)^4) +--R +--R +--R 1 2 2 1 1 2 +--R - - b x - -- a b x - -- a +--R 4 10 60 +--R (2) --------------------------------------------------------------- +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 952 + +--S 953 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +--R - 15b x - 6a b x - a +--R --------------------------------------------------------------------------- +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 953 + +--S 954 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 954 + +--S 955 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 955 + +)clear all + +--S 956 of 3330 +t0000:=x/(a+b*x)^7 +--R +--R +--R (1) +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 956 + +--S 957 of 3330 +r0000:=1/6*a/(b^2*(a+b*x)^6)+(-1/5)/(b^2*(a+b*x)^5) +--R +--R +--R 1 1 +--R - - b x - -- a +--R 5 30 +--R (2) --------------------------------------------------------------- +--R 8 6 7 5 2 6 4 3 5 3 4 4 2 5 3 6 2 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 957 + +--S 958 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R - 6b x - a +--R -------------------------------------------------------------------------- +--R 8 6 7 5 2 6 4 3 5 3 4 4 2 5 3 6 2 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x + 30a b +--R Type: Union(Expression(Integer),...) +--E 958 + +--S 959 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 959 + +--S 960 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 3330 +t0000:=1/(a+b*x)^7 +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 3330 +r0000:=(-1/6)/(b*(a+b*x)^6) +--R +--R +--R 1 +--R - +--R 6 +--R (2) - -------------------------------------------------------------- +--R 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 962 + +--S 963 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - ------------------------------------------------------------------- +--R 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 +--R 6b x + 36a b x + 90a b x + 120a b x + 90a b x + 36a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 964 + +--S 965 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 3330 +t0000:=1/(x*(a+b*x)^7) +--R +--R +--R (1) +--R 1 +--R -------------------------------------------------------------------------- +--R 7 8 6 7 2 5 6 3 4 5 4 3 4 5 2 3 6 2 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 966 + +--S 967 of 3330 +r0000:=1/6/(a*(a+b*x)^6)+1/5/(a^2*(a+b*x)^5)+1/4/(a^3*(a+b*x)^4)+_ + 1/3/(a^4*(a+b*x)^3)+1/2/(a^5*(a+b*x)^2)+1/(a^6*(a+b*x))+_ + log(x)/a^7-log(a+b*x)/a^7 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R - 60b x - 360a b x - 900a b x - 1200a b x - 900a b x - 360a b x +--R + +--R 6 +--R - 60a +--R * +--R log(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 +--R 60a +--R * +--R log(x) +--R + +--R 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R 60a b x + 330a b x + 740a b x + 855a b x + 522a b x + 147a +--R / +--R 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 12 +--R 60a b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 13 +--R 60a +--R Type: Expression(Integer) +--E 967 + +--S 968 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R - 60b x - 360a b x - 900a b x - 1200a b x - 900a b x - 360a b x +--R + +--R 6 +--R - 60a +--R * +--R log(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 +--R 60a +--R * +--R log(x) +--R + +--R 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R 60a b x + 330a b x + 740a b x + 855a b x + 522a b x + 147a +--R / +--R 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 12 +--R 60a b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 13 +--R 60a +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 969 + +--S 970 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 3330 +t0000:=1/(x^2*(a+b*x)^7) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 7 9 6 8 2 5 7 3 4 6 4 3 5 5 2 4 6 3 7 2 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 971 + +--S 972 of 3330 +r0000:=(-1)/(a^7*x)-1/6*b/(a^2*(a+b*x)^6)-2/5*b/(a^3*(a+b*x)^5)-_ + 3/4*b/(a^4*(a+b*x)^4)-4/3*b/(a^5*(a+b*x)^3)-5/2*b/(a^6*(a+b*x)^2)-_ + 6*b/(a^7*(a+b*x))-7*b*log(x)/a^8+7*b*log(a+b*x)/a^8 +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420b x + 2520a b x + 6300a b x + 8400a b x + 6300a b x +--R + +--R 5 2 2 6 +--R 2520a b x + 420a b x +--R * +--R log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 420b x - 2520a b x - 6300a b x - 8400a b x - 6300a b x +--R + +--R 5 2 2 6 +--R - 2520a b x - 420a b x +--R * +--R log(x) +--R + +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 420a b x - 2310a b x - 5180a b x - 5985a b x - 3654a b x +--R + +--R 6 7 +--R - 1029a b x - 60a +--R / +--R 8 6 7 9 5 6 10 4 5 11 3 4 12 2 3 13 2 +--R 60a b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 14 +--R 60a x +--R Type: Expression(Integer) +--E 972 + +--S 973 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420b x + 2520a b x + 6300a b x + 8400a b x + 6300a b x +--R + +--R 5 2 2 6 +--R 2520a b x + 420a b x +--R * +--R log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 420b x - 2520a b x - 6300a b x - 8400a b x - 6300a b x +--R + +--R 5 2 2 6 +--R - 2520a b x - 420a b x +--R * +--R log(x) +--R + +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 420a b x - 2310a b x - 5180a b x - 5985a b x - 3654a b x +--R + +--R 6 7 +--R - 1029a b x - 60a +--R / +--R 8 6 7 9 5 6 10 4 5 11 3 4 12 2 3 13 2 +--R 60a b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 14 +--R 60a x +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 3330 +t0000:=1/(x^3*(a+b*x)^7) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 7 10 6 9 2 5 8 3 4 7 4 3 6 5 2 5 6 4 7 3 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 976 + +--S 977 of 3330 +r0000:=(-1/2)/(a^7*x^2)+7*b/(a^8*x)+1/6*b^2/(a^3*(a+b*x)^6)+_ + 3/5*b^2/(a^4*(a+b*x)^5)+3/2*b^2/(a^5*(a+b*x)^4)+_ + 10/3*b^2/(a^6*(a+b*x)^3)+15/2*b^2/(a^7*(a+b*x)^2)+_ + 21*b^2/(a^8*(a+b*x))+28*b^2*log(x)/a^9-28*b^2*log(a+b*x)/a^9 +--R +--R +--R (2) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R - 840b x - 5040a b x - 12600a b x - 16800a b x - 12600a b x +--R + +--R 5 3 3 6 2 2 +--R - 5040a b x - 840a b x +--R * +--R log(b x + a) +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R 840b x + 5040a b x + 12600a b x + 16800a b x + 12600a b x +--R + +--R 5 3 3 6 2 2 +--R 5040a b x + 840a b x +--R * +--R log(x) +--R + +--R 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 840a b x + 4620a b x + 10360a b x + 11970a b x + 7308a b x +--R + +--R 6 2 2 7 8 +--R 2058a b x + 120a b x - 15a +--R / +--R 9 6 8 10 5 7 11 4 6 12 3 5 13 2 4 14 3 +--R 30a b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 15 2 +--R 30a x +--R Type: Expression(Integer) +--E 977 + +--S 978 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R - 840b x - 5040a b x - 12600a b x - 16800a b x - 12600a b x +--R + +--R 5 3 3 6 2 2 +--R - 5040a b x - 840a b x +--R * +--R log(b x + a) +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R 840b x + 5040a b x + 12600a b x + 16800a b x + 12600a b x +--R + +--R 5 3 3 6 2 2 +--R 5040a b x + 840a b x +--R * +--R log(x) +--R + +--R 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 840a b x + 4620a b x + 10360a b x + 11970a b x + 7308a b x +--R + +--R 6 2 2 7 8 +--R 2058a b x + 120a b x - 15a +--R / +--R 9 6 8 10 5 7 11 4 6 12 3 5 13 2 4 14 3 +--R 30a b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 15 2 +--R 30a x +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 3330 +t0000:=1/(x^4*(a+b*x)^7) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------------- +--R 7 11 6 10 2 5 9 3 4 8 4 3 7 5 2 6 6 5 7 4 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 981 + +--S 982 of 3330 +r0000:=(-1/3)/(a^7*x^3)+7/2*b/(a^8*x^2)-28*b^2/(a^9*x)-_ + 1/6*b^3/(a^4*(a+b*x)^6)-4/5*b^3/(a^5*(a+b*x)^5)-_ + 5/2*b^3/(a^6*(a+b*x)^4)-20/3*b^3/(a^7*(a+b*x)^3)-_ + 35/2*b^3/(a^8*(a+b*x)^2)-56*b^3/(a^9*(a+b*x))-_ + 84*b^3*log(x)/a^10+84*b^3*log(a+b*x)/a^10 +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 15120a b x + 37800a b x + 50400a b x + 37800a b x +--R + +--R 5 4 4 6 3 3 +--R 15120a b x + 2520a b x +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R - 2520b x - 15120a b x - 37800a b x - 50400a b x - 37800a b x +--R + +--R 5 4 4 6 3 3 +--R - 15120a b x - 2520a b x +--R * +--R log(x) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R - 2520a b x - 13860a b x - 31080a b x - 35910a b x - 21924a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R - 6174a b x - 360a b x + 45a b x - 10a +--R / +--R 10 6 9 11 5 8 12 4 7 13 3 6 14 2 5 +--R 30a b x + 180a b x + 450a b x + 600a b x + 450a b x +--R + +--R 15 4 16 3 +--R 180a b x + 30a x +--R Type: Expression(Integer) +--E 982 + +--S 983 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 15120a b x + 37800a b x + 50400a b x + 37800a b x +--R + +--R 5 4 4 6 3 3 +--R 15120a b x + 2520a b x +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R - 2520b x - 15120a b x - 37800a b x - 50400a b x - 37800a b x +--R + +--R 5 4 4 6 3 3 +--R - 15120a b x - 2520a b x +--R * +--R log(x) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R - 2520a b x - 13860a b x - 31080a b x - 35910a b x - 21924a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R - 6174a b x - 360a b x + 45a b x - 10a +--R / +--R 10 6 9 11 5 8 12 4 7 13 3 6 14 2 5 +--R 30a b x + 180a b x + 450a b x + 600a b x + 450a b x +--R + +--R 15 4 16 3 +--R 180a b x + 30a x +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 3330 +t0000:=x^12/(a+b*x)^10 +--R +--R +--R (1) +--R 12 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 986 + +--S 987 of 3330 +r0000:=55*a^2*x/b^12-5*a*x^2/b^11+1/3*x^3/b^10-1/9*a^12/(b^13*(a+b*x)^9)+_ + 3/2*a^11/(b^13*(a+b*x)^8)-66/7*a^10/(b^13*(a+b*x)^7)+_ + 110/3*a^9/(b^13*(a+b*x)^6)-99*a^8/(b^13*(a+b*x)^5)+_ + 198*a^7/(b^13*(a+b*x)^4)-308*a^6/(b^13*(a+b*x)^3)+_ + 396*a^5/(b^13*(a+b*x)^2)-495*a^4/(b^13*(a+b*x))-220*a^3*log(a+b*x)/b^13 +--R +--R +--R (2) +--R 3 9 9 4 8 8 5 7 7 6 6 6 +--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 7 5 5 8 4 4 9 3 3 10 2 2 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 11 12 +--R - 249480a b x - 27720a +--R * +--R log(b x + a) +--R + +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 +--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 +--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a +--R / +--R 22 9 21 8 2 20 7 3 19 6 4 18 5 +--R 126b x + 1134a b x + 4536a b x + 10584a b x + 15876a b x +--R + +--R 5 17 4 6 16 3 7 15 2 8 14 9 13 +--R 15876a b x + 10584a b x + 4536a b x + 1134a b x + 126a b +--R Type: Expression(Integer) +--E 987 + +--S 988 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 9 9 4 8 8 5 7 7 6 6 6 +--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 7 5 5 8 4 4 9 3 3 10 2 2 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 11 12 +--R - 249480a b x - 27720a +--R * +--R log(b x + a) +--R + +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 +--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 +--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a +--R / +--R 22 9 21 8 2 20 7 3 19 6 4 18 5 +--R 126b x + 1134a b x + 4536a b x + 10584a b x + 15876a b x +--R + +--R 5 17 4 6 16 3 7 15 2 8 14 9 13 +--R 15876a b x + 10584a b x + 4536a b x + 1134a b x + 126a b +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 3330 +t0000:=x^11/(a+b*x)^10 +--R +--R +--R (1) +--R 11 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 991 + +--S 992 of 3330 +r0000:=-10*a*x/b^11+1/2*x^2/b^10+1/9*a^11/(b^12*(a+b*x)^9)-_ + 11/8*a^10/(b^12*(a+b*x)^8)+55/7*a^9/(b^12*(a+b*x)^7)-_ + 55/2*a^8/(b^12*(a+b*x)^6)+66*a^7/(b^12*(a+b*x)^5)-_ + 231/2*a^6/(b^12*(a+b*x)^4)+154*a^5/(b^12*(a+b*x)^3)-_ + 165*a^4/(b^12*(a+b*x)^2)+165*a^3/(b^12*(a+b*x))+55*a^2*log(a+b*x)/b^12 +--R +--R +--R (2) +--R 2 9 9 3 8 8 4 7 7 5 6 6 +--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 10 11 +--R 249480a b x + 27720a +--R * +--R log(b x + a) +--R + +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 +--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 +--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x +--R + +--R 9 2 2 10 11 +--R 1281096a b x + 351459a b x + 42131a +--R / +--R 21 9 20 8 2 19 7 3 18 6 4 17 5 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 16 4 6 15 3 7 14 2 8 13 9 12 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 9 9 3 8 8 4 7 7 5 6 6 +--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 10 11 +--R 249480a b x + 27720a +--R * +--R log(b x + a) +--R + +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 +--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 +--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x +--R + +--R 9 2 2 10 11 +--R 1281096a b x + 351459a b x + 42131a +--R / +--R 21 9 20 8 2 19 7 3 18 6 4 17 5 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 16 4 6 15 3 7 14 2 8 13 9 12 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 3330 +t0000:=x^10/(a+b*x)^10 +--R +--R +--R (1) +--R 10 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 996 + +--S 997 of 3330 +r0000:=x/b^10-1/9*a^10/(b^11*(a+b*x)^9)+5/4*a^9/(b^11*(a+b*x)^8)-_ + 45/7*a^8/(b^11*(a+b*x)^7)+20*a^7/(b^11*(a+b*x)^6)-_ + 42*a^6/(b^11*(a+b*x)^5)+63*a^5/(b^11*(a+b*x)^4)-_ + 70*a^4/(b^11*(a+b*x)^3)+60*a^3/(b^11*(a+b*x)^2)-_ + 45*a^2/(b^11*(a+b*x))-10*a*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 9 9 2 8 8 3 7 7 4 6 6 +--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 9 10 +--R - 22680a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x - 41229a b x +--R + +--R 10 +--R - 4861a +--R / +--R 20 9 19 8 2 18 7 3 17 6 4 16 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 15 4 6 14 3 7 13 2 8 12 9 11 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Expression(Integer) +--E 997 + +--S 998 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 2 8 8 3 7 7 4 6 6 +--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 9 10 +--R - 22680a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x - 41229a b x +--R + +--R 10 +--R - 4861a +--R / +--R 20 9 19 8 2 18 7 3 17 6 4 16 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 15 4 6 14 3 7 13 2 8 12 9 11 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 3330 +t0000:=x^9/(a+b*x)^10 +--R +--R +--R (1) +--R 9 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1001 + +--S 1002 of 3330 +r0000:=1/9*a^9/(b^10*(a+b*x)^9)-9/8*a^8/(b^10*(a+b*x)^8)+_ + 36/7*a^7/(b^10*(a+b*x)^7)-14*a^6/(b^10*(a+b*x)^6)+_ + 126/5*a^5/(b^10*(a+b*x)^5)-63/2*a^4/(b^10*(a+b*x)^4)+_ + 28*a^3/(b^10*(a+b*x)^3)-18*a^2/(b^10*(a+b*x)^2)+_ + 9*a/(b^10*(a+b*x))+log(a+b*x)/b^10 +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R * +--R log(b x + a) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 22680a b x + 136080a b x + 388080a b x + 661500a b x + 725004a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R 518616a b x + 235224a b x + 61641a b x + 7129a +--R / +--R 19 9 18 8 2 17 7 3 16 6 4 15 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 14 4 6 13 3 7 12 2 8 11 9 10 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a b +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R * +--R log(b x + a) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 22680a b x + 136080a b x + 388080a b x + 661500a b x + 725004a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R 518616a b x + 235224a b x + 61641a b x + 7129a +--R / +--R 19 9 18 8 2 17 7 3 16 6 4 15 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 14 4 6 13 3 7 12 2 8 11 9 10 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a b +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 3330 +t0000:=x^8/(a+b*x)^10 +--R +--R +--R (1) +--R 8 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1006 + +--S 1007 of 3330 +r0000:=1/9*x^9/(a*(a+b*x)^9) +--R +--R +--R (2) +--R 1 9 +--R - x +--R 9 +--R / +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 6 4 4 7 3 3 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 8 2 2 9 10 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1007 + +--S 1008 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 2 7 8 +--R - 36a b x - 9a b x - a +--R / +--R 18 9 17 8 2 16 7 3 15 6 4 14 5 5 13 4 +--R 9b x + 81a b x + 324a b x + 756a b x + 1134a b x + 1134a b x +--R + +--R 6 12 3 7 11 2 8 10 9 9 +--R 756a b x + 324a b x + 81a b x + 9a b +--R Type: Union(Expression(Integer),...) +--E 1008 + +--S 1009 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ----- +--R 9 +--R 9a b +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +)clear all + +--S 1011 of 3330 +t0000:=x^7/(a+b*x)^10 +--R +--R +--R (1) +--R 7 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1011 + +--S 1012 of 3330 +r0000:=1/9*x^8/(a*(a+b*x)^9)+1/72*x^8/(a^2*(a+b*x)^8) +--R +--R +--R (2) +--R 1 9 1 8 +--R -- b x + - a x +--R 72 8 +--R / +--R 2 9 9 3 8 8 4 7 7 5 6 6 6 5 5 7 4 4 8 3 3 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 9 2 2 10 11 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1012 + +--S 1013 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 36b x - 84a b x - 126a b x - 126a b x - 84a b x - 36a b x +--R + +--R 6 7 +--R - 9a b x - a +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 72b x + 648a b x + 2592a b x + 6048a b x + 9072a b x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 9072a b x + 6048a b x + 2592a b x + 648a b x + 72a b +--R Type: Union(Expression(Integer),...) +--E 1013 + +--S 1014 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------ +--R 2 8 +--R 72a b +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1015 + +)clear all + +--S 1016 of 3330 +t0000:=x^6/(a+b*x)^10 +--R +--R +--R (1) +--R 6 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1016 + +--S 1017 of 3330 +r0000:=1/9*x^7/(a*(a+b*x)^9)+1/36*x^7/(a^2*(a+b*x)^8)+1/252*x^7/(a^3*(a+b*x)^7) +--R +--R +--R (2) +--R 1 2 9 1 8 1 2 7 +--R --- b x + -- a b x + - a x +--R 252 28 7 +--R / +--R 3 9 9 4 8 8 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 10 2 2 11 12 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1017 + +--S 1018 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R - 84b x - 126a b x - 126a b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 16 9 15 8 2 14 7 3 13 6 4 12 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 11 4 6 10 3 7 9 2 8 8 9 7 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 1018 + +--S 1019 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------- +--R 3 7 +--R 252a b +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 3330 +t0000:=x^5/(a+b*x)^10 +--R +--R +--R (1) +--R 5 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1021 + +--S 1022 of 3330 +r0000:=1/9*x^6/(a*(a+b*x)^9)+1/24*x^6/(a^2*(a+b*x)^8)+_ + 1/84*x^6/(a^3*(a+b*x)^7)+1/504*x^6/(a^4*(a+b*x)^6) +--R +--R +--R (2) +--R 1 3 9 1 2 8 1 2 7 1 3 6 +--R --- b x + -- a b x + -- a b x + - a x +--R 504 56 14 6 +--R / +--R 4 9 9 5 8 8 6 7 7 7 6 6 8 5 5 9 4 4 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 10 3 3 11 2 2 12 13 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1022 + +--S 1023 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R - 126b x - 126a b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 10 4 6 9 3 7 8 2 8 7 9 6 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------- +--R 4 6 +--R 504a b +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 3330 +t0000:=x^4/(a+b*x)^10 +--R +--R +--R (1) +--R 4 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1026 + +--S 1027 of 3330 +r0000:=-1/9*a^4/(b^5*(a+b*x)^9)+1/2*a^3/(b^5*(a+b*x)^8)-_ + 6/7*a^2/(b^5*(a+b*x)^7)+2/3*a/(b^5*(a+b*x)^6)+(-1/5)/(b^5*(a+b*x)^5) +--R +--R +--R (2) +--R 1 4 4 2 3 3 2 2 2 2 1 3 1 4 +--R - - b x - -- a b x - -- a b x - -- a b x - --- a +--R 5 15 35 70 630 +--R / +--R 14 9 13 8 2 12 7 3 11 6 4 10 5 5 9 4 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 8 3 7 7 2 8 6 9 5 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1027 + +--S 1028 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 4 +--R - 126b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 14 9 13 8 2 12 7 3 11 6 4 10 5 +--R 630b x + 5670a b x + 22680a b x + 52920a b x + 79380a b x +--R + +--R 5 9 4 6 8 3 7 7 2 8 6 9 5 +--R 79380a b x + 52920a b x + 22680a b x + 5670a b x + 630a b +--R Type: Union(Expression(Integer),...) +--E 1028 + +--S 1029 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 3330 +t0000:=x^3/(a+b*x)^10 +--R +--R +--R (1) +--R 3 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1031 + +--S 1032 of 3330 +r0000:=1/9*a^3/(b^4*(a+b*x)^9)-3/8*a^2/(b^4*(a+b*x)^8)+_ + 3/7*a/(b^4*(a+b*x)^7)+(-1/6)/(b^4*(a+b*x)^6) +--R +--R +--R (2) +--R 1 3 3 1 2 2 1 2 1 3 +--R - - b x - -- a b x - -- a b x - --- a +--R 6 14 56 504 +--R / +--R 13 9 12 8 2 11 7 3 10 6 4 9 5 5 8 4 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 7 3 7 6 2 8 5 9 4 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1032 + +--S 1033 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R - 84b x - 36a b x - 9a b x - a +--R / +--R 13 9 12 8 2 11 7 3 10 6 4 9 5 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 8 4 6 7 3 7 6 2 8 5 9 4 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1033 + +--S 1034 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 3330 +t0000:=x^2/(a+b*x)^10 +--R +--R +--R (1) +--R 2 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1036 + +--S 1037 of 3330 +r0000:=-1/9*a^2/(b^3*(a+b*x)^9)+1/4*a/(b^3*(a+b*x)^8)+(-1/7)/(b^3*(a+b*x)^7) +--R +--R +--R (2) +--R 1 2 2 1 1 2 +--R - - b x - -- a b x - --- a +--R 7 28 252 +--R / +--R 12 9 11 8 2 10 7 3 9 6 4 8 5 5 7 4 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 6 3 7 5 2 8 4 9 3 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1037 + +--S 1038 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +--R - 36b x - 9a b x - a +--R / +--R 12 9 11 8 2 10 7 3 9 6 4 8 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 7 4 6 6 3 7 5 2 8 4 9 3 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 1038 + +--S 1039 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 3330 +t0000:=x/(a+b*x)^10 +--R +--R +--R (1) +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1041 + +--S 1042 of 3330 +r0000:=1/9*a/(b^2*(a+b*x)^9)+(-1/8)/(b^2*(a+b*x)^8) +--R +--R +--R (2) +--R 1 1 +--R - - b x - -- a +--R 8 72 +--R / +--R 11 9 10 8 2 9 7 3 8 6 4 7 5 5 6 4 6 5 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 4 2 8 3 9 2 +--R 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1042 + +--S 1043 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R - 9b x - a +--R / +--R 11 9 10 8 2 9 7 3 8 6 4 7 5 5 6 4 +--R 72b x + 648a b x + 2592a b x + 6048a b x + 9072a b x + 9072a b x +--R + +--R 6 5 3 7 4 2 8 3 9 2 +--R 6048a b x + 2592a b x + 648a b x + 72a b +--R Type: Union(Expression(Integer),...) +--E 1043 + +--S 1044 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +)clear all + +--S 1046 of 3330 +t0000:=1/(a+b*x)^10 +--R +--R +--R (1) +--R 1 +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1046 + +--S 1047 of 3330 +r0000:=(-1/9)/(b*(a+b*x)^9) +--R +--R +--R (2) +--R - +--R 1 +--R - +--R 9 +--R / +--R 10 9 9 8 2 8 7 3 7 6 4 6 5 5 5 4 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 4 3 7 3 2 8 2 9 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1047 + +--S 1048 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 10 9 9 8 2 8 7 3 7 6 4 6 5 5 5 4 +--R 9b x + 81a b x + 324a b x + 756a b x + 1134a b x + 1134a b x +--R + +--R 6 4 3 7 3 2 8 2 9 +--R 756a b x + 324a b x + 81a b x + 9a b +--R Type: Union(Expression(Integer),...) +--E 1048 + +--S 1049 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1050 + +)clear all + +--S 1051 of 3330 +t0000:=1/(x*(a+b*x)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 11 9 10 2 8 9 3 7 8 4 6 7 5 5 6 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 5 7 3 4 8 2 3 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1051 + +--S 1052 of 3330 +r0000:=1/9/(a*(a+b*x)^9)+1/8/(a^2*(a+b*x)^8)+1/7/(a^3*(a+b*x)^7)+_ + 1/6/(a^4*(a+b*x)^6)+1/5/(a^5*(a+b*x)^5)+1/4/(a^6*(a+b*x)^4)+_ + 1/3/(a^7*(a+b*x)^3)+1/2/(a^8*(a+b*x)^2)+1/(a^9*(a+b*x))+_ + log(x)/a^10-log(a+b*x)/a^10 +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x - 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R - 317520a b x - 211680a b x - 90720a b x - 22680a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R * +--R log(x) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R 210756a b x + 120564a b x + 41481a b x + 7129a +--R / +--R 10 9 9 11 8 8 12 7 7 13 6 6 14 5 5 +--R 2520a b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 15 4 4 16 3 3 17 2 2 18 19 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x - 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R - 317520a b x - 211680a b x - 90720a b x - 22680a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R * +--R log(x) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R 210756a b x + 120564a b x + 41481a b x + 7129a +--R / +--R 10 9 9 11 8 8 12 7 7 13 6 6 14 5 5 +--R 2520a b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 15 4 4 16 3 3 17 2 2 18 19 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R Type: Union(Expression(Integer),...) +--E 1053 + +--S 1054 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1055 + +)clear all + +--S 1056 of 3330 +t0000:=1/(x^2*(a+b*x)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 12 9 11 2 8 10 3 7 9 4 6 8 5 5 7 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 6 7 3 5 8 2 4 9 3 10 2 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1056 + +--S 1057 of 3330 +r0000:=(-1)/(a^10*x)-1/9*b/(a^2*(a+b*x)^9)-1/4*b/(a^3*(a+b*x)^8)-_ + 3/7*b/(a^4*(a+b*x)^7)-2/3*b/(a^5*(a+b*x)^6)-b/(a^6*(a+b*x)^5)-_ + 3/2*b/(a^7*(a+b*x)^4)-7/3*b/(a^8*(a+b*x)^3)-4*b/(a^9*(a+b*x)^2)-_ + 9*b/(a^10*(a+b*x))-10*b*log(x)/a^11+10*b*log(a+b*x)/a^11 +--R +--R +--R (2) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a b x +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 8 2 2 9 +--R - 22680a b x - 2520a b x +--R * +--R log(x) +--R + +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x - 236754a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 210756a b x - 120564a b x - 41481a b x - 7129a b x - 252a +--R / +--R 11 9 10 12 8 9 13 7 8 14 6 7 15 5 6 +--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 16 4 5 17 3 4 18 2 3 19 2 20 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a b x +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 8 2 2 9 +--R - 22680a b x - 2520a b x +--R * +--R log(x) +--R + +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x - 236754a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 210756a b x - 120564a b x - 41481a b x - 7129a b x - 252a +--R / +--R 11 9 10 12 8 9 13 7 8 14 6 7 15 5 6 +--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 16 4 5 17 3 4 18 2 3 19 2 20 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x +--R Type: Union(Expression(Integer),...) +--E 1058 + +--S 1059 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1060 + +)clear all + +--S 1061 of 3330 +t0000:=1/(x^3*(a+b*x)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 13 9 12 2 8 11 3 7 10 4 6 9 5 5 8 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 7 7 3 6 8 2 5 9 4 10 3 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1061 + +--S 1062 of 3330 +r0000:=(-1/2)/(a^10*x^2)+10*b/(a^11*x)+1/9*b^2/(a^3*(a+b*x)^9)+_ + 3/8*b^2/(a^4*(a+b*x)^8)+6/7*b^2/(a^5*(a+b*x)^7)+_ + 5/3*b^2/(a^6*(a+b*x)^6)+3*b^2/(a^7*(a+b*x)^5)+_ + 21/4*b^2/(a^8*(a+b*x)^4)+28/3*b^2/(a^9*(a+b*x)^3)+_ + 18*b^2/(a^10*(a+b*x)^2)+45*b^2/(a^11*(a+b*x))+_ + 55*b^2*log(x)/a^12-55*b^2*log(a+b*x)/a^12 +--R +--R +--R (2) +--R 11 11 10 10 2 9 9 3 8 8 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 3 3 9 2 2 +--R - 249480a b x - 27720a b x +--R * +--R log(b x + a) +--R + +--R 11 11 10 10 2 9 9 3 8 8 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 3 3 9 2 2 +--R 249480a b x + 27720a b x +--R * +--R log(x) +--R + +--R 10 10 2 9 9 3 8 8 4 7 7 +--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 +--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x +--R + +--R 9 2 2 10 11 +--R 78419a b x + 2772a b x - 252a +--R / +--R 12 9 11 13 8 10 14 7 9 15 6 8 16 5 7 +--R 504a b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 17 4 6 18 3 5 19 2 4 20 3 21 2 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a x +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 11 11 10 10 2 9 9 3 8 8 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 3 3 9 2 2 +--R - 249480a b x - 27720a b x +--R * +--R log(b x + a) +--R + +--R 11 11 10 10 2 9 9 3 8 8 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 3 3 9 2 2 +--R 249480a b x + 27720a b x +--R * +--R log(x) +--R + +--R 10 10 2 9 9 3 8 8 4 7 7 +--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 +--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x +--R + +--R 9 2 2 10 11 +--R 78419a b x + 2772a b x - 252a +--R / +--R 12 9 11 13 8 10 14 7 9 15 6 8 16 5 7 +--R 504a b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 17 4 6 18 3 5 19 2 4 20 3 21 2 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a x +--R Type: Union(Expression(Integer),...) +--E 1063 + +--S 1064 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 3330 +t0000:=1/(x^4*(a+b*x)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 14 9 13 2 8 12 3 7 11 4 6 10 5 5 9 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 7 8 2 6 9 5 10 4 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1066 + +--S 1067 of 3330 +r0000:=(-1/3)/(a^10*x^3)+5*b/(a^11*x^2)-55*b^2/(a^12*x)-_ + 1/9*b^3/(a^4*(a+b*x)^9)-1/2*b^3/(a^5*(a+b*x)^8)-_ + 10/7*b^3/(a^6*(a+b*x)^7)-10/3*b^3/(a^7*(a+b*x)^6)-_ + 7*b^3/(a^8*(a+b*x)^5)-14*b^3/(a^9*(a+b*x)^4)-_ + 28*b^3/(a^10*(a+b*x)^3)-60*b^3/(a^11*(a+b*x)^2)-_ + 165*b^3/(a^12*(a+b*x))-220*b^3*log(x)/a^13+220*b^3*log(a+b*x)/a^13 +--R +--R +--R (2) +--R 12 12 11 11 2 10 10 3 9 9 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 4 4 9 3 3 +--R 249480a b x + 27720a b x +--R * +--R log(b x + a) +--R + +--R 12 12 11 11 2 10 10 3 9 9 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 4 4 9 3 3 +--R - 249480a b x - 27720a b x +--R * +--R log(x) +--R + +--R 11 11 2 10 10 3 9 9 4 8 8 +--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 +--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R - 78419a b x - 2772a b x + 252a b x - 42a +--R / +--R 13 9 12 14 8 11 15 7 10 16 6 9 17 5 8 +--R 126a b x + 1134a b x + 4536a b x + 10584a b x + 15876a b x +--R + +--R 18 4 7 19 3 6 20 2 5 21 4 22 3 +--R 15876a b x + 10584a b x + 4536a b x + 1134a b x + 126a x +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 12 12 11 11 2 10 10 3 9 9 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 4 4 9 3 3 +--R 249480a b x + 27720a b x +--R * +--R log(b x + a) +--R + +--R 12 12 11 11 2 10 10 3 9 9 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 4 4 9 3 3 +--R - 249480a b x - 27720a b x +--R * +--R log(x) +--R + +--R 11 11 2 10 10 3 9 9 4 8 8 +--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 +--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R - 78419a b x - 2772a b x + 252a b x - 42a +--R / +--R 13 9 12 14 8 11 15 7 10 16 6 9 17 5 8 +--R 126a b x + 1134a b x + 4536a b x + 10584a b x + 15876a b x +--R + +--R 18 4 7 19 3 6 20 2 5 21 4 22 3 +--R 15876a b x + 10584a b x + 4536a b x + 1134a b x + 126a x +--R Type: Union(Expression(Integer),...) +--E 1068 + +--S 1069 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +)clear all + +--S 1071 of 3330 +t0000:=(a+b*x)^12/x^10 +--R +--R +--R (1) +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x + 792a b x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924a b x + 792a b x + 495a b x + 220a b x + 66a b x + 12a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1071 + +--S 1072 of 3330 +r0000:=-1/9*a^12/x^9-3/2*a^11*b/x^8-66/7*a^10*b^2/x^7-_ + 110/3*a^9*b^3/x^6-99*a^8*b^4/x^5-198*a^7*b^5/x^4-_ + 308*a^6*b^6/x^3-396*a^5*b^7/x^2-495*a^4*b^8/x+66*a^2*b^10*x+_ + 6*a*b^11*x^2+1/3*b^12*x^3+220*a^3*b^9*log(x) +--R +--R +--R (2) +--R 3 9 9 12 12 11 11 2 10 10 4 8 8 +--R 27720a b x log(x) + 42b x + 756a b x + 8316a b x - 62370a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 +--R - 49896a b x - 38808a b x - 24948a b x - 12474a b x - 4620a b x +--R + +--R 10 2 2 11 12 +--R - 1188a b x - 189a b x - 14a +--R / +--R 9 +--R 126x +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 9 9 12 12 11 11 2 10 10 4 8 8 +--R 27720a b x log(x) + 42b x + 756a b x + 8316a b x - 62370a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 +--R - 49896a b x - 38808a b x - 24948a b x - 12474a b x - 4620a b x +--R + +--R 10 2 2 11 12 +--R - 1188a b x - 189a b x - 14a +--R / +--R 9 +--R 126x +--R Type: Union(Expression(Integer),...) +--E 1073 + +--S 1074 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 3330 +t0000:=(a+b*x)^11/x^10 +--R +--R +--R (1) +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R b x + 11a b x + 55a b x + 165a b x + 330a b x + 462a b x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462a b x + 330a b x + 165a b x + 55a b x + 11a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1076 + +--S 1077 of 3330 +r0000:=-1/9*a^11/x^9-11/8*a^10*b/x^8-55/7*a^9*b^2/x^7-55/2*a^8*b^3/x^6-_ + 66*a^7*b^4/x^5-231/2*a^6*b^5/x^4-154*a^5*b^6/x^3-165*a^4*b^7/x^2-_ + 165*a^3*b^8/x+11*a*b^10*x+1/2*b^11*x^2+55*a^2*b^9*log(x) +--R +--R +--R (2) +--R 2 9 9 11 11 10 10 3 8 8 4 7 7 +--R 27720a b x log(x) + 252b x + 5544a b x - 83160a b x - 83160a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 9 2 2 +--R - 77616a b x - 58212a b x - 33264a b x - 13860a b x - 3960a b x +--R + +--R 10 11 +--R - 693a b x - 56a +--R / +--R 9 +--R 504x +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 9 9 11 11 10 10 3 8 8 4 7 7 +--R 27720a b x log(x) + 252b x + 5544a b x - 83160a b x - 83160a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 9 2 2 +--R - 77616a b x - 58212a b x - 33264a b x - 13860a b x - 3960a b x +--R + +--R 10 11 +--R - 693a b x - 56a +--R / +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 3330 +t0000:=(a+b*x)^10/x^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1081 + +--S 1082 of 3330 +r0000:=-1/9*a^10/x^9-5/4*a^9*b/x^8-45/7*a^8*b^2/x^7-20*a^7*b^3/x^6-_ + 42*a^6*b^4/x^5-63*a^5*b^5/x^4-70*a^4*b^6/x^3-60*a^3*b^7/x^2-_ + 45*a^2*b^8/x+b^10*x+10*a*b^9*log(x) +--R +--R +--R (2) +--R 9 9 10 10 2 8 8 3 7 7 4 6 6 +--R 2520a b x log(x) + 252b x - 11340a b x - 15120a b x - 17640a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 15876a b x - 10584a b x - 5040a b x - 1620a b x - 315a b x - 28a +--R / +--R 9 +--R 252x +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 10 10 2 8 8 3 7 7 4 6 6 +--R 2520a b x log(x) + 252b x - 11340a b x - 15120a b x - 17640a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 15876a b x - 10584a b x - 5040a b x - 1620a b x - 315a b x - 28a +--R / +--R 9 +--R 252x +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 3330 +t0000:=(a+b*x)^9/x^10 +--R +--R +--R (1) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1086 + +--S 1087 of 3330 +r0000:=-1/9*a^9/x^9-9/8*a^8*b/x^8-36/7*a^7*b^2/x^7-14*a^6*b^3/x^6-_ + 126/5*a^5*b^4/x^5-63/2*a^4*b^5/x^4-28*a^3*b^6/x^3-_ + 18*a^2*b^7/x^2-9*a*b^8/x+b^9*log(x) +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x log(x) - 22680a b x - 45360a b x - 70560a b x - 79380a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R - 63504a b x - 35280a b x - 12960a b x - 2835a b x - 280a +--R / +--R 9 +--R 2520x +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x log(x) - 22680a b x - 45360a b x - 70560a b x - 79380a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R - 63504a b x - 35280a b x - 12960a b x - 2835a b x - 280a +--R / +--R 9 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 3330 +t0000:=(a+b*x)^8/x^10 +--R +--R +--R (1) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1091 + +--S 1092 of 3330 +r0000:=-1/9*(a+b*x)^9/(a*x^9) +--R +--R +--R (2) +--R 1 9 9 8 8 2 7 7 28 3 6 6 4 5 5 5 4 4 28 6 3 3 +--R - - b x - a b x - 4a b x - -- a b x - 14a b x - 14a b x - -- a b x +--R 9 3 3 +--R + +--R 7 2 2 8 1 9 +--R - 4a b x - a b x - - a +--R 9 +--R / +--R 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1092 + +--S 1093 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 2 7 8 +--R - 36a b x - 9a b x - a +--R / +--R 9 +--R 9x +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R b +--R (4) -- +--R 9a +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 3330 +t0000:=(a+b*x)^7/x^10 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1096 + +--S 1097 of 3330 +r0000:=-1/9*(a+b*x)^8/(a*x^9)+1/72*b*(a+b*x)^8/(a^2*x^8) +--R +--R +--R (2) +--R 1 9 9 1 2 7 7 7 3 6 6 21 4 5 5 5 4 4 35 6 3 3 7 2 2 +--R -- b x - - a b x - - a b x - -- a b x - 7a b x - -- a b x - 3a b x +--R 72 2 3 4 6 +--R + +--R 7 8 1 9 +--R - - a b x - - a +--R 8 9 +--R / +--R 2 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1097 + +--S 1098 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 36b x - 168a b x - 378a b x - 504a b x - 420a b x - 216a b x +--R + +--R 6 7 +--R - 63a b x - 8a +--R / +--R 9 +--R 72x +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R b +--R (4) - ---- +--R 2 +--R 72a +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 3330 +t0000:=(a+b*x)^6/x^10 +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (1) ------------------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1101 + +--S 1102 of 3330 +r0000:=-1/9*(a+b*x)^7/(a*x^9)+1/36*b*(a+b*x)^7/(a^2*x^8)-_ + 1/252*b^2*(a+b*x)^7/(a^3*x^7) +--R +--R +--R (2) +--R 1 9 9 1 3 6 6 3 4 5 5 5 4 4 10 6 3 3 15 7 2 2 +--R - --- b x - - a b x - - a b x - 3a b x - -- a b x - -- a b x +--R 252 3 2 3 7 +--R + +--R 3 8 1 9 +--R - - a b x - - a +--R 4 9 +--R / +--R 3 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1102 + +--S 1103 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R - 84b x - 378a b x - 756a b x - 840a b x - 540a b x - 189a b x - 28a +--R -------------------------------------------------------------------------- +--R 9 +--R 252x +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R b +--R (4) ----- +--R 3 +--R 252a +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 3330 +t0000:=(a+b*x)^5/x^10 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1106 + +--S 1107 of 3330 +r0000:=-1/9*a^5/x^9-5/8*a^4*b/x^8-10/7*a^3*b^2/x^7-5/3*a^2*b^3/x^6-_ + a*b^4/x^5-1/4*b^5/x^4 +--R +--R +--R 1 5 5 4 4 5 2 3 3 10 3 2 2 5 4 1 5 +--R - - b x - a b x - - a b x - -- a b x - - a b x - - a +--R 4 3 7 8 9 +--R (2) --------------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1107 + +--S 1108 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R - 126b x - 504a b x - 840a b x - 720a b x - 315a b x - 56a +--R (3) --------------------------------------------------------------- +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 1108 + +--S 1109 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1110 + +)clear all + +--S 1111 of 3330 +t0000:=(a+b*x)^4/x^10 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1111 + +--S 1112 of 3330 +r0000:=-1/9*a^4/x^9-1/2*a^3*b/x^8-6/7*a^2*b^2/x^7-2/3*a*b^3/x^6-1/5*b^4/x^5 +--R +--R +--R 1 4 4 2 3 3 6 2 2 2 1 3 1 4 +--R - - b x - - a b x - - a b x - - a b x - - a +--R 5 3 7 2 9 +--R (2) ----------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1112 + +--S 1113 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R - 126b x - 420a b x - 540a b x - 315a b x - 70a +--R (3) --------------------------------------------------- +--R 9 +--R 630x +--R Type: Union(Expression(Integer),...) +--E 1113 + +--S 1114 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 3330 +t0000:=(a+b*x)^3/x^10 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1116 + +--S 1117 of 3330 +r0000:=-1/9*a^3/x^9-3/8*a^2*b/x^8-3/7*a*b^2/x^7-1/6*b^3/x^6 +--R +--R +--R 1 3 3 3 2 2 3 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 6 7 8 9 +--R (2) ------------------------------------ +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1117 + +--S 1118 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 84b x - 216a b x - 189a b x - 56a +--R (3) -------------------------------------- +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 3330 +t0000:=(a+b*x)^2/x^10 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1121 + +--S 1122 of 3330 +r0000:=-1/9*a^2/x^9-1/4*a*b/x^8-1/7*b^2/x^7 +--R +--R +--R 1 2 2 1 1 2 +--R - - b x - - a b x - - a +--R 7 4 9 +--R (2) ------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1122 + +--S 1123 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 36b x - 63a b x - 28a +--R (3) ------------------------- +--R 9 +--R 252x +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 3330 +t0000:=(a+b*x)/x^10 +--R +--R +--R b x + a +--R (1) ------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1126 + +--S 1127 of 3330 +r0000:=-1/9*a/x^9-1/8*b/x^8 +--R +--R +--R 1 1 +--R - - b x - - a +--R 8 9 +--R (2) ------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1127 + +--S 1128 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 9b x - 8a +--R (3) ----------- +--R 9 +--R 72x +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 3330 +t0000:=1/x^10 +--R +--R +--R 1 +--R (1) --- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1131 + +--S 1132 of 3330 +r0000:=(-1/9)/x^9 +--R +--R +--R 1 +--R - +--R 9 +--R (2) - --- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1132 + +--S 1133 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --- +--R 9 +--R 9x +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 3330 +t0000:=1/(x^10*(a+b*x)) +--R +--R +--R 1 +--R (1) ------------- +--R 11 10 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1136 + +--S 1137 of 3330 +r0000:=(-1/9)/(a*x^9)+1/8*b/(a^2*x^8)-1/7*b^2/(a^3*x^7)+1/6*b^3/(a^4*x^6)-_ + 1/5*b^4/(a^5*x^5)+1/4*b^5/(a^6*x^4)-1/3*b^6/(a^7*x^3)+_ + 1/2*b^7/(a^8*x^2)-b^8/(a^9*x)-b^9*log(x)/a^10+b^9*log(a+b*x)/a^10 +--R +--R +--R (2) +--R 9 9 9 9 8 8 2 7 7 +--R 2520b x log(b x + a) - 2520b x log(x) - 2520a b x + 1260a b x +--R + +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 8 +--R - 840a b x + 630a b x - 504a b x + 420a b x - 360a b x + 315a b x +--R + +--R 9 +--R - 280a +--R / +--R 10 9 +--R 2520a x +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 9 9 8 8 2 7 7 +--R 2520b x log(b x + a) - 2520b x log(x) - 2520a b x + 1260a b x +--R + +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 8 +--R - 840a b x + 630a b x - 504a b x + 420a b x - 360a b x + 315a b x +--R + +--R 9 +--R - 280a +--R / +--R 10 9 +--R 2520a x +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 3330 +t0000:=1/(x^10*(a+b*x)^2) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 12 11 2 10 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1141 + +--S 1142 of 3330 +r0000:=(-1/9)/(a^2*x^9)+1/4*b/(a^3*x^8)-3/7*b^2/(a^4*x^7)+_ + 2/3*b^3/(a^5*x^6)-b^4/(a^6*x^5)+3/2*b^5/(a^7*x^4)-_ + 7/3*b^6/(a^8*x^3)+4*b^7/(a^9*x^2)-9*b^8/(a^10*x)-_ + b^9/(a^10*(a+b*x))-10*b^9*log(x)/a^11+10*b^9*log(a+b*x)/a^11 +--R +--R +--R (2) +--R 10 10 9 9 10 10 9 9 +--R (2520b x + 2520a b x )log(b x + a) + (- 2520b x - 2520a b x )log(x) +--R + +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 6 4 4 +--R - 2520a b x - 1260a b x + 420a b x - 210a b x + 126a b x - 84a b x +--R + +--R 7 3 3 8 2 2 9 10 +--R 60a b x - 45a b x + 35a b x - 28a +--R / +--R 11 10 12 9 +--R 252a b x + 252a x +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 10 10 9 9 +--R (2520b x + 2520a b x )log(b x + a) + (- 2520b x - 2520a b x )log(x) +--R + +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 6 4 4 +--R - 2520a b x - 1260a b x + 420a b x - 210a b x + 126a b x - 84a b x +--R + +--R 7 3 3 8 2 2 9 10 +--R 60a b x - 45a b x + 35a b x - 28a +--R / +--R 11 10 12 9 +--R 252a b x + 252a x +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 3330 +t0000:=1/(x^10*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 13 2 12 2 11 3 10 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1146 + +--S 1147 of 3330 +r0000:=(-1/9)/(a^3*x^9)+3/8*b/(a^4*x^8)-6/7*b^2/(a^5*x^7)+_ + 5/3*b^3/(a^6*x^6)-3*b^4/(a^7*x^5)+21/4*b^5/(a^8*x^4)-_ + 28/3*b^6/(a^9*x^3)+18*b^7/(a^10*x^2)-45*b^8/(a^11*x)-_ + 1/2*b^9/(a^10*(a+b*x)^2)-10*b^9/(a^11*(a+b*x))-_ + 55*b^9*log(x)/a^12+55*b^9*log(a+b*x)/a^12 +--R +--R +--R (2) +--R 11 11 10 10 2 9 9 +--R (27720b x + 55440a b x + 27720a b x )log(b x + a) +--R + +--R 11 11 10 10 2 9 9 10 10 +--R (- 27720b x - 55440a b x - 27720a b x )log(x) - 27720a b x +--R + +--R 2 9 9 3 8 8 4 7 7 5 6 6 6 5 5 +--R - 41580a b x - 9240a b x + 2310a b x - 924a b x + 462a b x +--R + +--R 7 4 4 8 3 3 9 2 2 10 11 +--R - 264a b x + 165a b x - 110a b x + 77a b x - 56a +--R / +--R 12 2 11 13 10 14 9 +--R 504a b x + 1008a b x + 504a x +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 11 11 10 10 2 9 9 +--R (27720b x + 55440a b x + 27720a b x )log(b x + a) +--R + +--R 11 11 10 10 2 9 9 10 10 +--R (- 27720b x - 55440a b x - 27720a b x )log(x) - 27720a b x +--R + +--R 2 9 9 3 8 8 4 7 7 5 6 6 6 5 5 +--R - 41580a b x - 9240a b x + 2310a b x - 924a b x + 462a b x +--R + +--R 7 4 4 8 3 3 9 2 2 10 11 +--R - 264a b x + 165a b x - 110a b x + 77a b x - 56a +--R / +--R 12 2 11 13 10 14 9 +--R 504a b x + 1008a b x + 504a x +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 3330 +t0000:=1/(x*(2+3*x)) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1151 + +--S 1152 of 3330 +r0000:=1/2*log(x)-1/2*log(2+3*x) +--R +--R +--R - log(3x + 2) + log(x) +--R (2) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - log(3x + 2) + log(x) +--R (3) ---------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 3330 +t0000:=1/(x*(4+6*x)) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1156 + +--S 1157 of 3330 +r0000:=1/4*log(x)-1/4*log(2+3*x) +--R +--R +--R - log(3x + 2) + log(x) +--R (2) ---------------------- +--R 4 +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - log(3x + 2) + log(x) +--R (3) ---------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 3330 +t0000:=1/(x^2*(4+6*x)) +--R +--R +--R 1 +--R (1) --------- +--R 3 2 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1161 + +--S 1162 of 3330 +r0000:=(-1/4)/x-3/8*log(x)+3/8*log(2+3*x) +--R +--R +--R 3x log(3x + 2) - 3x log(x) - 2 +--R (2) ------------------------------ +--R 8x +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3x log(3x + 2) - 3x log(x) - 2 +--R (3) ------------------------------ +--R 8x +--R Type: Union(Expression(Integer),...) +--E 1163 + +--S 1164 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 3330 +t0000:=1/(x^3*(4+6*x)) +--R +--R +--R 1 +--R (1) --------- +--R 4 3 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1166 + +--S 1167 of 3330 +r0000:=(-1/8)/x^2+3/8/x+9/16*log(x)-9/16*log(2+3*x) +--R +--R +--R 2 2 +--R - 9x log(3x + 2) + 9x log(x) + 6x - 2 +--R (2) ------------------------------------- +--R 2 +--R 16x +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +--R - 9x log(3x + 2) + 9x log(x) + 6x - 2 +--R (3) ------------------------------------- +--R 2 +--R 16x +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 3330 +t0000:=1/(x^4*(4+6*x)) +--R +--R +--R 1 +--R (1) --------- +--R 5 4 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1171 + +--S 1172 of 3330 +r0000:=(-1/12)/x^3+3/16/x^2+(-9/16)/x-27/32*log(x)+27/32*log(2+3*x) +--R +--R +--R 3 3 2 +--R 81x log(3x + 2) - 81x log(x) - 54x + 18x - 8 +--R (2) --------------------------------------------- +--R 3 +--R 96x +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 +--R 81x log(3x + 2) - 81x log(x) - 54x + 18x - 8 +--R (3) --------------------------------------------- +--R 3 +--R 96x +--R Type: Union(Expression(Integer),...) +--E 1173 + +--S 1174 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1175 + +)clear all + +--S 1176 of 3330 +t0000:=1/(x^5*(4+6*x)) +--R +--R +--R 1 +--R (1) --------- +--R 6 5 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1176 + +--S 1177 of 3330 +r0000:=(-1/16)/x^4+1/8/x^3+(-9/32)/x^2+27/32/x+81/64*log(x)-81/64*log(2+3*x) +--R +--R +--R 4 4 3 2 +--R - 81x log(3x + 2) + 81x log(x) + 54x - 18x + 8x - 4 +--R (2) ----------------------------------------------------- +--R 4 +--R 64x +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 2 +--R - 81x log(3x + 2) + 81x log(x) + 54x - 18x + 8x - 4 +--R (3) ----------------------------------------------------- +--R 4 +--R 64x +--R Type: Union(Expression(Integer),...) +--E 1178 + +--S 1179 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1180 + +)clear all + +--S 1181 of 3330 +t0000:=1/(x*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ----------------- +--R 3 2 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1181 + +--S 1182 of 3330 +r0000:=1/8/(2+3*x)+1/16*log(x)-1/16*log(2+3*x) +--R +--R +--R (- 3x - 2)log(3x + 2) + (3x + 2)log(x) + 2 +--R (2) ------------------------------------------ +--R 48x + 32 +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (- 3x - 2)log(3x + 2) + (3x + 2)log(x) + 2 +--R (3) ------------------------------------------ +--R 48x + 32 +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 3330 +t0000:=1/(x^2*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 4 3 2 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1186 + +--S 1187 of 3330 +r0000:=(-1/16)/x+(-3/16)/(2+3*x)-3/16*log(x)+3/16*log(2+3*x) +--R +--R +--R 2 2 +--R (9x + 6x)log(3x + 2) + (- 9x - 6x)log(x) - 6x - 2 +--R (2) --------------------------------------------------- +--R 2 +--R 48x + 32x +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +--R (9x + 6x)log(3x + 2) + (- 9x - 6x)log(x) - 6x - 2 +--R (3) --------------------------------------------------- +--R 2 +--R 48x + 32x +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 3330 +t0000:=1/(x^3*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 5 4 3 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1191 + +--S 1192 of 3330 +r0000:=(-1/32)/x^2+3/16/x+9/32/(2+3*x)+27/64*log(x)-27/64*log(2+3*x) +--R +--R +--R 3 2 3 2 2 +--R (- 81x - 54x )log(3x + 2) + (81x + 54x )log(x) + 54x + 18x - 4 +--R (2) ----------------------------------------------------------------- +--R 3 2 +--R 192x + 128x +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 3 2 2 +--R (- 81x - 54x )log(3x + 2) + (81x + 54x )log(x) + 54x + 18x - 4 +--R (3) ----------------------------------------------------------------- +--R 3 2 +--R 192x + 128x +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 3330 +t0000:=1/(x^4*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 6 5 4 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1196 + +--S 1197 of 3330 +r0000:=(-1/48)/x^3+3/32/x^2+(-27/64)/x+(-27/64)/(2+3*x)-_ + 27/32*log(x)+27/32*log(2+3*x) +--R +--R +--R (2) +--R 4 3 4 3 3 2 +--R (243x + 162x )log(3x + 2) + (- 243x - 162x )log(x) - 162x - 54x + 12x - 4 +--R ----------------------------------------------------------------------------- +--R 4 3 +--R 288x + 192x +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 4 3 3 2 +--R (243x + 162x )log(3x + 2) + (- 243x - 162x )log(x) - 162x - 54x + 12x - 4 +--R ----------------------------------------------------------------------------- +--R 4 3 +--R 288x + 192x +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 3330 +t0000:=1/(x^5*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 7 6 5 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1201 + +--S 1202 of 3330 +r0000:=(-1/64)/x^4+1/16/x^3+(-27/128)/x^2+27/32/x+_ + 81/128/(2+3*x)+405/256*log(x)-405/256*log(2+3*x) +--R +--R +--R (2) +--R 5 4 5 4 4 3 +--R (- 1215x - 810x )log(3x + 2) + (1215x + 810x )log(x) + 810x + 270x +--R + +--R 2 +--R - 60x + 20x - 8 +--R / +--R 5 4 +--R 768x + 512x +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 5 4 4 3 +--R (- 1215x - 810x )log(3x + 2) + (1215x + 810x )log(x) + 810x + 270x +--R + +--R 2 +--R - 60x + 20x - 8 +--R / +--R 5 4 +--R 768x + 512x +--R Type: Union(Expression(Integer),...) +--E 1203 + +--S 1204 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +)clear all + +--S 1206 of 3330 +t0000:=1/(x*(4+6*x)^3) +--R +--R +--R 1 +--R (1) --------------------------- +--R 4 3 2 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1206 + +--S 1207 of 3330 +r0000:=1/32/(2+3*x)^2+1/32/(2+3*x)+1/64*log(x)-1/64*log(2+3*x) +--R +--R +--R 2 2 +--R (- 9x - 12x - 4)log(3x + 2) + (9x + 12x + 4)log(x) + 6x + 6 +--R (2) ------------------------------------------------------------- +--R 2 +--R 576x + 768x + 256 +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +--R (- 9x - 12x - 4)log(3x + 2) + (9x + 12x + 4)log(x) + 6x + 6 +--R (3) ------------------------------------------------------------- +--R 2 +--R 576x + 768x + 256 +--R Type: Union(Expression(Integer),...) +--E 1208 + +--S 1209 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1210 + +)clear all + +--S 1211 of 3330 +t0000:=1/(x^2*(4+6*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 5 4 3 2 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1211 + +--S 1212 of 3330 +r0000:=(-1/64)/x+(-3/64)/(2+3*x)^2+(-3/32)/(2+3*x)-_ + 9/128*log(x)+9/128*log(2+3*x) +--R +--R +--R (2) +--R 3 2 3 2 2 +--R (81x + 108x + 36x)log(3x + 2) + (- 81x - 108x - 36x)log(x) - 54x +--R + +--R - 54x - 8 +--R / +--R 3 2 +--R 1152x + 1536x + 512x +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 3 2 2 +--R (81x + 108x + 36x)log(3x + 2) + (- 81x - 108x - 36x)log(x) - 54x +--R + +--R - 54x - 8 +--R / +--R 3 2 +--R 1152x + 1536x + 512x +--R Type: Union(Expression(Integer),...) +--E 1213 + +--S 1214 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1215 + +)clear all + +--S 1216 of 3330 +t0000:=1/(x^3*(4+6*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 6 5 4 3 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1216 + +--S 1217 of 3330 +r0000:=(-1/128)/x^2+9/128/x+9/128/(2+3*x)^2+27/128/(2+3*x)+_ + 27/128*log(x)-27/128*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 4 3 2 +--R (- 243x - 324x - 108x )log(3x + 2) + (243x + 324x + 108x )log(x) +--R + +--R 3 2 +--R 162x + 162x + 24x - 4 +--R / +--R 4 3 2 +--R 1152x + 1536x + 512x +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 4 3 2 +--R (- 243x - 324x - 108x )log(3x + 2) + (243x + 324x + 108x )log(x) +--R + +--R 3 2 +--R 162x + 162x + 24x - 4 +--R / +--R 4 3 2 +--R 1152x + 1536x + 512x +--R Type: Union(Expression(Integer),...) +--E 1218 + +--S 1219 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1220 + +)clear all + +--S 1221 of 3330 +t0000:=1/(x^4*(4+6*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 7 6 5 4 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1221 + +--S 1222 of 3330 +r0000:=(-1/192)/x^3+9/256/x^2+(-27/128)/x+(-27/256)/(2+3*x)^2+_ + (-27/64)/(2+3*x)-135/256*log(x)+135/256*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 +--R (3645x + 4860x + 1620x )log(3x + 2) +--R + +--R 5 4 3 4 3 2 +--R (- 3645x - 4860x - 1620x )log(x) - 2430x - 2430x - 360x + 60x - 16 +--R / +--R 5 4 3 +--R 6912x + 9216x + 3072x +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 +--R (3645x + 4860x + 1620x )log(3x + 2) +--R + +--R 5 4 3 4 3 2 +--R (- 3645x - 4860x - 1620x )log(x) - 2430x - 2430x - 360x + 60x - 16 +--R / +--R 5 4 3 +--R 6912x + 9216x + 3072x +--R Type: Union(Expression(Integer),...) +--E 1223 + +--S 1224 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1225 + +)clear all + +--S 1226 of 3330 +t0000:=1/(x^5*(4+6*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 8 7 6 5 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1226 + +--S 1227 of 3330 +r0000:=(-1/256)/x^4+3/128/x^3+(-27/256)/x^2+135/256/x+81/512/(2+3*x)^2+_ + 405/512/(2+3*x)+1215/1024*log(x)-1215/1024*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 +--R (- 10935x - 14580x - 4860x )log(3x + 2) +--R + +--R 6 5 4 5 4 3 2 +--R (10935x + 14580x + 4860x )log(x) + 7290x + 7290x + 1080x - 180x +--R + +--R 48x - 16 +--R / +--R 6 5 4 +--R 9216x + 12288x + 4096x +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 5 4 +--R (- 10935x - 14580x - 4860x )log(3x + 2) +--R + +--R 6 5 4 5 4 3 2 +--R (10935x + 14580x + 4860x )log(x) + 7290x + 7290x + 1080x - 180x +--R + +--R 48x - 16 +--R / +--R 6 5 4 +--R 9216x + 12288x + 4096x +--R Type: Union(Expression(Integer),...) +--E 1228 + +--S 1229 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1230 + +--R +--R +)clear all + +--S 1231 of 3330 +t0000:=1/(2+2*x) +--R +--R +--R 1 +--R (1) ------ +--R 2x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1231 + +--S 1232 of 3330 +r0000:=1/2*log(1+x) +--R +--R +--R log(x + 1) +--R (2) ---------- +--R 2 +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R log(x + 1) +--R (3) ---------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1233 + +--S 1234 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +)clear all + +--S 1236 of 3330 +t0000:=1/(4-6*x) +--R +--R +--R 1 +--R (1) - ------ +--R 6x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1236 + +--S 1237 of 3330 +r0000:=-1/6*log(2-3*x) +--R +--R +--R log(- 3x + 2) +--R (2) - ------------- +--R 6 +--R Type: Expression(Integer) +--E 1237 + +--S 1238 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R log(3x - 2) +--R (3) - ----------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1238 + +--S 1239 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R - log(3x - 2) + log(- 3x + 2) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1240 + +)clear all + +--S 1241 of 3330 +t0000:=1/(a+x*sqrt(a)) +--R +--R +--R 1 +--R (1) --------- +--R +-+ +--R x\|a + a +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 3330 +r0000:=log(x+sqrt(a))/sqrt(a) +--R +--R +--R +-+ +--R log(\|a + x) +--R (2) ------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R log(x\|a + a) +--R (3) -------------- +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 1243 + +--S 1244 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R +-+ +-+ +--R log(x\|a + a) - log(\|a + x) +--R (4) ------------------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1245 + +)clear all + +--S 1246 of 3330 +t0000:=1/(a+x*sqrt(-a)) +--R +--R +--R 1 +--R (1) ----------- +--R +---+ +--R x\|- a + a +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 3330 +r0000:=log(-x+sqrt(-a))/sqrt(-a) +--R +--R +--R +---+ +--R log(\|- a - x) +--R (2) --------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ +--R log(x\|- a + a) +--R (3) ---------------- +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1248 + +--S 1249 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R +---+ +---+ +--R log(x\|- a + a) - log(\|- a - x) +--R (4) ---------------------------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1250 + +)clear all + +--S 1251 of 3330 +t0000:=1/(a^2+x*sqrt(-a)) +--R +--R +--R 1 +--R (1) ------------ +--R +---+ 2 +--R x\|- a + a +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 3330 +r0000:=log((-a)^(3/2)+x)/sqrt(-a) +--R +--R +--R +---+ +--R log(- a\|- a + x) +--R (2) ------------------ +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ 2 +--R log(x\|- a + a ) +--R (3) ----------------- +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1253 + +--S 1254 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R +---+ 2 +---+ +--R log(x\|- a + a ) - log(- a\|- a + x) +--R (4) -------------------------------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1255 + +)clear all + +--S 1256 of 3330 +t0000:=1/(a^3+x*sqrt(-a)) +--R +--R +--R 1 +--R (1) ------------ +--R +---+ 3 +--R x\|- a + a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 3330 +r0000:=log((-a)^(5/2)-x)/sqrt(-a) +--R +--R +--R 2 +---+ +--R log(a \|- a - x) +--R (2) ----------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ 3 +--R log(x\|- a + a ) +--R (3) ----------------- +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1258 + +--S 1259 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R +---+ 3 2 +---+ +--R log(x\|- a + a ) - log(a \|- a - x) +--R (4) ------------------------------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1260 + +)clear all + +--S 1261 of 3330 +t0000:=1/(1/a+x*sqrt(-a)) +--R +--R +--R a +--R (1) ------------- +--R +---+ +--R a x\|- a + 1 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 3330 +r0000:=log(1-(-a)^(3/2)*x)/sqrt(-a) +--R +--R +--R +---+ +--R log(a x\|- a + 1) +--R (2) ------------------ +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ +--R log(a x\|- a + 1) +--R (3) ------------------ +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1263 + +--S 1264 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1265 + +)clear all + +--S 1266 of 3330 +t0000:=1/(1/a^2+x*sqrt(-a)) +--R +--R +--R 2 +--R a +--R (1) ------------- +--R 2 +---+ +--R a x\|- a + 1 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 3330 +r0000:=log(1+(-a)^(5/2)*x)/sqrt(-a) +--R +--R +--R 2 +---+ +--R log(a x\|- a + 1) +--R (2) ------------------ +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +---+ +--R log(a x\|- a + 1) +--R (3) ------------------ +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1268 + +--S 1269 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1270 + +)clear all + +--S 1271 of 3330 +t0000:=1/(x*(1+b*x)) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1271 + +--S 1272 of 3330 +r0000:=log(x)-log(1+b*x) +--R +--R +--R (2) - log(b x + 1) + log(x) +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) - log(b x + 1) + log(x) +--R Type: Union(Expression(Integer),...) +--E 1273 + +--S 1274 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1275 + +)clear all + +--S 1276 of 3330 +t0000:=1/(x*(-1+b*x)) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R b x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1276 + +--S 1277 of 3330 +r0000:=-log(x)+log(1-b*x) +--R +--R +--R (2) - log(x) + log(- b x + 1) +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) log(b x - 1) - log(x) +--R Type: Union(Expression(Integer),...) +--E 1278 + +--S 1279 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) log(b x - 1) - log(- b x + 1) +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1280 + +)clear all + +--S 1281 of 3330 +t0000:=1/(x^2*(1+b*x)) +--R +--R +--R 1 +--R (1) --------- +--R 3 2 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1281 + +--S 1282 of 3330 +r0000:=(-1)/x-b*log(x)+b*log(1+b*x) +--R +--R +--R b x log(b x + 1) - b x log(x) - 1 +--R (2) --------------------------------- +--R x +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(b x + 1) - b x log(x) - 1 +--R (3) --------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 1283 + +--S 1284 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1285 + +)clear all + +--S 1286 of 3330 +t0000:=1/(x^2*(-1+b*x)) +--R +--R +--R 1 +--R (1) --------- +--R 3 2 +--R b x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1286 + +--S 1287 of 3330 +r0000:=1/x-b*log(x)+b*log(1-b*x) +--R +--R +--R - b x log(x) + b x log(- b x + 1) + 1 +--R (2) ------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(b x - 1) - b x log(x) + 1 +--R (3) --------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 1288 + +--S 1289 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) b log(b x - 1) - b log(- b x + 1) +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1290 + +)clear all + +--S 1291 of 3330 +t0000:=b/x+1/(x^2*(1+b*x)) +--R +--R +--R 2 2 +--R b x + b x + 1 +--R (1) -------------- +--R 3 2 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1291 + +--S 1292 of 3330 +r0000:=(-1)/x+b*log(1+b*x) +--R +--R +--R b x log(b x + 1) - 1 +--R (2) -------------------- +--R x +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(b x + 1) - 1 +--R (3) -------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 1293 + +--S 1294 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1295 + +)clear all + +--S 1296 of 3330 +t0000:=x^m*sqrt(a+b*x) +--R +--R +--R m +-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 3330 +--r0000:=2*x^(1+m)*sqrt(a+b*x)/(3+2*m)+2*a*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b*(3+2*m)*(-b*x/a)^m) +--E 1297 + +--S 1298 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ m +--------+ +--R (2) | %N \|%N b + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 1298 + +--S 1299 of 3330 +--m0000:=a0000 - r0000 +--E 1299 + +--S 1300 of 3330 +--d0000:=D(m0000,x) +--E 1300 + +)clear all + +--S 1301 of 3330 +t0000:=x^3*sqrt(a+b*x) +--R +--R +--R 3 +-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 3330 +r0000:=-2/3*a^3*(a+b*x)^(3/2)/b^4+6/5*a^2*(a+b*x)^(5/2)/b^4-_ + 6/7*a*(a+b*x)^(7/2)/b^4+2/9*(a+b*x)^(9/2)/b^4 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 10a b x - 12a b x + 16a b x - 32a )\|b x + a +--R (2) --------------------------------------------------------- +--R 4 +--R 315b +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 10a b x - 12a b x + 16a b x - 32a )\|b x + a +--R (3) --------------------------------------------------------- +--R 4 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 1303 + +--S 1304 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1305 + +)clear all + +--S 1306 of 3330 +t0000:=x^2*sqrt(a+b*x) +--R +--R +--R 2 +-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 3330 +r0000:=2/3*a^2*(a+b*x)^(3/2)/b^3-4/5*a*(a+b*x)^(5/2)/b^3+2/7*(a+b*x)^(7/2)/b^3 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (30b x + 6a b x - 8a b x + 16a )\|b x + a +--R (2) -------------------------------------------- +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (30b x + 6a b x - 8a b x + 16a )\|b x + a +--R (3) -------------------------------------------- +--R 3 +--R 105b +--R Type: Union(Expression(Integer),...) +--E 1308 + +--S 1309 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1310 + +)clear all + +--S 1311 of 3330 +t0000:=x*sqrt(a+b*x) +--R +--R +--R +-------+ +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 3330 +r0000:=-2/3*a*(a+b*x)^(3/2)/b^2+2/5*(a+b*x)^(5/2)/b^2 +--R +--R +--R 2 2 2 +-------+ +--R (6b x + 2a b x - 4a )\|b x + a +--R (2) -------------------------------- +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-------+ +--R (6b x + 2a b x - 4a )\|b x + a +--R (3) -------------------------------- +--R 2 +--R 15b +--R Type: Union(Expression(Integer),...) +--E 1313 + +--S 1314 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1315 + +)clear all + +--S 1316 of 3330 +t0000:=sqrt(a+b*x) +--R +--R +--R +-------+ +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 3330 +r0000:=2/3*(a+b*x)^(3/2)/b +--R +--R +--R +-------+ +--R (2b x + 2a)\|b x + a +--R (2) --------------------- +--R 3b +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R (2b x + 2a)\|b x + a +--R (3) --------------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 1318 + +--S 1319 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 3330 +t0000:=sqrt(a+b*x)/x +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 3330 +r0000:=-2*atanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+2*sqrt(a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x + a +-------+ +--R (2) - 2\|a atanh(----------) + 2\|b x + a +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-------+ +--R [\|a log(----------------------------) + 2\|b x + a , +--R x +--R +-------+ +--R +---+ \|b x + a +-------+ +--R - 2\|- a atan(----------) + 2\|b x + a ] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1323 + +--S 1324 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R (4) \|a log(----------------------------) + 2\|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 2\|a atanh(----------) - 2\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1327 + +)clear all + +--S 1328 of 3330 +t0000:=sqrt(a+b*x)/x^2 +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 3330 +r0000:=-b*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-sqrt(a+b*x)/x +--R +--R +--R +-------+ +--R \|b x + a +-+ +-------+ +--R - b x atanh(----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R +-+ +--R x\|a +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R - 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R b x log(-------------------------------) - 2\|a \|b x + a +--R x +--R [----------------------------------------------------------, +--R +-+ +--R 2x\|a +--R +---+ +-------+ +--R \|- a \|b x + a +---+ +-------+ +--R - b x atan(----------------) - \|- a \|b x + a +--R a +--R -----------------------------------------------] +--R +---+ +--R x\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1330 + +--S 1331 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R b log(-------------------------------) + 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R b\|- a atanh(----------) - b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 3330 +t0000:=sqrt(a+b*x)/x^3 +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 3330 +r0000:=1/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-_ + 1/2*sqrt(a+b*x)/x^2-1/4*b*sqrt(a+b*x)/(a*x) +--R +--R +--R +-------+ +--R 2 2 \|b x + a +-+ +-------+ +--R b x atanh(----------) + (- b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------- +--R 2 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R 2 2 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R b x log(-----------------------------) + (- 2b x - 4a)\|a \|b x + a +--R x +--R [--------------------------------------------------------------------, +--R 2 +-+ +--R 8a x \|a +--R +---+ +-------+ +--R 2 2 \|- a \|b x + a +---+ +-------+ +--R b x atan(----------------) + (- b x - 2a)\|- a \|b x + a +--R a +--R ---------------------------------------------------------] +--R 2 +---+ +--R 4a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1337 + +--S 1338 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R b log(-----------------------------) - 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1341 + +)clear all + +--S 1342 of 3330 +t0000:=sqrt(a+b*x)/x^4 +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 3330 +r0000:=-1/8*b^3*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-1/3*sqrt(a+b*x)/x^3-_ + 1/12*b*sqrt(a+b*x)/(a*x^2)+1/8*b^2*sqrt(a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R 3 3 \|b x + a 2 2 2 +-+ +-------+ +--R - 3b x atanh(----------) + (3b x - 2a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 2 3 +-+ +--R 24a x \|a +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 - 2a\|b x + a + (b x + 2a)\|a +--R 3b x log(-------------------------------) +--R x +--R + +--R 2 2 2 +-+ +-------+ +--R (6b x - 4a b x - 16a )\|a \|b x + a +--R / +--R 2 3 +-+ +--R 48a x \|a +--R , +--R +---+ +-------+ +--R 3 3 \|- a \|b x + a 2 2 2 +---+ +-------+ +--R - 3b x atan(----------------) + (3b x - 2a b x - 8a )\|- a \|b x + a +--R a +--R ----------------------------------------------------------------------] +--R 2 3 +---+ +--R 24a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1344 + +--S 1345 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 3 - 2a\|b x + a + (b x + 2a)\|a 3 \|b x + a +--R b log(-------------------------------) + 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 3 +---+ \|b x + a 3 +-+ \|- a \|b x + a +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1348 + +)clear all + +--S 1349 of 3330 +t0000:=x^m*(a+b*x)^(3/2) +--R +--R +--R m +-------+ +--R (1) (b x + a)x \|b x + a +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 3330 +--r0000:=2*x^(1+m)*(a+b*x)^(3/2)/(5+2*m)+_ +-- 6*a*x^(1+m)*sqrt(a+b*x)/(15+16*m+4*m^2)+_ +-- 6*a^2*x^m*hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b*(15+16*m+4*m^2)*(-b*x/a)^m) +--E 1350 + +--S 1351 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ m +--------+ +--R (2) | (%N b + a)%N \|%N b + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 1351 + +--S 1352 of 3330 +--m0000:=a0000 - r0000 +--E 1352 + +--S 1353 of 3330 +--d0000:=D(m0000,x) +--E 1353 + +)clear all + +--S 1354 of 3330 +t0000:=x^3*(a+b*x)^(3/2) +--R +--R +--R 4 3 +-------+ +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1354 + +--S 1355 of 3330 +r0000:=-2/5*a^3*(a+b*x)^(5/2)/b^4+6/7*a^2*(a+b*x)^(7/2)/b^4-_ + 2/3*a*(a+b*x)^(9/2)/b^4+2/11*(a+b*x)^(11/2)/b^4 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (210b x + 280a b x + 10a b x - 12a b x + 16a b x - 32a )\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 4 +--R 1155b +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (210b x + 280a b x + 10a b x - 12a b x + 16a b x - 32a )\|b x + a +--R (3) ---------------------------------------------------------------------- +--R 4 +--R 1155b +--R Type: Union(Expression(Integer),...) +--E 1356 + +--S 1357 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1358 + +)clear all + +--S 1359 of 3330 +t0000:=x^2*(a+b*x)^(3/2) +--R +--R +--R 3 2 +-------+ +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 3330 +r0000:=2/5*a^2*(a+b*x)^(5/2)/b^3-4/7*a*(a+b*x)^(7/2)/b^3+2/9*(a+b*x)^(9/2)/b^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 100a b x + 6a b x - 8a b x + 16a )\|b x + a +--R (2) -------------------------------------------------------- +--R 3 +--R 315b +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 100a b x + 6a b x - 8a b x + 16a )\|b x + a +--R (3) -------------------------------------------------------- +--R 3 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 1361 + +--S 1362 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1363 + +)clear all + +--S 1364 of 3330 +t0000:=x*(a+b*x)^(3/2) +--R +--R +--R 2 +-------+ +--R (1) (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1364 + +--S 1365 of 3330 +r0000:=-2/5*a*(a+b*x)^(5/2)/b^2+2/7*(a+b*x)^(7/2)/b^2 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (10b x + 16a b x + 2a b x - 4a )\|b x + a +--R (2) -------------------------------------------- +--R 2 +--R 35b +--R Type: Expression(Integer) +--E 1365 + +--S 1366 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (10b x + 16a b x + 2a b x - 4a )\|b x + a +--R (3) -------------------------------------------- +--R 2 +--R 35b +--R Type: Union(Expression(Integer),...) +--E 1366 + +--S 1367 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1368 + +)clear all + +--S 1369 of 3330 +t0000:=(a+b*x)^(3/2) +--R +--R +--R +-------+ +--R (1) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1369 + +--S 1370 of 3330 +r0000:=2/5*(a+b*x)^(5/2)/b +--R +--R +--R 2 2 2 +-------+ +--R (2b x + 4a b x + 2a )\|b x + a +--R (2) -------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-------+ +--R (2b x + 4a b x + 2a )\|b x + a +--R (3) -------------------------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 1371 + +--S 1372 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1372 + +--S 1373 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1373 + +)clear all + +--S 1374 of 3330 +t0000:=(a+b*x)^(3/2)/x +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 1374 + +--S 1375 of 3330 +r0000:=2/3*(a+b*x)^(3/2)-2*a^(3/2)*atanh(sqrt(a+b*x)/sqrt(a))+2*a*sqrt(a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x + a +-------+ +--R - 6a\|a atanh(----------) + (2b x + 8a)\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-------+ +--R 3a\|a log(----------------------------) + (2b x + 8a)\|b x + a +--R x +--R [---------------------------------------------------------------, +--R 3 +--R +-------+ +--R +---+ \|b x + a +-------+ +--R - 6a\|- a atan(----------) + (2b x + 8a)\|b x + a +--R +---+ +--R \|- a +--R --------------------------------------------------] +--R 3 +--R Type: Union(List(Expression(Integer)),...) +--E 1376 + +--S 1377 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R (4) a\|a log(----------------------------) + 2a\|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1377 + +--S 1378 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1378 + +--S 1379 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 2a\|a atanh(----------) - 2a\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1379 + +--S 1380 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1380 + +)clear all + +--S 1381 of 3330 +t0000:=(a+b*x)^(3/2)/x^2 +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1381 + +--S 1382 of 3330 +r0000:=-(a+b*x)^(3/2)/x-3*b*atanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+3*b*sqrt(a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x + a +-------+ +--R - 3b x\|a atanh(----------) + (2b x - a)\|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1382 + +--S 1383 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-------+ +--R 3b x\|a log(----------------------------) + (4b x - 2a)\|b x + a +--R x +--R [-----------------------------------------------------------------, +--R 2x +--R +-------+ +--R +---+ \|b x + a +-------+ +--R - 3b x\|- a atan(----------) + (2b x - a)\|b x + a +--R +---+ +--R \|- a +--R ---------------------------------------------------] +--R x +--R Type: Union(List(Expression(Integer)),...) +--E 1383 + +--S 1384 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R 3b\|a log(----------------------------) + 6b\|a atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1384 + +--S 1385 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1385 + +--S 1386 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 3b\|a atanh(----------) - 3b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1386 + +--S 1387 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1387 + +)clear all + +--S 1388 of 3330 +t0000:=(a+b*x)^(3/2)/x^3 +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 3330 +r0000:=-1/2*(a+b*x)^(3/2)/x^2-3/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-_ + 3/4*b*sqrt(a+b*x)/x +--R +--R +--R +-------+ +--R 2 2 \|b x + a +-+ +-------+ +--R - 3b x atanh(----------) + (- 5b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 +-+ +--R 4x \|a +--R Type: Expression(Integer) +--E 1389 + +--S 1390 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R 2 2 - 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R 3b x log(-------------------------------) + (- 10b x - 4a)\|a \|b x + a +--R x +--R [------------------------------------------------------------------------, +--R 2 +-+ +--R 8x \|a +--R +---+ +-------+ +--R 2 2 \|- a \|b x + a +---+ +-------+ +--R - 3b x atan(----------------) + (- 5b x - 2a)\|- a \|b x + a +--R a +--R -------------------------------------------------------------] +--R 2 +---+ +--R 4x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1390 + +--S 1391 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R 3b log(-------------------------------) + 6b atanh(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 1391 + +--S 1392 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1392 + +--S 1393 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R 3b \|- a atanh(----------) - 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 4\|- a \|a +--R Type: Expression(Integer) +--E 1393 + +--S 1394 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1394 + +)clear all + +--S 1395 of 3330 +t0000:=(a+b*x)^(3/2)/x^4 +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1395 + +--S 1396 of 3330 +r0000:=-1/3*(a+b*x)^(3/2)/x^3+1/8*b^3*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-_ + 1/4*b*sqrt(a+b*x)/x^2-1/8*b^2*sqrt(a+b*x)/(a*x) +--R +--R +--R +-------+ +--R 3 3 \|b x + a 2 2 2 +-+ +-------+ +--R 3b x atanh(----------) + (- 3b x - 14a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------- +--R 3 +-+ +--R 24a x \|a +--R Type: Expression(Integer) +--E 1396 + +--S 1397 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 2a\|b x + a + (b x + 2a)\|a +--R 3b x log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +-------+ +--R (- 6b x - 28a b x - 16a )\|a \|b x + a +--R / +--R 3 +-+ +--R 48a x \|a +--R , +--R +---+ +-------+ +--R 3 3 \|- a \|b x + a 2 2 2 +---+ +-------+ +--R 3b x atan(----------------) + (- 3b x - 14a b x - 8a )\|- a \|b x + a +--R a +--R -----------------------------------------------------------------------] +--R 3 +---+ +--R 24a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1397 + +--S 1398 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 3 2a\|b x + a + (b x + 2a)\|a 3 \|b x + a +--R b log(-----------------------------) - 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 16a\|a +--R Type: Expression(Integer) +--E 1398 + +--S 1399 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1399 + +--S 1400 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 3 +---+ \|b x + a 3 +-+ \|- a \|b x + a +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression(Integer) +--E 1400 + +--S 1401 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1401 + +)clear all + +--S 1402 of 3330 +t0000:=x^m*(a+b*x)^(5/2) +--R +--R +--R 2 2 2 m +-------+ +--R (1) (b x + 2a b x + a )x \|b x + a +--R Type: Expression(Integer) +--E 1402 + +--S 1403 of 3330 +--r0000:=10*a*x^(1+m)*(a+b*x)^(3/2)/(35+24*m+4*m^2)+_ +-- 2*x^(1+m)*(a+b*x)^(5/2)/(7+2*m)+_ +-- 30*a^2*x^(1+m)*sqrt(a+b*x)/((7+2*m)*(15+16*m+4*m^2))+_ +-- 30*a^3*x^m*hypergeometric(1/2,-m,3/2,(a+b*x)/a)*_ +-- sqrt(a+b*x)/(b*(7+2*m)*(15+16*m+4*m^2)*(-b*x/a)^m) +--E 1403 + +--S 1404 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ 2 2 2 m +--------+ +--R (2) | (%N b + 2%N a b + a )%N \|%N b + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 1404 + +--S 1405 of 3330 +--m0000:=a0000 - r0000 +--E 1405 + +--S 1406 of 3330 +--d0000:=D(m0000,x) +--E 1406 + +)clear all + +--S 1407 of 3330 +t0000:=x^3*(a+b*x)^(5/2) +--R +--R +--R 2 5 4 2 3 +-------+ +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1407 + +--S 1408 of 3330 +r0000:=-2/7*a^3*(a+b*x)^(7/2)/b^4+2/3*a^2*(a+b*x)^(9/2)/b^4-_ + 6/11*a*(a+b*x)^(11/2)/b^4+2/13*(a+b*x)^(13/2)/b^4 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (462b x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32a ) +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 +--R 3003b +--R Type: Expression(Integer) +--E 1408 + +--S 1409 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (462b x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32a ) +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 +--R 3003b +--R Type: Union(Expression(Integer),...) +--E 1409 + +--S 1410 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1410 + +--S 1411 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1411 + +)clear all + +--S 1412 of 3330 +t0000:=x^2*(a+b*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +-------+ +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1412 + +--S 1413 of 3330 +r0000:=2/7*a^2*(a+b*x)^(7/2)/b^3-4/9*a*(a+b*x)^(9/2)/b^3+_ + 2/11*(a+b*x)^(11/2)/b^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (126b x + 322a b x + 226a b x + 6a b x - 8a b x + 16a )\|b x + a +--R (2) --------------------------------------------------------------------- +--R 3 +--R 693b +--R Type: Expression(Integer) +--E 1413 + +--S 1414 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (126b x + 322a b x + 226a b x + 6a b x - 8a b x + 16a )\|b x + a +--R (3) --------------------------------------------------------------------- +--R 3 +--R 693b +--R Type: Union(Expression(Integer),...) +--E 1414 + +--S 1415 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1415 + +--S 1416 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1416 + +)clear all + +--S 1417 of 3330 +t0000:=x*(a+b*x)^(5/2) +--R +--R +--R 2 3 2 2 +-------+ +--R (1) (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1417 + +--S 1418 of 3330 +r0000:=-2/7*a*(a+b*x)^(7/2)/b^2+2/9*(a+b*x)^(9/2)/b^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (14b x + 38a b x + 30a b x + 2a b x - 4a )\|b x + a +--R (2) ------------------------------------------------------- +--R 2 +--R 63b +--R Type: Expression(Integer) +--E 1418 + +--S 1419 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (14b x + 38a b x + 30a b x + 2a b x - 4a )\|b x + a +--R (3) ------------------------------------------------------- +--R 2 +--R 63b +--R Type: Union(Expression(Integer),...) +--E 1419 + +--S 1420 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1420 + +--S 1421 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1421 + +)clear all + +--S 1422 of 3330 +t0000:=(a+b*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (1) (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1422 + +--S 1423 of 3330 +r0000:=2/7*(a+b*x)^(7/2)/b +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R (2) ------------------------------------------ +--R 7b +--R Type: Expression(Integer) +--E 1423 + +--S 1424 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R (3) ------------------------------------------ +--R 7b +--R Type: Union(Expression(Integer),...) +--E 1424 + +--S 1425 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1425 + +--S 1426 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1426 + +)clear all + +--S 1427 of 3330 +t0000:=(a+b*x)^(5/2)/x +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 1427 + +--S 1428 of 3330 +r0000:=2/3*a*(a+b*x)^(3/2)+2/5*(a+b*x)^(5/2)-_ + 2*a^(5/2)*atanh(sqrt(a+b*x)/sqrt(a))+2*a^2*sqrt(a+b*x) +--R +--R +--R +-------+ +--R 2 +-+ \|b x + a 2 2 2 +-------+ +--R - 30a \|a atanh(----------) + (6b x + 22a b x + 46a )\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 1428 + +--S 1429 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 2 +-+ - 2\|a \|b x + a + b x + 2a +--R 15a \|a log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (6b x + 22a b x + 46a )\|b x + a +--R / +--R 15 +--R , +--R +-------+ +--R 2 +---+ \|b x + a 2 2 2 +-------+ +--R - 30a \|- a atan(----------) + (6b x + 22a b x + 46a )\|b x + a +--R +---+ +--R \|- a +--R -----------------------------------------------------------------] +--R 15 +--R Type: Union(List(Expression(Integer)),...) +--E 1429 + +--S 1430 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 +-+ - 2\|a \|b x + a + b x + 2a 2 +-+ \|b x + a +--R (4) a \|a log(----------------------------) + 2a \|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1430 + +--S 1431 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1431 + +--S 1432 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 2 +-+ \|b x + a 2 +---+ \|b x + a +--R (6) 2a \|a atanh(----------) - 2a \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1432 + +--S 1433 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1433 + +)clear all + +--S 1434 of 3330 +t0000:=(a+b*x)^(5/2)/x^2 +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1434 + +--S 1435 of 3330 +r0000:=5/3*b*(a+b*x)^(3/2)-(a+b*x)^(5/2)/x-_ + 5*a^(3/2)*b*atanh(sqrt(a+b*x)/sqrt(a))+5*a*b*sqrt(a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x + a 2 2 2 +-------+ +--R - 15a b x\|a atanh(----------) + (2b x + 14a b x - 3a )\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3x +--R Type: Expression(Integer) +--E 1435 + +--S 1436 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +--R 15a b x\|a log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (4b x + 28a b x - 6a )\|b x + a +--R / +--R 6x +--R , +--R +-------+ +--R +---+ \|b x + a 2 2 2 +-------+ +--R - 15a b x\|- a atan(----------) + (2b x + 14a b x - 3a )\|b x + a +--R +---+ +--R \|- a +--R -------------------------------------------------------------------] +--R 3x +--R Type: Union(List(Expression(Integer)),...) +--E 1436 + +--S 1437 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R 5a b\|a log(----------------------------) + 10a b\|a atanh(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1437 + +--S 1438 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1438 + +--S 1439 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 5a b\|a atanh(----------) - 5a b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1439 + +--S 1440 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1440 + +)clear all + +--S 1441 of 3330 +t0000:=(a+b*x)^(5/2)/x^3 +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 1441 + +--S 1442 of 3330 +r0000:=-5/4*b*(a+b*x)^(3/2)/x-1/2*(a+b*x)^(5/2)/x^2-_ + 15/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+15/4*b^2*sqrt(a+b*x) +--R +--R +--R +-------+ +--R 2 2 +-+ \|b x + a 2 2 2 +-------+ +--R - 15b x \|a atanh(----------) + (8b x - 9a b x - 2a )\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 1442 + +--S 1443 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 2 2 +-+ - 2\|a \|b x + a + b x + 2a +--R 15b x \|a log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (16b x - 18a b x - 4a )\|b x + a +--R / +--R 2 +--R 8x +--R , +--R +-------+ +--R 2 2 +---+ \|b x + a 2 2 2 +-------+ +--R - 15b x \|- a atan(----------) + (8b x - 9a b x - 2a )\|b x + a +--R +---+ +--R \|- a +--R -----------------------------------------------------------------] +--R 2 +--R 4x +--R Type: Union(List(Expression(Integer)),...) +--E 1443 + +--S 1444 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 +-+ - 2\|a \|b x + a + b x + 2a 2 +-+ \|b x + a +--R 15b \|a log(----------------------------) + 30b \|a atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 1444 + +--S 1445 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1445 + +--S 1446 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 2 +-+ \|b x + a 2 +---+ \|b x + a +--R 15b \|a atanh(----------) - 15b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ------------------------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 1446 + +--S 1447 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1447 + +)clear all + +--S 1448 of 3330 +t0000:=(a+b*x)^(5/2)/x^4 +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 1448 + +--S 1449 of 3330 +r0000:=-5/12*b*(a+b*x)^(3/2)/x^2-1/3*(a+b*x)^(5/2)/x^3-_ + 5/8*b^3*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-5/8*b^2*sqrt(a+b*x)/x +--R +--R +--R +-------+ +--R 3 3 \|b x + a 2 2 2 +-+ +-------+ +--R - 15b x atanh(----------) + (- 33b x - 26a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------------- +--R 3 +-+ +--R 24x \|a +--R Type: Expression(Integer) +--E 1449 + +--S 1450 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 - 2a\|b x + a + (b x + 2a)\|a +--R 15b x log(-------------------------------) +--R x +--R + +--R 2 2 2 +-+ +-------+ +--R (- 66b x - 52a b x - 16a )\|a \|b x + a +--R / +--R 3 +-+ +--R 48x \|a +--R , +--R +---+ +-------+ +--R 3 3 \|- a \|b x + a 2 2 2 +---+ +-------+ +--R - 15b x atan(----------------) + (- 33b x - 26a b x - 8a )\|- a \|b x + a +--R a +--R ---------------------------------------------------------------------------] +--R 3 +---+ +--R 24x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1450 + +--S 1451 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 3 - 2a\|b x + a + (b x + 2a)\|a 3 \|b x + a +--R 5b log(-------------------------------) + 10b atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 16\|a +--R Type: Expression(Integer) +--E 1451 + +--S 1452 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1452 + +--S 1453 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 3 +---+ \|b x + a 3 +-+ \|- a \|b x + a +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 8\|- a \|a +--R Type: Expression(Integer) +--E 1453 + +--S 1454 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1454 + +)clear all + +--S 1455 of 3330 +t0000:=(a+b*x)^(5/2)/x^5 +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 1455 + +--S 1456 of 3330 +r0000:=-5/24*b*(a+b*x)^(3/2)/x^3-1/4*(a+b*x)^(5/2)/x^4+_ + 5/64*b^4*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-5/32*b^2*sqrt(a+b*x)/x^2-_ + 5/64*b^3*sqrt(a+b*x)/(a*x) +--R +--R +--R (2) +--R +-------+ +--R 4 4 \|b x + a +--R 15b x atanh(----------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +-------+ +--R (- 15b x - 118a b x - 136a b x - 48a )\|a \|b x + a +--R / +--R 4 +-+ +--R 192a x \|a +--R Type: Expression(Integer) +--E 1456 + +--S 1457 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 4 4 2a\|b x + a + (b x + 2a)\|a +--R 15b x log(-----------------------------) +--R x +--R + +--R 3 3 2 2 2 3 +-+ +-------+ +--R (- 30b x - 236a b x - 272a b x - 96a )\|a \|b x + a +--R / +--R 4 +-+ +--R 384a x \|a +--R , +--R +--R +---+ +-------+ +--R 4 4 \|- a \|b x + a +--R 15b x atan(----------------) +--R a +--R + +--R 3 3 2 2 2 3 +---+ +-------+ +--R (- 15b x - 118a b x - 136a b x - 48a )\|- a \|b x + a +--R / +--R 4 +---+ +--R 192a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1457 + +--S 1458 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 4 2a\|b x + a + (b x + 2a)\|a 4 \|b x + a +--R 5b log(-----------------------------) - 10b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R 128a\|a +--R Type: Expression(Integer) +--E 1458 + +--S 1459 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1459 + +--S 1460 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 4 +---+ \|b x + a 4 +-+ \|- a \|b x + a +--R - 5b \|- a atanh(----------) + 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 64a\|- a \|a +--R Type: Expression(Integer) +--E 1460 + +--S 1461 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1461 + +)clear all + +--S 1462 of 3330 +t0000:=x^7*(a+b*x)^(9/2) +--R +--R +--R 4 11 3 10 2 2 9 3 8 4 7 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1462 + +--S 1463 of 3330 +r0000:=-2/11*a^7*(a+b*x)^(11/2)/b^8+14/13*a^6*(a+b*x)^(13/2)/b^8-_ + 14/5*a^5*(a+b*x)^(15/2)/b^8+70/17*a^4*(a+b*x)^(17/2)/b^8-_ + 70/19*a^3*(a+b*x)^(19/2)/b^8+2*a^2*(a+b*x)^(21/2)/b^8-_ + 14/23*a*(a+b*x)^(23/2)/b^8+2/25*(a+b*x)^(25/2)/b^8 +--R +--R +--R (2) +--R 12 12 11 11 2 10 10 3 9 9 +--R 2124694b x + 9330178a b x + 15519504a b x + 11620180a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 8 4 4 +--R 3319030a b x + 858a b x - 924a b x + 1008a b x - 1120a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R 1280a b x - 1536a b x + 2048a b x - 4096a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 8 +--R 26558675b +--R Type: Expression(Integer) +--E 1463 + +--S 1464 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 12 12 11 11 2 10 10 3 9 9 +--R 2124694b x + 9330178a b x + 15519504a b x + 11620180a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 8 4 4 +--R 3319030a b x + 858a b x - 924a b x + 1008a b x - 1120a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R 1280a b x - 1536a b x + 2048a b x - 4096a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 8 +--R 26558675b +--R Type: Union(Expression(Integer),...) +--E 1464 + +--S 1465 of 3330 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+--S 1469 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 11 11 10 10 2 9 9 3 8 8 +--R 646646b x + 2863718a b x + 4813380a b x + 3652220a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 8 3 3 +--R 1061918a b x + 462a b x - 504a b x + 560a b x - 640a b x +--R + +--R 9 2 2 10 11 +--R 768a b x - 1024a b x + 2048a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 7 +--R 7436429b +--R Type: Union(Expression(Integer),...) +--E 1469 + +--S 1470 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1470 + +--S 1471 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1471 + +)clear all + +--S 1472 of 3330 +t0000:=x^5*(a+b*x)^(9/2) +--R +--R +--R 4 9 3 8 2 2 7 3 6 4 5 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1472 + +--S 1473 of 3330 +r0000:=-2/11*a^5*(a+b*x)^(11/2)/b^6+10/13*a^4*(a+b*x)^(13/2)/b^6-_ + 4/3*a^3*(a+b*x)^(15/2)/b^6+20/17*a^2*(a+b*x)^(17/2)/b^6-_ + 10/19*a*(a+b*x)^(19/2)/b^6+2/21*(a+b*x)^(21/2)/b^6 +--R +--R +--R (2) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 92378b x + 413270a b x + 703560a b x + 542828a b x + 161546a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R 126a b x - 140a b x + 160a b x - 192a b x + 256a b x - 512a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 6 +--R 969969b +--R Type: Expression(Integer) +--E 1473 + +--S 1474 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 92378b x + 413270a b x + 703560a b x + 542828a b x + 161546a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R 126a b x - 140a b x + 160a b x - 192a b x + 256a b x - 512a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 6 +--R 969969b +--R Type: Union(Expression(Integer),...) +--E 1474 + +--S 1475 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1475 + +--S 1476 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1476 + +)clear all + +--S 1477 of 3330 +t0000:=x^4*(a+b*x)^(9/2) +--R +--R +--R 4 8 3 7 2 2 6 3 5 4 4 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1477 + +--S 1478 of 3330 +r0000:=2/11*a^4*(a+b*x)^(11/2)/b^5-8/13*a^3*(a+b*x)^(13/2)/b^5+_ + 4/5*a^2*(a+b*x)^(15/2)/b^5-8/17*a*(a+b*x)^(17/2)/b^5+_ + 2/19*(a+b*x)^(19/2)/b^5 +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 24310b x + 110110a b x + 190476a b x + 150172a b x + 46126a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 70a b x - 80a b x + 96a b x - 128a b x + 256a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 +--R 230945b +--R Type: Expression(Integer) +--E 1478 + +--S 1479 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 24310b x + 110110a b x + 190476a b x + 150172a b x + 46126a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 70a b x - 80a b x + 96a b x - 128a b x + 256a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 +--R 230945b +--R Type: Union(Expression(Integer),...) +--E 1479 + +--S 1480 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1480 + +--S 1481 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1481 + +)clear all + +--S 1482 of 3330 +t0000:=x^3*(a+b*x)^(9/2) +--R +--R +--R 4 7 3 6 2 2 5 3 4 4 3 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1482 + +--S 1483 of 3330 +r0000:=-2/11*a^3*(a+b*x)^(11/2)/b^4+6/13*a^2*(a+b*x)^(13/2)/b^4-_ + 2/5*a*(a+b*x)^(15/2)/b^4+2/17*(a+b*x)^(17/2)/b^4 +--R +--R +--R (2) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R 1430b x + 6578a b x + 11616a b x + 9428a b x + 3030a b x +--R + +--R 5 3 3 6 2 2 7 8 +--R 10a b x - 12a b x + 16a b x - 32a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 +--R 12155b +--R Type: Expression(Integer) +--E 1483 + +--S 1484 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R 1430b x + 6578a b x + 11616a b x + 9428a b x + 3030a b x +--R + +--R 5 3 3 6 2 2 7 8 +--R 10a b x - 12a b x + 16a b x - 32a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 +--R 12155b +--R Type: Union(Expression(Integer),...) +--E 1484 + +--S 1485 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1485 + +--S 1486 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1486 + +)clear all + +--S 1487 of 3330 +t0000:=x^2*(a+b*x)^(9/2) +--R +--R +--R 4 6 3 5 2 2 4 3 3 4 2 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1487 + +--S 1488 of 3330 +r0000:=2/11*a^2*(a+b*x)^(11/2)/b^3-4/13*a*(a+b*x)^(13/2)/b^3+_ + 2/15*(a+b*x)^(15/2)/b^3 +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R 286b x + 1342a b x + 2436a b x + 2060a b x + 710a b x + 6a b x +--R + +--R 6 7 +--R - 8a b x + 16a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 +--R 2145b +--R Type: Expression(Integer) +--E 1488 + +--S 1489 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R 286b x + 1342a b x + 2436a b x + 2060a b x + 710a b x + 6a b x +--R + +--R 6 7 +--R - 8a b x + 16a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 +--R 2145b +--R Type: Union(Expression(Integer),...) +--E 1489 + +--S 1490 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1490 + +--S 1491 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1491 + +)clear all + +--S 1492 of 3330 +t0000:=x*(a+b*x)^(9/2) +--R +--R +--R 4 5 3 4 2 2 3 3 2 4 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1492 + +--S 1493 of 3330 +r0000:=-2/11*a*(a+b*x)^(11/2)/b^2+2/13*(a+b*x)^(13/2)/b^2 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (22b x + 106a b x + 200a b x + 180a b x + 70a b x + 2a b x - 4a ) +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 143b +--R Type: Expression(Integer) +--E 1493 + +--S 1494 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (22b x + 106a b x + 200a b x + 180a b x + 70a b x + 2a b x - 4a ) +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 143b +--R Type: Union(Expression(Integer),...) +--E 1494 + +--S 1495 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1495 + +--S 1496 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1496 + +)clear all + +--S 1497 of 3330 +t0000:=(a+b*x)^(9/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1497 + +--S 1498 of 3330 +r0000:=2/11*(a+b*x)^(11/2)/b +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a )\|b x + a +--R (2) ------------------------------------------------------------------ +--R 11b +--R Type: Expression(Integer) +--E 1498 + +--S 1499 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a )\|b x + a +--R (3) ------------------------------------------------------------------ +--R 11b +--R Type: Union(Expression(Integer),...) +--E 1499 + +--S 1500 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1500 + +--S 1501 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1501 + +)clear all + +--S 1502 of 3330 +t0000:=(a+b*x)^(9/2)/x +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1502 + +--S 1503 of 3330 +r0000:=2/3*a^3*(a+b*x)^(3/2)+2/5*a^2*(a+b*x)^(5/2)+2/7*a*(a+b*x)^(7/2)+_ + 2/9*(a+b*x)^(9/2)-2*a^(9/2)*atanh(sqrt(a+b*x)/sqrt(a))+2*a^4*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 4 +-+ \|b x + a +--R - 630a \|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 370a b x + 816a b x + 1012a b x + 1126a )\|b x + a +--R / +--R 315 +--R Type: Expression(Integer) +--E 1503 + +--S 1504 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 4 +-+ - 2\|a \|b x + a + b x + 2a +--R 315a \|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 370a b x + 816a b x + 1012a b x + 1126a )\|b x + a +--R / +--R 315 +--R , +--R +--R +-------+ +--R 4 +---+ \|b x + a +--R - 630a \|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 370a b x + 816a b x + 1012a b x + 1126a )\|b x + a +--R / +--R 315 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1504 + +--S 1505 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 4 +-+ - 2\|a \|b x + a + b x + 2a 4 +-+ \|b x + a +--R (4) a \|a log(----------------------------) + 2a \|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1505 + +--S 1506 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1506 + +--S 1507 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 4 +-+ \|b x + a 4 +---+ \|b x + a +--R (6) 2a \|a atanh(----------) - 2a \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1507 + +--S 1508 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1508 + +)clear all + +--S 1509 of 3330 +t0000:=(a+b*x)^(9/2)/x^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1509 + +--S 1510 of 3330 +r0000:=3*a^2*b*(a+b*x)^(3/2)+9/5*a*b*(a+b*x)^(5/2)+9/7*b*(a+b*x)^(7/2)-_ + (a+b*x)^(9/2)/x-9*a^(7/2)*b*atanh(sqrt(a+b*x)/sqrt(a))+_ + 9*a^3*b*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 3 +-+ \|b x + a +--R - 315a b x\|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (10b x + 58a b x + 156a b x + 388a b x - 35a )\|b x + a +--R / +--R 35x +--R Type: Expression(Integer) +--E 1510 + +--S 1511 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 3 +-+ - 2\|a \|b x + a + b x + 2a +--R 315a b x\|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (20b x + 116a b x + 312a b x + 776a b x - 70a )\|b x + a +--R / +--R 70x +--R , +--R +--R +-------+ +--R 3 +---+ \|b x + a +--R - 315a b x\|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (10b x + 58a b x + 156a b x + 388a b x - 35a )\|b x + a +--R / +--R 35x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1511 + +--S 1512 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 3 +-+ - 2\|a \|b x + a + b x + 2a 3 +-+ \|b x + a +--R 9a b\|a log(----------------------------) + 18a b\|a atanh(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1512 + +--S 1513 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1513 + +--S 1514 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 3 +-+ \|b x + a 3 +---+ \|b x + a +--R (6) 9a b\|a atanh(----------) - 9a b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1514 + +--S 1515 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1515 + +)clear all + +--S 1516 of 3330 +t0000:=(a+b*x)^(9/2)/x^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1516 + +--S 1517 of 3330 +r0000:=21/4*a*b^2*(a+b*x)^(3/2)+63/20*b^2*(a+b*x)^(5/2)-_ + 9/4*b*(a+b*x)^(7/2)/x-1/2*(a+b*x)^(9/2)/x^2-_ + 63/4*a^(5/2)*b^2*atanh(sqrt(a+b*x)/sqrt(a))+63/4*a^2*b^2*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 2 2 2 +-+ \|b x + a +--R - 315a b x \|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (8b x + 56a b x + 288a b x - 85a b x - 10a )\|b x + a +--R / +--R 2 +--R 20x +--R Type: Expression(Integer) +--E 1517 + +--S 1518 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 2 2 2 +-+ - 2\|a \|b x + a + b x + 2a +--R 315a b x \|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (16b x + 112a b x + 576a b x - 170a b x - 20a )\|b x + a +--R / +--R 2 +--R 40x +--R , +--R +--R +-------+ +--R 2 2 2 +---+ \|b x + a +--R - 315a b x \|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (8b x + 56a b x + 288a b x - 85a b x - 10a )\|b x + a +--R / +--R 2 +--R 20x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1518 + +--S 1519 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-+ +-------+ +-------+ +--R 2 2 +-+ - 2\|a \|b x + a + b x + 2a 2 2 +-+ \|b x + a +--R 63a b \|a log(----------------------------) + 126a b \|a atanh(----------) +--R x +-+ +--R \|a +--R -------------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 1519 + +--S 1520 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1520 + +--S 1521 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 2 2 +-+ \|b x + a 2 2 +---+ \|b x + a +--R 63a b \|a atanh(----------) - 63a b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ---------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 1521 + +--S 1522 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1522 + +)clear all + +--S 1523 of 3330 +t0000:=(a+b*x)^(9/2)/x^4 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1523 + +--S 1524 of 3330 +r0000:=35/8*b^3*(a+b*x)^(3/2)-21/8*b^2*(a+b*x)^(5/2)/x-_ + 3/4*b*(a+b*x)^(7/2)/x^2-1/3*(a+b*x)^(9/2)/x^3-_ + 105/8*a^(3/2)*b^3*atanh(sqrt(a+b*x)/sqrt(a))+105/8*a*b^3*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 3 3 +-+ \|b x + a +--R - 315a b x \|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (16b x + 208a b x - 165a b x - 50a b x - 8a )\|b x + a +--R / +--R 3 +--R 24x +--R Type: Expression(Integer) +--E 1524 + +--S 1525 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 3 3 +-+ - 2\|a \|b x + a + b x + 2a +--R 315a b x \|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (32b x + 416a b x - 330a b x - 100a b x - 16a )\|b x + a +--R / +--R 3 +--R 48x +--R , +--R +--R +-------+ +--R 3 3 +---+ \|b x + a +--R - 315a b x \|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (16b x + 208a b x - 165a b x - 50a b x - 8a )\|b x + a +--R / +--R 3 +--R 24x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1525 + +--S 1526 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-+ +-------+ +-------+ +--R 3 +-+ - 2\|a \|b x + a + b x + 2a 3 +-+ \|b x + a +--R 105a b \|a log(----------------------------) + 210a b \|a atanh(----------) +--R x +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1526 + +--S 1527 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1527 + +--S 1528 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 3 +-+ \|b x + a 3 +---+ \|b x + a +--R 105a b \|a atanh(----------) - 105a b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ------------------------------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 1528 + +--S 1529 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1529 + +)clear all + +--S 1530 of 3330 +t0000:=(a+b*x)^(9/2)/x^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 1530 + +--S 1531 of 3330 +r0000:=-105/64*b^3*(a+b*x)^(3/2)/x-21/32*b^2*(a+b*x)^(5/2)/x^2-_ + 3/8*b*(a+b*x)^(7/2)/x^3-1/4*(a+b*x)^(9/2)/x^4-_ + 315/64*b^4*atanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+315/64*b^4*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 4 4 +-+ \|b x + a +--R - 315b x \|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (128b x - 325a b x - 210a b x - 88a b x - 16a )\|b x + a +--R / +--R 4 +--R 64x +--R Type: Expression(Integer) +--E 1531 + +--S 1532 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 4 4 +-+ - 2\|a \|b x + a + b x + 2a +--R 315b x \|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (256b x - 650a b x - 420a b x - 176a b x - 32a )\|b x + a +--R / +--R 4 +--R 128x +--R , +--R +--R +-------+ +--R 4 4 +---+ \|b x + a +--R - 315b x \|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (128b x - 325a b x - 210a b x - 88a b x - 16a )\|b x + a +--R / +--R 4 +--R 64x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1532 + +--S 1533 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-+ +-------+ +-------+ +--R 4 +-+ - 2\|a \|b x + a + b x + 2a 4 +-+ \|b x + a +--R 315b \|a log(----------------------------) + 630b \|a atanh(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 1533 + +--S 1534 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1534 + +--S 1535 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 4 +-+ \|b x + a 4 +---+ \|b x + a +--R 315b \|a atanh(----------) - 315b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) -------------------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 1535 + +--S 1536 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1536 + +)clear all + +--S 1537 of 3330 +t0000:=(a+b*x)^(9/2)/x^6 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 1537 + +--S 1538 of 3330 +r0000:=-21/64*b^3*(a+b*x)^(3/2)/x^2-21/80*b^2*(a+b*x)^(5/2)/x^3-_ + 9/40*b*(a+b*x)^(7/2)/x^4-1/5*(a+b*x)^(9/2)/x^5-_ + 63/128*b^5*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-63/128*b^4*sqrt(a+b*x)/x +--R +--R +--R (2) +--R +-------+ +--R 5 5 \|b x + a +--R - 315b x atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-------+ +--R (- 965b x - 1490a b x - 1368a b x - 656a b x - 128a )\|a \|b x + a +--R / +--R 5 +-+ +--R 640x \|a +--R Type: Expression(Integer) +--E 1538 + +--S 1539 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 5 5 - 2a\|b x + a + (b x + 2a)\|a +--R 315b x log(-------------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-------+ +--R (- 1930b x - 2980a b x - 2736a b x - 1312a b x - 256a )\|a \|b x + a +--R / +--R 5 +-+ +--R 1280x \|a +--R , +--R +--R +---+ +-------+ +--R 5 5 \|- a \|b x + a +--R - 315b x atan(----------------) +--R a +--R + +--R 4 4 3 3 2 2 2 3 4 +---+ +-------+ +--R (- 965b x - 1490a b x - 1368a b x - 656a b x - 128a )\|- a \|b x + a +--R / +--R 5 +---+ +--R 640x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1539 + +--S 1540 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 5 - 2a\|b x + a + (b x + 2a)\|a 5 \|b x + a +--R 63b log(-------------------------------) + 126b atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R +-+ +--R 256\|a +--R Type: Expression(Integer) +--E 1540 + +--S 1541 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1541 + +--S 1542 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 5 +---+ \|b x + a 5 +-+ \|- a \|b x + a +--R 63b \|- a atanh(----------) - 63b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 128\|- a \|a +--R Type: Expression(Integer) +--E 1542 + +--S 1543 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1543 + +)clear all + +--S 1544 of 3330 +t0000:=(a+b*x)^(9/2)/x^7 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 1544 + +--S 1545 of 3330 +r0000:=-7/64*b^3*(a+b*x)^(3/2)/x^3-21/160*b^2*(a+b*x)^(5/2)/x^4-_ + 3/20*b*(a+b*x)^(7/2)/x^5-1/6*(a+b*x)^(9/2)/x^6+_ + 21/512*b^6*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-_ + 21/256*b^4*sqrt(a+b*x)/x^2-21/512*b^5*sqrt(a+b*x)/(a*x) +--R +--R +--R (2) +--R +-------+ +--R 6 6 \|b x + a +--R 315b x atanh(----------) +--R +-+ +--R \|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 +--R - 315b x - 4910a b x - 11432a b x - 12144a b x - 6272a b x +--R + +--R 5 +--R - 1280a +--R * +--R +-+ +-------+ +--R \|a \|b x + a +--R / +--R 6 +-+ +--R 7680a x \|a +--R Type: Expression(Integer) +--E 1545 + +--S 1546 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 6 6 2a\|b x + a + (b x + 2a)\|a +--R 315b x log(-----------------------------) +--R x +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 +--R - 630b x - 9820a b x - 22864a b x - 24288a b x - 12544a b x +--R + +--R 5 +--R - 2560a +--R * +--R +-+ +-------+ +--R \|a \|b x + a +--R / +--R 6 +-+ +--R 15360a x \|a +--R , +--R +--R +---+ +-------+ +--R 6 6 \|- a \|b x + a +--R 315b x atan(----------------) +--R a +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 +--R - 315b x - 4910a b x - 11432a b x - 12144a b x - 6272a b x +--R + +--R 5 +--R - 1280a +--R * +--R +---+ +-------+ +--R \|- a \|b x + a +--R / +--R 6 +---+ +--R 7680a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1546 + +--S 1547 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 6 2a\|b x + a + (b x + 2a)\|a 6 \|b x + a +--R 21b log(-----------------------------) - 42b atanh(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 1024a\|a +--R Type: Expression(Integer) +--E 1547 + +--S 1548 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1548 + +--S 1549 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 6 +---+ \|b x + a 6 +-+ \|- a \|b x + a +--R - 21b \|- a atanh(----------) + 21b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R +---+ +-+ +--R 512a\|- a \|a +--R Type: Expression(Integer) +--E 1549 + +--S 1550 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1550 + +)clear all + +--S 1551 of 3330 +t0000:=(a+b*x)^(9/2)/x^8 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 1551 + +--S 1552 of 3330 +r0000:=-3/64*b^3*(a+b*x)^(3/2)/x^4-3/40*b^2*(a+b*x)^(5/2)/x^5-_ + 3/28*b*(a+b*x)^(7/2)/x^6-1/7*(a+b*x)^(9/2)/x^7-_ + 9/1024*b^7*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-_ + 3/128*b^4*sqrt(a+b*x)/x^3-3/512*b^5*sqrt(a+b*x)/(a*x^2)+_ + 9/1024*b^6*sqrt(a+b*x)/(a^2*x) +--R +--R +--R (2) +--R +-------+ +--R 7 7 \|b x + a +--R - 315b x atanh(----------) +--R +-+ +--R \|a +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R 315b x - 210a b x - 14168a b x - 39056a b x - 44928a b x +--R + +--R 5 6 +--R - 24320a b x - 5120a +--R * +--R +-+ +-------+ +--R \|a \|b x + a +--R / +--R 2 7 +-+ +--R 35840a x \|a +--R Type: Expression(Integer) +--E 1552 + +--S 1553 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 7 7 - 2a\|b x + a + (b x + 2a)\|a +--R 315b x log(-------------------------------) +--R x +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R 630b x - 420a b x - 28336a b x - 78112a b x - 89856a b x +--R + +--R 5 6 +--R - 48640a b x - 10240a +--R * +--R +-+ +-------+ +--R \|a \|b x + a +--R / +--R 2 7 +-+ +--R 71680a x \|a +--R , +--R +--R +---+ +-------+ +--R 7 7 \|- a \|b x + a +--R - 315b x atan(----------------) +--R a +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R 315b x - 210a b x - 14168a b x - 39056a b x - 44928a b x +--R + +--R 5 6 +--R - 24320a b x - 5120a +--R * +--R +---+ +-------+ +--R \|- a \|b x + a +--R / +--R 2 7 +---+ +--R 35840a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1553 + +--S 1554 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 7 - 2a\|b x + a + (b x + 2a)\|a 7 \|b x + a +--R 9b log(-------------------------------) + 18b atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 2 +-+ +--R 2048a \|a +--R Type: Expression(Integer) +--E 1554 + +--S 1555 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1555 + +--S 1556 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 7 +---+ \|b x + a 7 +-+ \|- a \|b x + a +--R 9b \|- a atanh(----------) - 9b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 1024a \|- a \|a +--R Type: Expression(Integer) +--E 1556 + +--S 1557 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1557 + +)clear all + +--S 1558 of 3330 +t0000:=sqrt(-a+b*x)/x +--R +--R +--R +-------+ +--R \|b x - a +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 1558 + +--S 1559 of 3330 +r0000:=-2*atan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+2*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x - a +-------+ +--R (2) - 2\|a atan(----------) + 2\|b x - a +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1559 + +--S 1560 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-------+ +--R +---+ - 2\|- a \|b x - a + b x - 2a +-------+ +--R [\|- a log(------------------------------) + 2\|b x - a , +--R x +--R +-------+ +--R +-+ \|b x - a +-------+ +--R - 2\|a atan(----------) + 2\|b x - a ] +--R +-+ +--R \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1560 + +--S 1561 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +-------+ +-------+ +--R +---+ - 2\|- a \|b x - a + b x - 2a +-+ \|b x - a +--R (4) \|- a log(------------------------------) + 2\|a atan(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1561 + +--S 1562 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1562 + +--S 1563 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1563 + +--S 1564 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1564 + +)clear all + +--S 1565 of 3330 +t0000:=sqrt(-a+b*x)/x^2 +--R +--R +--R +-------+ +--R \|b x - a +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1565 + +--S 1566 of 3330 +r0000:=b*atan(sqrt(-a+b*x)/sqrt(a))/sqrt(a)-sqrt(-a+b*x)/x +--R +--R +--R +-------+ +--R \|b x - a +-+ +-------+ +--R b x atan(----------) - \|a \|b x - a +--R +-+ +--R \|a +--R (2) ------------------------------------- +--R +-+ +--R x\|a +--R Type: Expression(Integer) +--E 1566 + +--S 1567 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R b x log(-------------------------------) - 2\|- a \|b x - a +--R x +--R [------------------------------------------------------------, +--R +---+ +--R 2x\|- a +--R +-+ +-------+ +--R \|a \|b x - a +-+ +-------+ +--R b x atan(--------------) - \|a \|b x - a +--R a +--R -----------------------------------------] +--R +-+ +--R x\|a +--R Type: Union(List(Expression(Integer)),...) +--E 1567 + +--S 1568 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R b\|a log(-------------------------------) - 2b\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 1568 + +--S 1569 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1569 + +--S 1570 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R b atan(--------------) - b atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1570 + +--S 1571 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1571 + +)clear all + +--S 1572 of 3330 +t0000:=sqrt(-a+b*x)/x^3 +--R +--R +--R +-------+ +--R \|b x - a +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1572 + +--S 1573 of 3330 +r0000:=1/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)-_ + 1/2*sqrt(-a+b*x)/x^2+1/4*b*sqrt(-a+b*x)/(a*x) +--R +--R +--R +-------+ +--R 2 2 \|b x - a +-+ +-------+ +--R b x atan(----------) + (b x - 2a)\|a \|b x - a +--R +-+ +--R \|a +--R (2) ----------------------------------------------- +--R 2 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 1573 + +--S 1574 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2 2 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R b x log(-------------------------------) + (2b x - 4a)\|- a \|b x - a +--R x +--R [----------------------------------------------------------------------, +--R 2 +---+ +--R 8a x \|- a +--R +-+ +-------+ +--R 2 2 \|a \|b x - a +-+ +-------+ +--R b x atan(--------------) + (b x - 2a)\|a \|b x - a +--R a +--R ---------------------------------------------------] +--R 2 +-+ +--R 4a x \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1574 + +--S 1575 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +-+ 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R b \|a log(-------------------------------) - 2b \|- a atan(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression(Integer) +--E 1575 + +--S 1576 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1576 + +--S 1577 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R b atan(--------------) - b atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 1577 + +--S 1578 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1578 + +)clear all + +--S 1579 of 3330 +t0000:=(-a+b*x)^(3/2)/x +--R +--R +--R +-------+ +--R (b x - a)\|b x - a +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 1579 + +--S 1580 of 3330 +r0000:=2/3*(-a+b*x)^(3/2)+2*a^(3/2)*atan(sqrt(-a+b*x)/sqrt(a))-2*a*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x - a +-------+ +--R 6a\|a atan(----------) + (2b x - 8a)\|b x - a +--R +-+ +--R \|a +--R (2) ---------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1580 + +--S 1581 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-------+ +--R +---+ 2\|- a \|b x - a + b x - 2a +-------+ +--R 3a\|- a log(----------------------------) + (2b x - 8a)\|b x - a +--R x +--R [-----------------------------------------------------------------, +--R 3 +--R +-------+ +--R +-+ \|b x - a +-------+ +--R 6a\|a atan(----------) + (2b x - 8a)\|b x - a +--R +-+ +--R \|a +--R ----------------------------------------------] +--R 3 +--R Type: Union(List(Expression(Integer)),...) +--E 1581 + +--S 1582 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +-------+ +-------+ +--R +---+ 2\|- a \|b x - a + b x - 2a +-+ \|b x - a +--R (4) a\|- a log(----------------------------) - 2a\|a atan(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1582 + +--S 1583 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1583 + +--S 1584 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1584 + +--S 1585 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1585 + +)clear all + +--S 1586 of 3330 +t0000:=(-a+b*x)^(3/2)/x^2 +--R +--R +--R +-------+ +--R (b x - a)\|b x - a +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1586 + +--S 1587 of 3330 +r0000:=-(-a+b*x)^(3/2)/x-3*b*atan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+_ + 3*b*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x - a +-------+ +--R - 3b x\|a atan(----------) + (2b x + a)\|b x - a +--R +-+ +--R \|a +--R (2) ------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1587 + +--S 1588 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-------+ +--R +---+ - 2\|- a \|b x - a + b x - 2a +-------+ +--R 3b x\|- a log(------------------------------) + (4b x + 2a)\|b x - a +--R x +--R [---------------------------------------------------------------------, +--R 2x +--R +-------+ +--R +-+ \|b x - a +-------+ +--R - 3b x\|a atan(----------) + (2b x + a)\|b x - a +--R +-+ +--R \|a +--R -------------------------------------------------] +--R x +--R Type: Union(List(Expression(Integer)),...) +--E 1588 + +--S 1589 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +-------+ +-------+ +--R +---+ - 2\|- a \|b x - a + b x - 2a +-+ \|b x - a +--R 3b\|- a log(------------------------------) + 6b\|a atan(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1589 + +--S 1590 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1590 + +--S 1591 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1591 + +--S 1592 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1592 + +)clear all + +--S 1593 of 3330 +t0000:=(-a+b*x)^(3/2)/x^3 +--R +--R +--R +-------+ +--R (b x - a)\|b x - a +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1593 + +--S 1594 of 3330 +r0000:=-1/2*(-a+b*x)^(3/2)/x^2+3/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/sqrt(a)-_ + 3/4*b*sqrt(-a+b*x)/x +--R +--R +--R +-------+ +--R 2 2 \|b x - a +-+ +-------+ +--R 3b x atan(----------) + (- 5b x + 2a)\|a \|b x - a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 +-+ +--R 4x \|a +--R Type: Expression(Integer) +--E 1594 + +--S 1595 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2 2 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R 3b x log(-------------------------------) + (- 10b x + 4a)\|- a \|b x - a +--R x +--R [--------------------------------------------------------------------------, +--R 2 +---+ +--R 8x \|- a +--R +-+ +-------+ +--R 2 2 \|a \|b x - a +-+ +-------+ +--R 3b x atan(--------------) + (- 5b x + 2a)\|a \|b x - a +--R a +--R -------------------------------------------------------] +--R 2 +-+ +--R 4x \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1595 + +--S 1596 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R 2 +-+ 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R 3b \|a log(-------------------------------) - 6b \|- a atan(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R +---+ +-+ +--R 8\|- a \|a +--R Type: Expression(Integer) +--E 1596 + +--S 1597 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1597 + +--S 1598 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R 3b atan(--------------) - 3b atan(----------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R +-+ +--R 4\|a +--R Type: Expression(Integer) +--E 1598 + +--S 1599 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1599 + +)clear all + +--S 1600 of 3330 +t0000:=(-a+b*x)^(5/2)/x +--R +--R +--R 2 2 2 +-------+ +--R (b x - 2a b x + a )\|b x - a +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 1600 + +--S 1601 of 3330 +r0000:=-2/3*a*(-a+b*x)^(3/2)+2/5*(-a+b*x)^(5/2)-_ + 2*a^(5/2)*atan(sqrt(-a+b*x)/sqrt(a))+2*a^2*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R 2 +-+ \|b x - a 2 2 2 +-------+ +--R - 30a \|a atan(----------) + (6b x - 22a b x + 46a )\|b x - a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 1601 + +--S 1602 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +-------+ +--R 2 +---+ - 2\|- a \|b x - a + b x - 2a +--R 15a \|- a log(------------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (6b x - 22a b x + 46a )\|b x - a +--R / +--R 15 +--R , +--R +-------+ +--R 2 +-+ \|b x - a 2 2 2 +-------+ +--R - 30a \|a atan(----------) + (6b x - 22a b x + 46a )\|b x - a +--R +-+ +--R \|a +--R ---------------------------------------------------------------] +--R 15 +--R Type: Union(List(Expression(Integer)),...) +--E 1602 + +--S 1603 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +-------+ +-------+ +--R 2 +---+ - 2\|- a \|b x - a + b x - 2a 2 +-+ \|b x - a +--R (4) a \|- a log(------------------------------) + 2a \|a atan(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1603 + +--S 1604 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1604 + +--S 1605 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1605 + +--S 1606 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1606 + +)clear all + +--S 1607 of 3330 +t0000:=(-a+b*x)^(5/2)/x^2 +--R +--R +--R 2 2 2 +-------+ +--R (b x - 2a b x + a )\|b x - a +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1607 + +--S 1608 of 3330 +r0000:=5/3*b*(-a+b*x)^(3/2)-(-a+b*x)^(5/2)/x+_ + 5*a^(3/2)*b*atan(sqrt(-a+b*x)/sqrt(a))-5*a*b*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x - a 2 2 2 +-------+ +--R 15a b x\|a atan(----------) + (2b x - 14a b x - 3a )\|b x - a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 1608 + +--S 1609 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +-------+ +--R +---+ 2\|- a \|b x - a + b x - 2a +--R 15a b x\|- a log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (4b x - 28a b x - 6a )\|b x - a +--R / +--R 6x +--R , +--R +-------+ +--R +-+ \|b x - a 2 2 2 +-------+ +--R 15a b x\|a atan(----------) + (2b x - 14a b x - 3a )\|b x - a +--R +-+ +--R \|a +--R ---------------------------------------------------------------] +--R 3x +--R Type: Union(List(Expression(Integer)),...) +--E 1609 + +--S 1610 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +---+ +-------+ +-------+ +--R +---+ 2\|- a \|b x - a + b x - 2a +-+ \|b x - a +--R 5a b\|- a log(----------------------------) - 10a b\|a atan(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1610 + +--S 1611 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1611 + +--S 1612 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1612 + +--S 1613 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1613 + +)clear all + +--S 1614 of 3330 +t0000:=(-a+b*x)^(5/2)/x^3 +--R +--R +--R 2 2 2 +-------+ +--R (b x - 2a b x + a )\|b x - a +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 1614 + +--S 1615 of 3330 +r0000:=-5/4*b*(-a+b*x)^(3/2)/x-1/2*(-a+b*x)^(5/2)/x^2-_ + 15/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+15/4*b^2*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R 2 2 +-+ \|b x - a 2 2 2 +-------+ +--R - 15b x \|a atan(----------) + (8b x + 9a b x - 2a )\|b x - a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 1615 + +--S 1616 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +-------+ +--R 2 2 +---+ - 2\|- a \|b x - a + b x - 2a +--R 15b x \|- a log(------------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (16b x + 18a b x - 4a )\|b x - a +--R / +--R 2 +--R 8x +--R , +--R +-------+ +--R 2 2 +-+ \|b x - a 2 2 2 +-------+ +--R - 15b x \|a atan(----------) + (8b x + 9a b x - 2a )\|b x - a +--R +-+ +--R \|a +--R ---------------------------------------------------------------] +--R 2 +--R 4x +--R Type: Union(List(Expression(Integer)),...) +--E 1616 + +--S 1617 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +---+ +-------+ +-------+ +--R 2 +---+ - 2\|- a \|b x - a + b x - 2a 2 +-+ \|b x - a +--R 15b \|- a log(------------------------------) + 30b \|a atan(----------) +--R x +-+ +--R \|a +--R ------------------------------------------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 1617 + +--S 1618 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1618 + +--S 1619 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1619 + +--S 1620 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1620 + +)clear all + +--S 1621 of 3330 +t0000:=x^m/sqrt(a+b*x) +--R +--R +--R m +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1621 + +--S 1622 of 3330 +--r0000:=2*x^m*hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(b*(-b*x/a)^m) +--E 1622 + +--S 1623 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1623 + +--S 1624 of 3330 +--m0000:=a0000 - r0000 +--E 1624 + +--S 1625 of 3330 +--d0000:=D(m0000,x) +--E 1625 + +)clear all + +--S 1626 of 3330 +t0000:=x^4/sqrt(a+b*x) +--R +--R +--R 4 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1626 + +--S 1627 of 3330 +r0000:=-8/3*a^3*(a+b*x)^(3/2)/b^5+12/5*a^2*(a+b*x)^(5/2)/b^5-_ + 8/7*a*(a+b*x)^(7/2)/b^5+2/9*(a+b*x)^(9/2)/b^5+2*a^4*sqrt(a+b*x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x - 80a b x + 96a b x - 128a b x + 256a )\|b x + a +--R (2) ----------------------------------------------------------- +--R 5 +--R 315b +--R Type: Expression(Integer) +--E 1627 + +--S 1628 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x - 80a b x + 96a b x - 128a b x + 256a )\|b x + a +--R (3) ----------------------------------------------------------- +--R 5 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 1628 + +--S 1629 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1629 + +--S 1630 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1630 + +)clear all + +--S 1631 of 3330 +t0000:=x^3/sqrt(a+b*x) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1631 + +--S 1632 of 3330 +r0000:=2*a^2*(a+b*x)^(3/2)/b^4-6/5*a*(a+b*x)^(5/2)/b^4+_ + 2/7*(a+b*x)^(7/2)/b^4-2*a^3*sqrt(a+b*x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (10b x - 12a b x + 16a b x - 32a )\|b x + a +--R (2) ---------------------------------------------- +--R 4 +--R 35b +--R Type: Expression(Integer) +--E 1632 + +--S 1633 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (10b x - 12a b x + 16a b x - 32a )\|b x + a +--R (3) ---------------------------------------------- +--R 4 +--R 35b +--R Type: Union(Expression(Integer),...) +--E 1633 + +--S 1634 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1634 + +--S 1635 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1635 + +)clear all + +--S 1636 of 3330 +t0000:=x^2/sqrt(a+b*x) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1636 + +--S 1637 of 3330 +r0000:=-4/3*a*(a+b*x)^(3/2)/b^3+2/5*(a+b*x)^(5/2)/b^3+2*a^2*sqrt(a+b*x)/b^3 +--R +--R +--R 2 2 2 +-------+ +--R (6b x - 8a b x + 16a )\|b x + a +--R (2) --------------------------------- +--R 3 +--R 15b +--R Type: Expression(Integer) +--E 1637 + +--S 1638 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-------+ +--R (6b x - 8a b x + 16a )\|b x + a +--R (3) --------------------------------- +--R 3 +--R 15b +--R Type: Union(Expression(Integer),...) +--E 1638 + +--S 1639 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1639 + +--S 1640 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1640 + +)clear all + +--S 1641 of 3330 +t0000:=x/sqrt(a+b*x) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1641 + +--S 1642 of 3330 +r0000:=2/3*(a+b*x)^(3/2)/b^2-2*a*sqrt(a+b*x)/b^2 +--R +--R +--R +-------+ +--R (2b x - 4a)\|b x + a +--R (2) --------------------- +--R 2 +--R 3b +--R Type: Expression(Integer) +--E 1642 + +--S 1643 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R (2b x - 4a)\|b x + a +--R (3) --------------------- +--R 2 +--R 3b +--R Type: Union(Expression(Integer),...) +--E 1643 + +--S 1644 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1644 + +--S 1645 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1645 + +)clear all + +--S 1646 of 3330 +t0000:=1/sqrt(a+b*x) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1646 + +--S 1647 of 3330 +r0000:=2*sqrt(a+b*x)/b +--R +--R +--R +-------+ +--R 2\|b x + a +--R (2) ----------- +--R b +--R Type: Expression(Integer) +--E 1647 + +--S 1648 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R 2\|b x + a +--R (3) ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1648 + +--S 1649 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1649 + +--S 1650 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1650 + +)clear all + +--S 1651 of 3330 +t0000:=1/(x*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R x\|b x + a +--R Type: Expression(Integer) +--E 1651 + +--S 1652 of 3330 +r0000:=-2*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a) +--R +--R +--R +-------+ +--R \|b x + a +--R 2atanh(----------) +--R +-+ +--R \|a +--R (2) - ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1652 + +--S 1653 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-+ +---+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|- a \|b x + a +--R log(-------------------------------) 2atan(----------------) +--R x a +--R (3) [------------------------------------,- -----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1653 + +--S 1654 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(-------------------------------) + 2atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1654 + +--S 1655 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1655 + +--S 1656 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(----------) - 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1656 + +--S 1657 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1657 + +)clear all + +--S 1658 of 3330 +t0000:=1/(x^2*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 +-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 1658 + +--S 1659 of 3330 +r0000:=b*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-sqrt(a+b*x)/(a*x) +--R +--R +--R +-------+ +--R \|b x + a +-+ +-------+ +--R b x atanh(----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R +-+ +--R a x\|a +--R Type: Expression(Integer) +--E 1659 + +--S 1660 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R b x log(-----------------------------) - 2\|a \|b x + a +--R x +--R [--------------------------------------------------------, +--R +-+ +--R 2a x\|a +--R +---+ +-------+ +--R \|- a \|b x + a +---+ +-------+ +--R b x atan(----------------) - \|- a \|b x + a +--R a +--R ---------------------------------------------] +--R +---+ +--R a x\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1660 + +--S 1661 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R b log(-----------------------------) - 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 1661 + +--S 1662 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1662 + +--S 1663 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R - b\|- a atanh(----------) + b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1663 + +--S 1664 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1664 + +)clear all + +--S 1665 of 3330 +t0000:=1/(x^3*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 1665 + +--S 1666 of 3330 +r0000:=-3/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-_ + 1/2*sqrt(a+b*x)/(a*x^2)+3/4*b*sqrt(a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R 2 2 \|b x + a +-+ +-------+ +--R - 3b x atanh(----------) + (3b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------- +--R 2 2 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 1666 + +--S 1667 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R 2 2 - 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R 3b x log(-------------------------------) + (6b x - 4a)\|a \|b x + a +--R x +--R [---------------------------------------------------------------------, +--R 2 2 +-+ +--R 8a x \|a +--R +---+ +-------+ +--R 2 2 \|- a \|b x + a +---+ +-------+ +--R - 3b x atan(----------------) + (3b x - 2a)\|- a \|b x + a +--R a +--R -----------------------------------------------------------] +--R 2 2 +---+ +--R 4a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1667 + +--S 1668 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R 3b log(-------------------------------) + 6b atanh(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1668 + +--S 1669 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1669 + +--S 1670 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R 3b \|- a atanh(----------) - 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1670 + +--S 1671 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1671 + +)clear all + +--S 1672 of 3330 +t0000:=1/(x^4*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 4 +-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 1672 + +--S 1673 of 3330 +r0000:=5/8*b^3*atanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)-_ + 1/3*sqrt(a+b*x)/(a*x^3)+5/12*b*sqrt(a+b*x)/(a^2*x^2)-_ + 5/8*b^2*sqrt(a+b*x)/(a^3*x) +--R +--R +--R +-------+ +--R 3 3 \|b x + a 2 2 2 +-+ +-------+ +--R 15b x atanh(----------) + (- 15b x + 10a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3 3 +-+ +--R 24a x \|a +--R Type: Expression(Integer) +--E 1673 + +--S 1674 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 2a\|b x + a + (b x + 2a)\|a +--R 15b x log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +-------+ +--R (- 30b x + 20a b x - 16a )\|a \|b x + a +--R / +--R 3 3 +-+ +--R 48a x \|a +--R , +--R +---+ +-------+ +--R 3 3 \|- a \|b x + a 2 2 2 +---+ +-------+ +--R 15b x atan(----------------) + (- 15b x + 10a b x - 8a )\|- a \|b x + a +--R a +--R -------------------------------------------------------------------------] +--R 3 3 +---+ +--R 24a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1674 + +--S 1675 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 3 2a\|b x + a + (b x + 2a)\|a 3 \|b x + a +--R 5b log(-----------------------------) - 10b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1675 + +--S 1676 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1676 + +--S 1677 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 3 +---+ \|b x + a 3 +-+ \|- a \|b x + a +--R - 5b \|- a atanh(----------) + 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1677 + +--S 1678 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1678 + +)clear all + +--S 1679 of 3330 +t0000:=x^m/(a+b*x)^(3/2) +--R +--R +--R m +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1679 + +--S 1680 of 3330 +--r0000:=2*x^(1+m)/(a*sqrt(a+b*x))-2*(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(a*b*(-b*x/a)^m) +--E 1680 + +--S 1681 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | --------------------- d%N +--R ++ +--------+ +--R (%N b + a)\|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1681 + +--S 1682 of 3330 +--m0000:=a0000 - r0000 +--E 1682 + +--S 1683 of 3330 +--d0000:=D(m0000,x) +--E 1683 + +)clear all + +--S 1684 of 3330 +t0000:=x^4/(a+b*x)^(3/2) +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1684 + +--S 1685 of 3330 +r0000:=4*a^2*(a+b*x)^(3/2)/b^5-8/5*a*(a+b*x)^(5/2)/b^5+_ + 2/7*(a+b*x)^(7/2)/b^5-2*a^4/(b^5*sqrt(a+b*x))-8*a^3*sqrt(a+b*x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 10b x - 16a b x + 32a b x - 128a b x - 256a +--R (2) ----------------------------------------------- +--R 5 +-------+ +--R 35b \|b x + a +--R Type: Expression(Integer) +--E 1685 + +--S 1686 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 10b x - 16a b x + 32a b x - 128a b x - 256a +--R (3) ----------------------------------------------- +--R 5 +-------+ +--R 35b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1686 + +--S 1687 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1687 + +--S 1688 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1688 + +)clear all + +--S 1689 of 3330 +t0000:=x^3/(a+b*x)^(3/2) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1689 + +--S 1690 of 3330 +r0000:=-2*a*(a+b*x)^(3/2)/b^4+2/5*(a+b*x)^(5/2)/b^4+_ + 2*a^3/(b^4*sqrt(a+b*x))+6*a^2*sqrt(a+b*x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R 2b x - 4a b x + 16a b x + 32a +--R (2) -------------------------------- +--R 4 +-------+ +--R 5b \|b x + a +--R Type: Expression(Integer) +--E 1690 + +--S 1691 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x - 4a b x + 16a b x + 32a +--R (3) -------------------------------- +--R 4 +-------+ +--R 5b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1691 + +--S 1692 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1692 + +--S 1693 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1693 + +)clear all + +--S 1694 of 3330 +t0000:=x^2/(a+b*x)^(3/2) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1694 + +--S 1695 of 3330 +r0000:=2/3*(a+b*x)^(3/2)/b^3-2*a^2/(b^3*sqrt(a+b*x))-4*a*sqrt(a+b*x)/b^3 +--R +--R +--R 2 2 2 +--R 2b x - 8a b x - 16a +--R (2) --------------------- +--R 3 +-------+ +--R 3b \|b x + a +--R Type: Expression(Integer) +--E 1695 + +--S 1696 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2b x - 8a b x - 16a +--R (3) --------------------- +--R 3 +-------+ +--R 3b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1696 + +--S 1697 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1697 + +--S 1698 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1698 + +)clear all + +--S 1699 of 3330 +t0000:=x/(a+b*x)^(3/2) +--R +--R +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1699 + +--S 1700 of 3330 +r0000:=2*a/(b^2*sqrt(a+b*x))+2*sqrt(a+b*x)/b^2 +--R +--R +--R 2b x + 4a +--R (2) ------------ +--R 2 +-------+ +--R b \|b x + a +--R Type: Expression(Integer) +--E 1700 + +--S 1701 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2b x + 4a +--R (3) ------------ +--R 2 +-------+ +--R b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1701 + +--S 1702 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1702 + +--S 1703 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1703 + +)clear all + +--S 1704 of 3330 +t0000:=1/(a+b*x)^(3/2) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1704 + +--S 1705 of 3330 +r0000:=(-2)/(b*sqrt(a+b*x)) +--R +--R +--R 2 +--R (2) - ----------- +--R +-------+ +--R b\|b x + a +--R Type: Expression(Integer) +--E 1705 + +--S 1706 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ----------- +--R +-------+ +--R b\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1706 + +--S 1707 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1707 + +--S 1708 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1708 + +)clear all + +--S 1709 of 3330 +t0000:=1/(x*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 +-------+ +--R (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1709 + +--S 1710 of 3330 +r0000:=-2*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)+2/(a*sqrt(a+b*x)) +--R +--R +--R +-------+ +--R +-------+ \|b x + a +-+ +--R - 2\|b x + a atanh(----------) + 2\|a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R +-+ +-------+ +--R a\|a \|b x + a +--R Type: Expression(Integer) +--E 1710 + +--S 1711 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R +-------+ - 2a\|b x + a + (b x + 2a)\|a +-+ +--R \|b x + a log(-------------------------------) + 2\|a +--R x +--R [------------------------------------------------------, +--R +-+ +-------+ +--R a\|a \|b x + a +--R +---+ +-------+ +--R +-------+ \|- a \|b x + a +---+ +--R - 2\|b x + a atan(----------------) + 2\|- a +--R a +--R ---------------------------------------------] +--R +---+ +-------+ +--R a\|- a \|b x + a +--R Type: Union(List(Expression(Integer)),...) +--E 1711 + +--S 1712 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(-------------------------------) + 2atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1712 + +--S 1713 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1713 + +--S 1714 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(----------) - 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1714 + +--S 1715 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1715 + +)clear all + +--S 1716 of 3330 +t0000:=1/(x^2*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 3 2 +-------+ +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1716 + +--S 1717 of 3330 +r0000:=3*b*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+2/(a*x*sqrt(a+b*x))-_ + 3*sqrt(a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R +-------+ \|b x + a +-+ +--R 3b x\|b x + a atanh(----------) + (- 3b x - a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------- +--R 2 +-+ +-------+ +--R a x\|a \|b x + a +--R Type: Expression(Integer) +--E 1717 + +--S 1718 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R +-------+ 2a\|b x + a + (b x + 2a)\|a +-+ +--R 3b x\|b x + a log(-----------------------------) + (- 6b x - 2a)\|a +--R x +--R [--------------------------------------------------------------------, +--R 2 +-+ +-------+ +--R 2a x\|a \|b x + a +--R +---+ +-------+ +--R +-------+ \|- a \|b x + a +---+ +--R 3b x\|b x + a atan(----------------) + (- 3b x - a)\|- a +--R a +--R ---------------------------------------------------------] +--R 2 +---+ +-------+ +--R a x\|- a \|b x + a +--R Type: Union(List(Expression(Integer)),...) +--E 1718 + +--S 1719 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R 3b log(-----------------------------) - 6b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------ +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1719 + +--S 1720 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1720 + +--S 1721 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R - 3b\|- a atanh(----------) + 3b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1721 + +--S 1722 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1722 + +)clear all + +--S 1723 of 3330 +t0000:=1/(x^3*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 3 +-------+ +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1723 + +--S 1724 of 3330 +r0000:=-15/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+2/(a*x^2*sqrt(a+b*x))-_ + 5/2*sqrt(a+b*x)/(a^2*x^2)+15/4*b*sqrt(a+b*x)/(a^3*x) +--R +--R +--R +-------+ +--R 2 2 +-------+ \|b x + a 2 2 2 +-+ +--R - 15b x \|b x + a atanh(----------) + (15b x + 5a b x - 2a )\|a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------------- +--R 3 2 +-+ +-------+ +--R 4a x \|a \|b x + a +--R Type: Expression(Integer) +--E 1724 + +--S 1725 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 2 2 +-------+ - 2a\|b x + a + (b x + 2a)\|a +--R 15b x \|b x + a log(-------------------------------) +--R x +--R + +--R 2 2 2 +-+ +--R (30b x + 10a b x - 4a )\|a +--R / +--R 3 2 +-+ +-------+ +--R 8a x \|a \|b x + a +--R , +--R +---+ +-------+ +--R 2 2 +-------+ \|- a \|b x + a 2 2 2 +---+ +--R - 15b x \|b x + a atan(----------------) + (15b x + 5a b x - 2a )\|- a +--R a +--R ------------------------------------------------------------------------] +--R 3 2 +---+ +-------+ +--R 4a x \|- a \|b x + a +--R Type: Union(List(Expression(Integer)),...) +--E 1725 + +--S 1726 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R 15b log(-------------------------------) + 30b atanh(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1726 + +--S 1727 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1727 + +--S 1728 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R 15b \|- a atanh(----------) - 15b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 3 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1728 + +--S 1729 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1729 + +)clear all + +--S 1730 of 3330 +t0000:=x^m/(a+b*x)^(5/2) +--R +--R +--R m +--R x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1730 + +--S 1731 of 3330 +--r0000:=2/3*x^(1+m)/(a*(a+b*x)^(3/2))+2/3*(1-2*m)*x^(1+m)/(a^2*sqrt(a+b*x))-_ +-- 2/3*(1-2*m)*(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(a^2*b*(-b*x/a)^m) +--E 1731 + +--S 1732 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | --------------------------------- d%N +--R ++ 2 2 2 +--------+ +--R (%N b + 2%N a b + a )\|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1732 + +--S 1733 of 3330 +--m0000:=a0000 - r0000 +--E 1733 + +--S 1734 of 3330 +--d0000:=D(m0000,x) +--E 1734 + +)clear all + +--S 1735 of 3330 +--t0000:=x^4/(a+b*x)^(5/2) +--E 1735 + +--S 1736 of 3330 +r0000:=-2/3*a^4/(b^5*(a+b*x)^(3/2))-8/3*a*(a+b*x)^(3/2)/b^5+_ + 2/5*(a+b*x)^(5/2)/b^5+8*a^3/(b^5*sqrt(a+b*x))+12*a^2*sqrt(a+b*x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 6b x - 16a b x + 96a b x + 384a b x + 256a +--R (1) ---------------------------------------------- +--R 6 5 +-------+ +--R (15b x + 15a b )\|b x + a +--R Type: Expression(Integer) +--E 1736 + +--S 1737 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (2) t0000 x +--R Type: Polynomial(Fraction(Integer)) +--E 1737 + +--S 1738 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (3) +--R 6 2 5 +-------+ 4 4 3 3 2 2 2 +--R (15b t0000 x + 15a b t0000 x)\|b x + a - 6b x + 16a b x - 96a b x +--R + +--R 3 4 +--R - 384a b x - 256a +--R / +--R 6 5 +-------+ +--R (15b x + 15a b )\|b x + a +--R Type: Expression(Integer) +--E 1738 + +--S 1739 of 3330 +d0000:=D(m0000,x) +--R +--R +--R 2 2 2 +-------+ 4 +--R (b t0000 x + 2a b t0000 x + a t0000)\|b x + a - x +--R (4) ---------------------------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1739 + +)clear all + +--S 1740 of 3330 +t0000:=x^3/(a+b*x)^(5/2) +--R +--R +--R 3 +--R x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1740 + +--S 1741 of 3330 +r0000:=2/3*a^3/(b^4*(a+b*x)^(3/2))+2/3*(a+b*x)^(3/2)/b^4-_ + 6*a^2/(b^4*sqrt(a+b*x))-6*a*sqrt(a+b*x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R 2b x - 12a b x - 48a b x - 32a +--R (2) --------------------------------- +--R 5 4 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 1741 + +--S 1742 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x - 12a b x - 48a b x - 32a +--R (3) --------------------------------- +--R 5 4 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1742 + +--S 1743 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1743 + +--S 1744 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1744 + +)clear all + +--S 1745 of 3330 +t0000:=x^2/(a+b*x)^(5/2) +--R +--R +--R 2 +--R x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1745 + +--S 1746 of 3330 +r0000:=-2/3*a^2/(b^3*(a+b*x)^(3/2))+4*a/(b^3*sqrt(a+b*x))+2*sqrt(a+b*x)/b^3 +--R +--R +--R 2 2 2 +--R 6b x + 24a b x + 16a +--R (2) ------------------------ +--R 4 3 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 1746 + +--S 1747 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 6b x + 24a b x + 16a +--R (3) ------------------------ +--R 4 3 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1747 + +--S 1748 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1748 + +--S 1749 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1749 + +)clear all + +--S 1750 of 3330 +t0000:=x/(a+b*x)^(5/2) +--R +--R +--R x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1750 + +--S 1751 of 3330 +r0000:=2/3*a/(b^2*(a+b*x)^(3/2))+(-2)/(b^2*sqrt(a+b*x)) +--R +--R +--R - 6b x - 4a +--R (2) ------------------------ +--R 3 2 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 1751 + +--S 1752 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 6b x - 4a +--R (3) ------------------------ +--R 3 2 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1752 + +--S 1753 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1753 + +--S 1754 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1754 + +)clear all + +--S 1755 of 3330 +t0000:=1/(a+b*x)^(5/2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1755 + +--S 1756 of 3330 +r0000:=(-2/3)/(b*(a+b*x)^(3/2)) +--R +--R +--R 2 +--R (2) - ----------------------- +--R 2 +-------+ +--R (3b x + 3a b)\|b x + a +--R Type: Expression(Integer) +--E 1756 + +--S 1757 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ----------------------- +--R 2 +-------+ +--R (3b x + 3a b)\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1757 + +--S 1758 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1758 + +--S 1759 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1759 + +)clear all + +--S 1760 of 3330 +t0000:=1/(x*(a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 2 3 2 2 +-------+ +--R (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1760 + +--S 1761 of 3330 +r0000:=2/3/(a*(a+b*x)^(3/2))-2*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+_ + 2/(a^2*sqrt(a+b*x)) +--R +--R +--R +-------+ +--R +-------+ \|b x + a +-+ +--R (- 6b x - 6a)\|b x + a atanh(----------) + (6b x + 8a)\|a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------- +--R 2 3 +-+ +-------+ +--R (3a b x + 3a )\|a \|b x + a +--R Type: Expression(Integer) +--E 1761 + +--S 1762 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R +-------+ - 2a\|b x + a + (b x + 2a)\|a +-+ +--R (3b x + 3a)\|b x + a log(-------------------------------) + (6b x + 8a)\|a +--R x +--R [---------------------------------------------------------------------------, +--R 2 3 +-+ +-------+ +--R (3a b x + 3a )\|a \|b x + a +--R +---+ +-------+ +--R +-------+ \|- a \|b x + a +---+ +--R (- 6b x - 6a)\|b x + a atan(----------------) + (6b x + 8a)\|- a +--R a +--R -----------------------------------------------------------------] +--R 2 3 +---+ +-------+ +--R (3a b x + 3a )\|- a \|b x + a +--R Type: Union(List(Expression(Integer)),...) +--E 1762 + +--S 1763 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(-------------------------------) + 2atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1763 + +--S 1764 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1764 + +--S 1765 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(----------) - 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1765 + +--S 1766 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1766 + +)clear all + +--S 1767 of 3330 +t0000:=1/(x^2*(a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1767 + +--S 1768 of 3330 +r0000:=2/3/(a*x*(a+b*x)^(3/2))+5*b*atanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+_ + 10/3/(a^2*x*sqrt(a+b*x))-5*sqrt(a+b*x)/(a^3*x) +--R +--R +--R (2) +--R +-------+ +--R 2 2 +-------+ \|b x + a +--R (15b x + 15a b x)\|b x + a atanh(----------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (- 15b x - 20a b x - 3a )\|a +--R / +--R 3 2 4 +-+ +-------+ +--R (3a b x + 3a x)\|a \|b x + a +--R Type: Expression(Integer) +--E 1768 + +--S 1769 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 2 2 +-------+ 2a\|b x + a + (b x + 2a)\|a +--R (15b x + 15a b x)\|b x + a log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +--R (- 30b x - 40a b x - 6a )\|a +--R / +--R 3 2 4 +-+ +-------+ +--R (6a b x + 6a x)\|a \|b x + a +--R , +--R +--R +---+ +-------+ +--R 2 2 +-------+ \|- a \|b x + a +--R (15b x + 15a b x)\|b x + a atan(----------------) +--R a +--R + +--R 2 2 2 +---+ +--R (- 15b x - 20a b x - 3a )\|- a +--R / +--R 3 2 4 +---+ +-------+ +--R (3a b x + 3a x)\|- a \|b x + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1769 + +--S 1770 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R 5b log(-----------------------------) - 10b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1770 + +--S 1771 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1771 + +--S 1772 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R - 5b\|- a atanh(----------) + 5b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1772 + +--S 1773 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1773 + +)clear all + +--S 1774 of 3330 +t0000:=1/(x^3*(a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 5 4 2 3 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1774 + +--S 1775 of 3330 +r0000:=2/3/(a*x^2*(a+b*x)^(3/2))-_ + 35/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)+_ + 14/3/(a^2*x^2*sqrt(a+b*x))-35/6*sqrt(a+b*x)/(a^3*x^2)+_ + 35/4*b*sqrt(a+b*x)/(a^4*x) +--R +--R +--R (2) +--R +-------+ +--R 3 3 2 2 +-------+ \|b x + a +--R (- 105b x - 105a b x )\|b x + a atanh(----------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x + 140a b x + 21a b x - 6a )\|a +--R / +--R 4 3 5 2 +-+ +-------+ +--R (12a b x + 12a x )\|a \|b x + a +--R Type: Expression(Integer) +--E 1775 + +--S 1776 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 2 2 +-------+ - 2a\|b x + a + (b x + 2a)\|a +--R (105b x + 105a b x )\|b x + a log(-------------------------------) +--R x +--R + +--R 3 3 2 2 2 3 +-+ +--R (210b x + 280a b x + 42a b x - 12a )\|a +--R / +--R 4 3 5 2 +-+ +-------+ +--R (24a b x + 24a x )\|a \|b x + a +--R , +--R +--R +---+ +-------+ +--R 3 3 2 2 +-------+ \|- a \|b x + a +--R (- 105b x - 105a b x )\|b x + a atan(----------------) +--R a +--R + +--R 3 3 2 2 2 3 +---+ +--R (105b x + 140a b x + 21a b x - 6a )\|- a +--R / +--R 4 3 5 2 +---+ +-------+ +--R (12a b x + 12a x )\|- a \|b x + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1776 + +--S 1777 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R 35b log(-------------------------------) + 70b atanh(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1777 + +--S 1778 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1778 + +--S 1779 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R 35b \|- a atanh(----------) - 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 4 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1779 + +--S 1780 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1780 + +)clear all + +--S 1781 of 3330 +t0000:=1/(x*sqrt(-a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R x\|b x - a +--R Type: Expression(Integer) +--E 1781 + +--S 1782 of 3330 +r0000:=2*atan(sqrt(-a+b*x)/sqrt(a))/sqrt(a) +--R +--R +--R +-------+ +--R \|b x - a +--R 2atan(----------) +--R +-+ +--R \|a +--R (2) ----------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1782 + +--S 1783 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +---+ +-+ +-------+ +--R 2a\|b x - a + (b x - 2a)\|- a \|a \|b x - a +--R log(-------------------------------) 2atan(--------------) +--R x a +--R (3) [------------------------------------,---------------------] +--R +---+ +-+ +--R \|- a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1783 + +--S 1784 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R \|a log(-------------------------------) - 2\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1784 + +--S 1785 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1785 + +--S 1786 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R 2atan(--------------) - 2atan(----------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1786 + +--S 1787 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1787 + +)clear all + +--S 1788 of 3330 +t0000:=1/(x^2*sqrt(-a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 +-------+ +--R x \|b x - a +--R Type: Expression(Integer) +--E 1788 + +--S 1789 of 3330 +r0000:=b*atan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)+sqrt(-a+b*x)/(a*x) +--R +--R +--R +-------+ +--R \|b x - a +-+ +-------+ +--R b x atan(----------) + \|a \|b x - a +--R +-+ +--R \|a +--R (2) ------------------------------------- +--R +-+ +--R a x\|a +--R Type: Expression(Integer) +--E 1789 + +--S 1790 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R b x log(-------------------------------) + 2\|- a \|b x - a +--R x +--R [------------------------------------------------------------, +--R +---+ +--R 2a x\|- a +--R +-+ +-------+ +--R \|a \|b x - a +-+ +-------+ +--R b x atan(--------------) + \|a \|b x - a +--R a +--R -----------------------------------------] +--R +-+ +--R a x\|a +--R Type: Union(List(Expression(Integer)),...) +--E 1790 + +--S 1791 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R b\|a log(-------------------------------) - 2b\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 1791 + +--S 1792 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1792 + +--S 1793 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R b atan(--------------) - b atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1793 + +--S 1794 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1794 + +)clear all + +--S 1795 of 3330 +t0000:=1/(x^3*sqrt(-a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +-------+ +--R x \|b x - a +--R Type: Expression(Integer) +--E 1795 + +--S 1796 of 3330 +r0000:=3/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)+_ + 1/2*sqrt(-a+b*x)/(a*x^2)+3/4*b*sqrt(-a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R 2 2 \|b x - a +-+ +-------+ +--R 3b x atan(----------) + (3b x + 2a)\|a \|b x - a +--R +-+ +--R \|a +--R (2) ------------------------------------------------- +--R 2 2 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 1796 + +--S 1797 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2 2 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R 3b x log(-------------------------------) + (6b x + 4a)\|- a \|b x - a +--R x +--R [-----------------------------------------------------------------------, +--R 2 2 +---+ +--R 8a x \|- a +--R +-+ +-------+ +--R 2 2 \|a \|b x - a +-+ +-------+ +--R 3b x atan(--------------) + (3b x + 2a)\|a \|b x - a +--R a +--R -----------------------------------------------------] +--R 2 2 +-+ +--R 4a x \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1797 + +--S 1798 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R 2 +-+ 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R 3b \|a log(-------------------------------) - 6b \|- a atan(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1798 + +--S 1799 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1799 + +--S 1800 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R 3b atan(--------------) - 3b atan(----------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1800 + +--S 1801 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1801 + +)clear all + +--S 1802 of 3330 +t0000:=1/(x*(-a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 +-------+ +--R (b x - a x)\|b x - a +--R Type: Expression(Integer) +--E 1802 + +--S 1803 of 3330 +r0000:=-2*atan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)+(-2)/(a*sqrt(-a+b*x)) +--R +--R +--R +-------+ +--R +-------+ \|b x - a +-+ +--R - 2\|b x - a atan(----------) - 2\|a +--R +-+ +--R \|a +--R (2) ------------------------------------- +--R +-+ +-------+ +--R a\|a \|b x - a +--R Type: Expression(Integer) +--E 1803 + +--S 1804 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R +-------+ - 2a\|b x - a + (b x - 2a)\|- a +---+ +--R \|b x - a log(---------------------------------) - 2\|- a +--R x +--R [----------------------------------------------------------, +--R +---+ +-------+ +--R a\|- a \|b x - a +--R +-+ +-------+ +--R +-------+ \|a \|b x - a +-+ +--R - 2\|b x - a atan(--------------) - 2\|a +--R a +--R -----------------------------------------] +--R +-+ +-------+ +--R a\|a \|b x - a +--R Type: Union(List(Expression(Integer)),...) +--E 1804 + +--S 1805 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ - 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R \|a log(---------------------------------) + 2\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1805 + +--S 1806 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1806 + +--S 1807 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R - 2atan(--------------) + 2atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1807 + +--S 1808 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1808 + +)clear all + +--S 1809 of 3330 +t0000:=1/(x^2*(-a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 3 2 +-------+ +--R (b x - a x )\|b x - a +--R Type: Expression(Integer) +--E 1809 + +--S 1810 of 3330 +r0000:=-3*b*atan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)+(-2)/(a*x*sqrt(-a+b*x))-_ + 3*sqrt(-a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R +-------+ \|b x - a +-+ +--R - 3b x\|b x - a atan(----------) + (- 3b x + a)\|a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 +-+ +-------+ +--R a x\|a \|b x - a +--R Type: Expression(Integer) +--E 1810 + +--S 1811 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R +-------+ - 2a\|b x - a + (b x - 2a)\|- a +---+ +--R 3b x\|b x - a log(---------------------------------) + (- 6b x + 2a)\|- a +--R x +--R [--------------------------------------------------------------------------, +--R 2 +---+ +-------+ +--R 2a x\|- a \|b x - a +--R +-+ +-------+ +--R +-------+ \|a \|b x - a +-+ +--R - 3b x\|b x - a atan(--------------) + (- 3b x + a)\|a +--R a +--R -------------------------------------------------------] +--R 2 +-+ +-------+ +--R a x\|a \|b x - a +--R Type: Union(List(Expression(Integer)),...) +--E 1811 + +--S 1812 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R +-+ - 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R 3b\|a log(---------------------------------) + 6b\|- a atan(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 2a \|- a \|a +--R Type: Expression(Integer) +--E 1812 + +--S 1813 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1813 + +--S 1814 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R - 3b atan(--------------) + 3b atan(----------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1814 + +--S 1815 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1815 + +)clear all + +--S 1816 of 3330 +t0000:=1/(x^3*(-a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 3 +-------+ +--R (b x - a x )\|b x - a +--R Type: Expression(Integer) +--E 1816 + +--S 1817 of 3330 +r0000:=-15/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/a^(7/2)+_ + (-2)/(a*x^2*sqrt(-a+b*x))-5/2*sqrt(-a+b*x)/(a^2*x^2)-_ + 15/4*b*sqrt(-a+b*x)/(a^3*x) +--R +--R +--R +-------+ +--R 2 2 +-------+ \|b x - a 2 2 2 +-+ +--R - 15b x \|b x - a atan(----------) + (- 15b x + 5a b x + 2a )\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3 2 +-+ +-------+ +--R 4a x \|a \|b x - a +--R Type: Expression(Integer) +--E 1817 + +--S 1818 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +---+ +--R 2 2 +-------+ - 2a\|b x - a + (b x - 2a)\|- a +--R 15b x \|b x - a log(---------------------------------) +--R x +--R + +--R 2 2 2 +---+ +--R (- 30b x + 10a b x + 4a )\|- a +--R / +--R 3 2 +---+ +-------+ +--R 8a x \|- a \|b x - a +--R , +--R +-+ +-------+ +--R 2 2 +-------+ \|a \|b x - a 2 2 2 +-+ +--R - 15b x \|b x - a atan(--------------) + (- 15b x + 5a b x + 2a )\|a +--R a +--R ----------------------------------------------------------------------] +--R 3 2 +-+ +-------+ +--R 4a x \|a \|b x - a +--R Type: Union(List(Expression(Integer)),...) +--E 1818 + +--S 1819 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R 2 +-+ - 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R 15b \|a log(---------------------------------) + 30b \|- a atan(----------) +--R x +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1819 + +--S 1820 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1820 + +--S 1821 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R - 15b atan(--------------) + 15b atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1821 + +--S 1822 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1822 + +)clear all + +--S 1823 of 3330 +t0000:=1/(x*(-a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 2 3 2 2 +-------+ +--R (b x - 2a b x + a x)\|b x - a +--R Type: Expression(Integer) +--E 1823 + +--S 1824 of 3330 +r0000:=(-2/3)/(a*(-a+b*x)^(3/2))+2*atan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)+_ + 2/(a^2*sqrt(-a+b*x)) +--R +--R +--R +-------+ +--R +-------+ \|b x - a +-+ +--R (6b x - 6a)\|b x - a atan(----------) + (6b x - 8a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 2 3 +-+ +-------+ +--R (3a b x - 3a )\|a \|b x - a +--R Type: Expression(Integer) +--E 1824 + +--S 1825 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +---+ +--R +-------+ 2a\|b x - a + (b x - 2a)\|- a +--R (3b x - 3a)\|b x - a log(-------------------------------) +--R x +--R + +--R +---+ +--R (6b x - 8a)\|- a +--R / +--R 2 3 +---+ +-------+ +--R (3a b x - 3a )\|- a \|b x - a +--R , +--R +-+ +-------+ +--R +-------+ \|a \|b x - a +-+ +--R (6b x - 6a)\|b x - a atan(--------------) + (6b x - 8a)\|a +--R a +--R -----------------------------------------------------------] +--R 2 3 +-+ +-------+ +--R (3a b x - 3a )\|a \|b x - a +--R Type: Union(List(Expression(Integer)),...) +--E 1825 + +--S 1826 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R \|a log(-------------------------------) - 2\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1826 + +--S 1827 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1827 + +--S 1828 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R 2atan(--------------) - 2atan(----------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1828 + +--S 1829 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1829 + +)clear all + +--S 1830 of 3330 +t0000:=1/(x^2*(-a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (b x - 2a b x + a x )\|b x - a +--R Type: Expression(Integer) +--E 1830 + +--S 1831 of 3330 +r0000:=(-2/3)/(a*x*(-a+b*x)^(3/2))+5*b*atan(sqrt(-a+b*x)/sqrt(a))/a^(7/2)+_ + 10/3/(a^2*x*sqrt(-a+b*x))+5*sqrt(-a+b*x)/(a^3*x) +--R +--R +--R (2) +--R +-------+ +--R 2 2 +-------+ \|b x - a 2 2 2 +-+ +--R (15b x - 15a b x)\|b x - a atan(----------) + (15b x - 20a b x + 3a )\|a +--R +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R 3 2 4 +-+ +-------+ +--R (3a b x - 3a x)\|a \|b x - a +--R Type: Expression(Integer) +--E 1831 + +--S 1832 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +---+ +--R 2 2 +-------+ 2a\|b x - a + (b x - 2a)\|- a +--R (15b x - 15a b x)\|b x - a log(-------------------------------) +--R x +--R + +--R 2 2 2 +---+ +--R (30b x - 40a b x + 6a )\|- a +--R / +--R 3 2 4 +---+ +-------+ +--R (6a b x - 6a x)\|- a \|b x - a +--R , +--R +--R +-+ +-------+ +--R 2 2 +-------+ \|a \|b x - a +--R (15b x - 15a b x)\|b x - a atan(--------------) +--R a +--R + +--R 2 2 2 +-+ +--R (15b x - 20a b x + 3a )\|a +--R / +--R 3 2 4 +-+ +-------+ +--R (3a b x - 3a x)\|a \|b x - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1832 + +--S 1833 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R 5b\|a log(-------------------------------) - 10b\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------------- +--R 3 +---+ +-+ +--R 2a \|- a \|a +--R Type: Expression(Integer) +--E 1833 + +--S 1834 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1834 + +--S 1835 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R 5b atan(--------------) - 5b atan(----------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1835 + +--S 1836 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1836 + +)clear all + +--S 1837 of 3330 +t0000:=1/(x^3*(-a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 5 4 2 3 +-------+ +--R (b x - 2a b x + a x )\|b x - a +--R Type: Expression(Integer) +--E 1837 + +--S 1838 of 3330 +r0000:=(-2/3)/(a*x^2*(-a+b*x)^(3/2))+_ + 35/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/a^(9/2)+_ + 14/3/(a^2*x^2*sqrt(-a+b*x))+35/6*sqrt(-a+b*x)/(a^3*x^2)+_ + 35/4*b*sqrt(-a+b*x)/(a^4*x) +--R +--R +--R (2) +--R +-------+ +--R 3 3 2 2 +-------+ \|b x - a +--R (105b x - 105a b x )\|b x - a atan(----------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 140a b x + 21a b x + 6a )\|a +--R / +--R 4 3 5 2 +-+ +-------+ +--R (12a b x - 12a x )\|a \|b x - a +--R Type: Expression(Integer) +--E 1838 + +--S 1839 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +---+ +--R 3 3 2 2 +-------+ 2a\|b x - a + (b x - 2a)\|- a +--R (105b x - 105a b x )\|b x - a log(-------------------------------) +--R x +--R + +--R 3 3 2 2 2 3 +---+ +--R (210b x - 280a b x + 42a b x + 12a )\|- a +--R / +--R 4 3 5 2 +---+ +-------+ +--R (24a b x - 24a x )\|- a \|b x - a +--R , +--R +--R +-+ +-------+ +--R 3 3 2 2 +-------+ \|a \|b x - a +--R (105b x - 105a b x )\|b x - a atan(--------------) +--R a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 140a b x + 21a b x + 6a )\|a +--R / +--R 4 3 5 2 +-+ +-------+ +--R (12a b x - 12a x )\|a \|b x - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1839 + +--S 1840 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R 2 +-+ 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R 35b \|a log(-------------------------------) - 70b \|- a atan(----------) +--R x +-+ +--R \|a +--R ------------------------------------------------------------------------- +--R 4 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1840 + +--S 1841 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1841 + +--S 1842 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R 35b atan(--------------) - 35b atan(----------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1842 + +--S 1843 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1843 + +)clear all + +--S 1844 of 3330 +t0000:=x^(3+m)/sqrt(a+b*x) +--R +--R +--R m + 3 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1844 + +--S 1845 of 3330 +--r0000:=8*a^2*(2+m)*(3+m)*x^(1+m)*sqrt(a+b*x)/(b^3*(3+2*m)*(5+2*m)*(7+2*m))-_ +-- 4*a*(3+m)*x^(2+m)*sqrt(a+b*x)/(b^2*(5+2*m)*(7+2*m))+_ +-- 2*x^(3+m)*sqrt(a+b*x)/(b*(7+2*m))-16*a^3*(1+m)*(2+m)*(3+m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b^4*(3+2*m)*(5+2*m)*(7+2*m)*(-b*x/a)^m) +--E 1845 + +--S 1846 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m + 3 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1846 + +--S 1847 of 3330 +--m0000:=a0000 - r0000 +--E 1847 + +--S 1848 of 3330 +--d0000:=D(m0000,x) +--E 1848 + +)clear all + +--S 1849 of 3330 +t0000:=x^(2+m)/sqrt(a+b*x) +--R +--R +--R m + 2 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1849 + +--S 1850 of 3330 +--r0000:=-4*a*(2+m)*x^(1+m)*sqrt(a+b*x)/(b^2*(3+2*m)*(5+2*m))+_ +-- 2*x^(2+m)*sqrt(a+b*x)/(b*(5+2*m))+8*a^2*(1+m)*(2+m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b^3*(3+2*m)*(5+2*m)*(-b*x/a)^m) +--E 1850 + +--S 1851 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m + 2 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1851 + +--S 1852 of 3330 +--m0000:=a0000 - r0000 +--E 1852 + +--S 1853 of 3330 +--d0000:=D(m0000,x) +--E 1853 + +)clear all + +--S 1854 of 3330 +t0000:=x^(1+m)/sqrt(a+b*x) +--R +--R +--R m + 1 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1854 + +--S 1855 of 3330 +--r0000:=2*x^(1+m)*sqrt(a+b*x)/(b*(3+2*m))-4*a*(1+m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b^2*(3+2*m)*(-b*x/a)^m) +--E 1855 + +--S 1856 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m + 1 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1856 + +--S 1857 of 3330 +--m0000:=a0000 - r0000 +--E 1857 + +--S 1858 of 3330 +--d0000:=D(m0000,x) +--E 1858 + +)clear all + +--S 1859 of 3330 +t0000:=x^m/sqrt(a+b*x) +--R +--R +--R m +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1859 + +--S 1860 of 3330 +--r0000:=2*x^m*hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(b*(-b*x/a)^m) +--E 1860 + +--S 1861 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1861 + +--S 1862 of 3330 +--m0000:=a0000 - r0000 +--E 1862 + +--S 1863 of 3330 +--d0000:=D(m0000,x) +--E 1863 + +)clear all + +--S 1864 of 3330 +t0000:=x^(-1+m)/sqrt(a+b*x) +--R +--R +--R m - 1 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1864 + +--S 1865 of 3330 +--r0000:=x^m*sqrt(a+b*x)/(a*m)-(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(a*m*(-b*x/a)^m) +--E 1865 + +--S 1866 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m - 1 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1866 + +--S 1867 of 3330 +--m0000:=a0000 - r0000 +--E 1867 + +--S 1868 of 3330 +--d0000:=D(m0000,x) +--E 1868 + +)clear all + +--S 1869 of 3330 +t0000:=x^(-2+m)/sqrt(a+b*x) +--R +--R +--R m - 2 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1869 + +--S 1870 of 3330 +--r0000:=-x^(-1+m)*sqrt(a+b*x)/(a*(1-m))-1/2*b*(1-2*m)*x^m*_ +-- sqrt(a+b*x)/(a^2*(1-m)*m)+1/2*b*(1-2*m)*(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (a^2*(1-m)*m*(-b*x/a)^m) +--E 1870 + +--S 1871 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m - 2 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1871 + +--S 1872 of 3330 +--m0000:=a0000 - r0000 +--E 1872 + +--S 1873 of 3330 +--d0000:=D(m0000,x) +--E 1873 + +)clear all + +--S 1874 of 3330 +t0000:=x^(-3+m)/sqrt(a+b*x) +--R +--R +--R m - 3 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1874 + +--S 1875 of 3330 +--r0000:=-x^(-2+m)*sqrt(a+b*x)/(a*(2-m))+1/2*b*(3-2*m)*x^(-1+m)*_ +-- sqrt(a+b*x)/(a^2*(1-m)*(2-m))+1/4*b^2*(1-2*m)*(3-2*m)*x^m*_ +-- sqrt(a+b*x)/(a^3*(1-m)*(2-m)*m)-1/4*b^2*(1-2*m)*(3-2*m)*(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (a^3*(1-m)*(2-m)*m*(-b*x/a)^m) +--E 1875 + +--S 1876 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m - 3 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1876 + +--S 1877 of 3330 +--m0000:=a0000 - r0000 +--E 1877 + +--S 1878 of 3330 +--d0000:=D(m0000,x) +--E 1878 + +)clear all + +--S 1879 of 3330 +t0000:=1/2*x^(-1+m)*(2*a*m+b*(-1+2*m)*x)/(a+b*x)^(3/2) +--R +--R +--R m - 1 +--R ((2b m - b)x + 2a m)x +--R (1) -------------------------- +--R +-------+ +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1879 + +--S 1880 of 3330 +r0000:=x^m/sqrt(a+b*x) +--R +--R +--R m +--R x +--R (2) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1880 + +--S 1881 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (m - 1)log(x) +--R x %e +--R (3) ----------------- +--R +-------+ +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1881 + +--S 1882 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (m - 1)log(x) m +--R x %e - x +--R (4) ---------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1882 + +--S 1883 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (m - 1)log(x) m m - 1 +--R ((2b m - b)x + 2a m)%e + b x + (- 2b m x - 2a m)x +--R (5) -------------------------------------------------------------------- +--R +-------+ +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1883 + +)clear all + +--S 1884 of 3330 +t0000:=-1/2*b*x^m/(a+b*x)^(3/2)+m*x^(-1+m)/sqrt(a+b*x) +--R +--R +--R m m - 1 +--R - b x + (2b m x + 2a m)x +--R (1) ------------------------------ +--R +-------+ +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1884 + +--S 1885 of 3330 +r0000:=x^m/sqrt(a+b*x),-b*x^(1+m)/(a*sqrt(a+b*x))+x^m*sqrt(a+b*x)/a +--R +--R +--R m m + 1 m +--R x - b x + (b x + a)x +--R (2) [----------,------------------------] +--R +-------+ +-------+ +--R \|b x + a a\|b x + a +--R Type: Tuple(Expression(Integer)) +--E 1885 + +--S 1886 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (m - 1)log(x) +--R x %e +--R (3) ----------------- +--R +-------+ +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1886 + +--S 1887 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (m - 1)log(x) m +--R x %e - x +--R (4) ---------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1887 + +--S 1888 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (m - 1)log(x) m m - 1 +--R ((2b m - b)x + 2a m)%e + b x + (- 2b m x - 2a m)x +--R (5) -------------------------------------------------------------------- +--R +-------+ +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1888 + +)clear all + +--S 1889 of 3330 +t0000:=x^(1/2*(1-n)+1/2*(-3+n))/sqrt(a+b*x) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R x\|b x + a +--R Type: Expression(Integer) +--E 1889 + +--S 1890 of 3330 +r0000:=-2*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a) +--R +--R +--R +-------+ +--R \|b x + a +--R 2atanh(----------) +--R +-+ +--R \|a +--R (2) - ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1890 + +--S 1891 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-+ +---+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|- a \|b x + a +--R log(-------------------------------) 2atan(----------------) +--R x a +--R (3) [------------------------------------,- -----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1891 + +--S 1892 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(-------------------------------) + 2atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1892 + +--S 1893 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1893 + +--S 1894 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(----------) - 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1894 + +--S 1895 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1895 + +)clear all + +--S 1896 of 3330 +t0000:=x^3*(a+b*x)^(1/3) +--R +--R +--R 3 3+-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1896 + +--S 1897 of 3330 +r0000:=-3/4*a^3*(a+b*x)^(4/3)/b^4+9/7*a^2*(a+b*x)^(7/3)/b^4-_ + 9/10*a*(a+b*x)^(10/3)/b^4+3/13*(a+b*x)^(13/3)/b^4 +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+ +--R (420b x + 42a b x - 54a b x + 81a b x - 243a )\|b x + a +--R (2) ----------------------------------------------------------- +--R 4 +--R 1820b +--R Type: Expression(Integer) +--E 1897 + +--S 1898 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+ +--R (420b x + 42a b x - 54a b x + 81a b x - 243a )\|b x + a +--R (3) ----------------------------------------------------------- +--R 4 +--R 1820b +--R Type: Union(Expression(Integer),...) +--E 1898 + +--S 1899 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1899 + +--S 1900 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1900 + +)clear all + +--S 1901 of 3330 +t0000:=x^2*(a+b*x)^(1/3) +--R +--R +--R 2 3+-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1901 + +--S 1902 of 3330 +r0000:=3/4*a^2*(a+b*x)^(4/3)/b^3-6/7*a*(a+b*x)^(7/3)/b^3+_ + 3/10*(a+b*x)^(10/3)/b^3 +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (42b x + 6a b x - 9a b x + 27a )\|b x + a +--R (2) -------------------------------------------- +--R 3 +--R 140b +--R Type: Expression(Integer) +--E 1902 + +--S 1903 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (42b x + 6a b x - 9a b x + 27a )\|b x + a +--R (3) -------------------------------------------- +--R 3 +--R 140b +--R Type: Union(Expression(Integer),...) +--E 1903 + +--S 1904 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1904 + +--S 1905 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1905 + +)clear all + +--S 1906 of 3330 +t0000:=x*(a+b*x)^(1/3) +--R +--R +--R 3+-------+ +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 1906 + +--S 1907 of 3330 +r0000:=-3/4*a*(a+b*x)^(4/3)/b^2+3/7*(a+b*x)^(7/3)/b^2 +--R +--R +--R 2 2 2 3+-------+ +--R (12b x + 3a b x - 9a )\|b x + a +--R (2) --------------------------------- +--R 2 +--R 28b +--R Type: Expression(Integer) +--E 1907 + +--S 1908 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+ +--R (12b x + 3a b x - 9a )\|b x + a +--R (3) --------------------------------- +--R 2 +--R 28b +--R Type: Union(Expression(Integer),...) +--E 1908 + +--S 1909 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1909 + +--S 1910 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1910 + +)clear all + +--S 1911 of 3330 +t0000:=(a+b*x)^(1/3) +--R +--R +--R 3+-------+ +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 1911 + +--S 1912 of 3330 +r0000:=3/4*(a+b*x)^(4/3)/b +--R +--R +--R 3+-------+ +--R (3b x + 3a)\|b x + a +--R (2) --------------------- +--R 4b +--R Type: Expression(Integer) +--E 1912 + +--S 1913 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+ +--R (3b x + 3a)\|b x + a +--R (3) --------------------- +--R 4b +--R Type: Union(Expression(Integer),...) +--E 1913 + +--S 1914 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1914 + +--S 1915 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1915 + +)clear all + +--S 1916 of 3330 +t0000:=(a+b*x)^(1/3)/x +--R +--R +--R 3+-------+ +--R \|b x + a +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 1916 + +--S 1917 of 3330 +r0000:=3*(a+b*x)^(1/3)+a^(1/3)*log(a^(1/3)-(a+b*x)^(1/3))-_ + 1/2*a^(1/3)*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))-_ + a^(1/3)*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3) +--R +--R +--R (2) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 2\|a log(- \|b x + a + \|a ) - 2\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+ +--R 6\|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 1917 + +--S 1918 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 2\|a log(\|b x + a - \|a ) - 2\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+ +--R 6\|b x + a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1918 + +--S 1919 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 3+-+ 3+-------+ 3+-+ 3+-+ 3+-------+ 3+-+ +--R (4) \|a log(\|b x + a - \|a ) - \|a log(- \|b x + a + \|a ) +--R Type: Expression(Integer) +--E 1919 + +--S 1920 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1920 + +)clear all + +--S 1921 of 3330 +t0000:=(a+b*x)^(1/3)/x^2 +--R +--R +--R 3+-------+ +--R \|b x + a +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1921 + +--S 1922 of 3330 +r0000:=-(a+b*x)^(1/3)/x+1/3*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(2/3)-_ + 1/6*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(2/3)-_ + b*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b x\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x + a + \|a +--R 2b x\|3 log(- \|b x + a + \|a ) - 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R - 6\|3 \|a \|b x + a +--R / +--R +-+3+-+2 +--R 6x\|3 \|a +--R Type: Expression(Integer) +--E 1922 + +--S 1923 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+2 +--+ +--R +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b x\|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R +-+ 3| 2 3+-------+ +--R 2b x\|3 log(\|a \|b x + a - a) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--+ +--R 2\|3 \|a \|b x + a + a\|3 +-+3| 2 3+-------+ +--R - 6b x atan(----------------------------) - 6\|3 \|a \|b x + a +--R 3a +--R / +--R +--+ +--R +-+3| 2 +--R 6x\|3 \|a +--R Type: Union(Expression(Integer),...) +--E 1923 + +--S 1924 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+2 +--+ +--R +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b\|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R b\|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--+ +--R +-+3+-+2 3| 2 3+-------+ +-+3| 2 3+-------+ 3+-+ +--R 2b\|3 \|a log(\|a \|b x + a - a) - 2b\|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 6b \|a atan(----------------------------) +--R 3a +--R + +--R +--+ 3+-------+ 3+-+ +--R 3| 2 2\|b x + a + \|a +--R 6b\|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 6\|3 \|a \|a +--R Type: Expression(Integer) +--E 1924 + +--S 1925 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1925 + +)clear all + +--S 1926 of 3330 +t0000:=(a+b*x)^(1/3)/x^3 +--R +--R +--R 3+-------+ +--R \|b x + a +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1926 + +--S 1927 of 3330 +r0000:=-1/2*(a+b*x)^(1/3)/x^2-1/6*b*(a+b*x)^(1/3)/(a*x)-_ + 1/9*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(5/3)+_ + 1/18*b^2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))/a^(5/3)+1/3*b^2*_ + atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R - 2b x \|3 log(- \|b x + a + \|a ) + 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R (- 3b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 +-+3+-+2 +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 1927 + +--S 1928 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +----+2 +----+ +--R 2 2 +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b x \|3 log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--R 2 2 +-+ 3| 2 3+-------+ +--R 2b x \|3 log(\|- a \|b x + a + a) +--R + +--R +----+ +--R +-+3| 2 3+-------+ +-+ +--R 2 2 2\|3 \|- a \|b x + a - a\|3 +--R 6b x atan(------------------------------) +--R 3a +--R + +--R +----+ +--R +-+3| 2 3+-------+ +--R (- 3b x - 9a)\|3 \|- a \|b x + a +--R / +--R +----+ +--R 2 +-+3| 2 +--R 18a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 1928 + +--S 1929 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +----+2 +----+ +--R 2 +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b \|3 \|a log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--R 2 +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b \|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +----+ +--R 2 +-+3+-+2 3| 2 3+-------+ +--R 2b \|3 \|a log(\|- a \|b x + a + a) +--R + +--R +----+ +--R 2 +-+3| 2 3+-------+ 3+-+ +--R 2b \|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +----+ +--R +-+3| 2 3+-------+ +-+ +--R 2 3+-+2 2\|3 \|- a \|b x + a - a\|3 +--R 6b \|a atan(------------------------------) +--R 3a +--R + +--R +----+ 3+-------+ 3+-+ +--R 2 3| 2 2\|b x + a + \|a +--R - 6b \|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 18a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 1929 + +--S 1930 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1930 + +)clear all + +--S 1931 of 3330 +t0000:=x^3*(a+b*x)^(2/3) +--R +--R +--R 3 3+-------+2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1931 + +--S 1932 of 3330 +r0000:=-3/5*a^3*(a+b*x)^(5/3)/b^4+9/8*a^2*(a+b*x)^(8/3)/b^4-_ + 9/11*a*(a+b*x)^(11/3)/b^4+3/14*(a+b*x)^(14/3)/b^4 +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+2 +--R (660b x + 120a b x - 135a b x + 162a b x - 243a )\|b x + a +--R (2) --------------------------------------------------------------- +--R 4 +--R 3080b +--R Type: Expression(Integer) +--E 1932 + +--S 1933 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+2 +--R (660b x + 120a b x - 135a b x + 162a b x - 243a )\|b x + a +--R (3) --------------------------------------------------------------- +--R 4 +--R 3080b +--R Type: Union(Expression(Integer),...) +--E 1933 + +--S 1934 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1934 + +--S 1935 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1935 + +)clear all + +--S 1936 of 3330 +t0000:=x^2*(a+b*x)^(2/3) +--R +--R +--R 2 3+-------+2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1936 + +--S 1937 of 3330 +r0000:=3/5*a^2*(a+b*x)^(5/3)/b^3-3/4*a*(a+b*x)^(8/3)/b^3+_ + 3/11*(a+b*x)^(11/3)/b^3 +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (60b x + 15a b x - 18a b x + 27a )\|b x + a +--R (2) ----------------------------------------------- +--R 3 +--R 220b +--R Type: Expression(Integer) +--E 1937 + +--S 1938 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (60b x + 15a b x - 18a b x + 27a )\|b x + a +--R (3) ----------------------------------------------- +--R 3 +--R 220b +--R Type: Union(Expression(Integer),...) +--E 1938 + +--S 1939 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1939 + +--S 1940 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1940 + +)clear all + +--S 1941 of 3330 +t0000:=x*(a+b*x)^(2/3) +--R +--R +--R 3+-------+2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1941 + +--S 1942 of 3330 +r0000:=-3/5*a*(a+b*x)^(5/3)/b^2+3/8*(a+b*x)^(8/3)/b^2 +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x + 6a b x - 9a )\|b x + a +--R (2) ---------------------------------- +--R 2 +--R 40b +--R Type: Expression(Integer) +--E 1942 + +--S 1943 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x + 6a b x - 9a )\|b x + a +--R (3) ---------------------------------- +--R 2 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 1943 + +--S 1944 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1944 + +--S 1945 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1945 + +)clear all + +--S 1946 of 3330 +t0000:=(a+b*x)^(2/3) +--R +--R +--R 3+-------+2 +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 1946 + +--S 1947 of 3330 +r0000:=3/5*(a+b*x)^(5/3)/b +--R +--R +--R 3+-------+2 +--R (3b x + 3a)\|b x + a +--R (2) ---------------------- +--R 5b +--R Type: Expression(Integer) +--E 1947 + +--S 1948 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R (3b x + 3a)\|b x + a +--R (3) ---------------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 1948 + +--S 1949 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1949 + +--S 1950 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1950 + +)clear all + +--S 1951 of 3330 +t0000:=(a+b*x)^(2/3)/x +--R +--R +--R 3+-------+2 +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 1951 + +--S 1952 of 3330 +r0000:=3/2*(a+b*x)^(2/3)+a^(2/3)*log(a^(1/3)-(a+b*x)^(1/3))-_ + 1/2*a^(2/3)*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))+_ + a^(2/3)*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3) +--R +--R +--R (2) +--R 3+-+2 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+2 3+-------+ 3+-+ +-+3+-+2 2\|b x + a + \|a +--R 2\|a log(- \|b x + a + \|a ) + 2\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+2 +--R 3\|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 1952 + +--S 1953 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+ +--+2 +--+ +--R 3| 2 3+-------+2 3| 2 3+-------+ 3| 2 +--R - \|a log(a \|b x + a + \|a \|b x + a + a\|a ) +--R + +--R +--+2 +--R +--+ +--+2 +--+ 3+-------+ 3| 2 +--R 3| 2 3+-------+ 3| 2 +-+3| 2 2a\|b x + a + \|a +--R 2\|a log(a\|b x + a - \|a ) + 2\|3 \|a atan(---------------------) +--R +--+2 +--R +-+3| 2 +--R \|3 \|a +--R + +--R 3+-------+2 +--R 3\|b x + a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1953 + +--S 1954 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+ +--+2 +--+ +--R 3| 2 3+-------+2 3| 2 3+-------+ 3| 2 +--R - \|a log(a \|b x + a + \|a \|b x + a + a\|a ) +--R + +--R 3+-+2 3+-------+2 3+-+3+-------+ 3+-+2 +--R \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--+2 +--R 3| 2 3+-------+ 3| 2 3+-+2 3+-------+ 3+-+ +--R 2\|a log(a\|b x + a - \|a ) - 2\|a log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+3+-+2 2\|b x + a + \|a +--R - 2\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--+2 +--R +--+ 3+-------+ 3| 2 +--R +-+3| 2 2a\|b x + a + \|a +--R 2\|3 \|a atan(---------------------) +--R +--+2 +--R +-+3| 2 +--R \|3 \|a +--R / +--R 2 +--R Type: Expression(Integer) +--E 1954 + +--S 1955 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1955 + +)clear all + +--S 1956 of 3330 +t0000:=(a+b*x)^(2/3)/x^2 +--R +--R +--R 3+-------+2 +--R \|b x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1956 + +--S 1957 of 3330 +r0000:=-(a+b*x)^(2/3)/x+2/3*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(1/3)-_ + 1/3*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(1/3)+_ + 2*b*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b x\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x + a + \|a +--R 2b x\|3 log(- \|b x + a + \|a ) + 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R - 3\|3 \|a \|b x + a +--R / +--R +-+3+-+ +--R 3x\|3 \|a +--R Type: Expression(Integer) +--E 1957 + +--S 1958 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - b x\|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +-+ 3+-+2 3+-------+ +--R 2b x\|3 log(\|a \|b x + a - a) +--R + +--R +-+3+-+2 3+-------+ +-+ +--R 2\|3 \|a \|b x + a + a\|3 +-+3+-+3+-------+2 +--R 6b x atan(----------------------------) - 3\|3 \|a \|b x + a +--R 3a +--R / +--R +-+3+-+ +--R 3x\|3 \|a +--R Type: Union(Expression(Integer),...) +--E 1958 + +--S 1959 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - b\|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+ 3+-+2 3+-------+ +-+ 3+-------+ 3+-+ +--R 2b\|3 log(\|a \|b x + a - a) - 2b\|3 log(- \|b x + a + \|a ) +--R + +--R +-+3+-+2 3+-------+ +-+ 3+-------+ 3+-+ +--R 2\|3 \|a \|b x + a + a\|3 2\|b x + a + \|a +--R 6b atan(----------------------------) - 6b atan(------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 3\|3 \|a +--R Type: Expression(Integer) +--E 1959 + +--S 1960 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1960 + +)clear all + +--S 1961 of 3330 +t0000:=(a+b*x)^(2/3)/x^3 +--R +--R +--R 3+-------+2 +--R \|b x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1961 + +--S 1962 of 3330 +r0000:=-1/2*(a+b*x)^(2/3)/x^2-1/3*b*(a+b*x)^(2/3)/(a*x)-_ + 1/9*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)+1/18*b^2*log(a^(2/3)+_ + a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(4/3)-_ + 1/3*b^2*atan((a^(1/3)+2*(a+b*x)^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R - 2b x \|3 log(- \|b x + a + \|a ) - 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R (- 6b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 1962 + +--S 1963 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b x \|3 log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R 2 2 +-+ 3+---+2 3+-------+ +--R 2b x \|3 log(\|- a \|b x + a - a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2 2 2\|3 \|- a \|b x + a + a\|3 +--R 6b x atan(------------------------------) +--R 3a +--R + +--R +-+3+---+3+-------+2 +--R (- 6b x - 9a)\|3 \|- a \|b x + a +--R / +--R 2 +-+3+---+ +--R 18a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 1963 + +--S 1964 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b \|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R 2 +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b \|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 2 +-+3+-+ 3+---+2 3+-------+ +--R 2b \|3 \|a log(\|- a \|b x + a - a) +--R + +--R 2 +-+3+---+ 3+-------+ 3+-+ +--R 2b \|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2 3+-+ 2\|3 \|- a \|b x + a + a\|3 +--R 6b \|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 2 3+---+ 2\|b x + a + \|a +--R 6b \|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+---+3+-+ +--R 18a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 1964 + +--S 1965 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1965 + +)clear all + +--S 1966 of 3330 +t0000:=x^3*(a+b*x)^(4/3) +--R +--R +--R 4 3 3+-------+ +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1966 + +--S 1967 of 3330 +r0000:=-3/7*a^3*(a+b*x)^(7/3)/b^4+9/10*a^2*(a+b*x)^(10/3)/b^4-_ + 9/13*a*(a+b*x)^(13/3)/b^4+3/16*(a+b*x)^(16/3)/b^4 +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 3 2 2 4 5 3+-------+ +--R (1365b x + 1785a b x + 42a b x - 54a b x + 81a b x - 243a )\|b x + a +--R ------------------------------------------------------------------------- +--R 4 +--R 7280b +--R Type: Expression(Integer) +--E 1967 + +--S 1968 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 4 5 3+-------+ +--R (1365b x + 1785a b x + 42a b x - 54a b x + 81a b x - 243a )\|b x + a +--R ------------------------------------------------------------------------- +--R 4 +--R 7280b +--R Type: Union(Expression(Integer),...) +--E 1968 + +--S 1969 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1969 + +--S 1970 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1970 + +)clear all + +--S 1971 of 3330 +t0000:=x^2*(a+b*x)^(4/3) +--R +--R +--R 3 2 3+-------+ +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1971 + +--S 1972 of 3330 +r0000:=3/7*a^2*(a+b*x)^(7/3)/b^3-3/5*a*(a+b*x)^(10/3)/b^3+_ + 3/13*(a+b*x)^(13/3)/b^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+ +--R (105b x + 147a b x + 6a b x - 9a b x + 27a )\|b x + a +--R (2) --------------------------------------------------------- +--R 3 +--R 455b +--R Type: Expression(Integer) +--E 1972 + +--S 1973 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+ +--R (105b x + 147a b x + 6a b x - 9a b x + 27a )\|b x + a +--R (3) --------------------------------------------------------- +--R 3 +--R 455b +--R Type: Union(Expression(Integer),...) +--E 1973 + +--S 1974 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1974 + +--S 1975 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1975 + +)clear all + +--S 1976 of 3330 +t0000:=x*(a+b*x)^(4/3) +--R +--R +--R 2 3+-------+ +--R (1) (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1976 + +--S 1977 of 3330 +r0000:=-3/7*a*(a+b*x)^(7/3)/b^2+3/10*(a+b*x)^(10/3)/b^2 +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (21b x + 33a b x + 3a b x - 9a )\|b x + a +--R (2) -------------------------------------------- +--R 2 +--R 70b +--R Type: Expression(Integer) +--E 1977 + +--S 1978 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (21b x + 33a b x + 3a b x - 9a )\|b x + a +--R (3) -------------------------------------------- +--R 2 +--R 70b +--R Type: Union(Expression(Integer),...) +--E 1978 + +--S 1979 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1979 + +--S 1980 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1980 + +)clear all + +--S 1981 of 3330 +t0000:=(a+b*x)^(4/3) +--R +--R +--R 3+-------+ +--R (1) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1981 + +--S 1982 of 3330 +r0000:=3/7*(a+b*x)^(7/3)/b +--R +--R +--R 2 2 2 3+-------+ +--R (3b x + 6a b x + 3a )\|b x + a +--R (2) -------------------------------- +--R 7b +--R Type: Expression(Integer) +--E 1982 + +--S 1983 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+ +--R (3b x + 6a b x + 3a )\|b x + a +--R (3) -------------------------------- +--R 7b +--R Type: Union(Expression(Integer),...) +--E 1983 + +--S 1984 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1984 + +--S 1985 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1985 + +)clear all + +--S 1986 of 3330 +t0000:=(a+b*x)^(4/3)/x +--R +--R +--R 3+-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 1986 + +--S 1987 of 3330 +r0000:=3*a*(a+b*x)^(1/3)+3/4*(a+b*x)^(4/3)+a^(4/3)*log(a^(1/3)-_ + (a+b*x)^(1/3))-1/2*a^(4/3)*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))-a^(4/3)*atan((a^(1/3)+_ + 2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3) +--R +--R +--R (2) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2a\|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 4a\|a log(- \|b x + a + \|a ) - 4a\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+ +--R (3b x + 15a)\|b x + a +--R / +--R 4 +--R Type: Expression(Integer) +--E 1987 + +--S 1988 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2a\|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 4a\|a log(\|b x + a - \|a ) - 4a\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+ +--R (3b x + 15a)\|b x + a +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 1988 + +--S 1989 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 3+-+ 3+-------+ 3+-+ 3+-+ 3+-------+ 3+-+ +--R (4) a\|a log(\|b x + a - \|a ) - a\|a log(- \|b x + a + \|a ) +--R Type: Expression(Integer) +--E 1989 + +--S 1990 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1990 + +)clear all + +--S 1991 of 3330 +t0000:=(a+b*x)^(4/3)/x^2 +--R +--R +--R 3+-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1991 + +--S 1992 of 3330 +r0000:=4*b*(a+b*x)^(1/3)-(a+b*x)^(4/3)/x+4/3*a^(1/3)*b*log(a^(1/3)-_ + (a+b*x)^(1/3))-2/3*a^(1/3)*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))-4*a^(1/3)*b*atan((a^(1/3)+_ + 2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3) +--R +--R +--R (2) +--R +-+3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b x\|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+3+-+ 3+-------+ 3+-+ 3+-+ 2\|b x + a + \|a +--R 4b x\|3 \|a log(- \|b x + a + \|a ) - 12b x\|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-------+ +--R (9b x - 3a)\|3 \|b x + a +--R / +--R +-+ +--R 3x\|3 +--R Type: Expression(Integer) +--E 1992 + +--S 1993 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b x\|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+3+-+ 3+-------+ 3+-+ +--R 4b x\|3 \|a log(\|b x + a - \|a ) +--R + +--R +-+3+-------+ +-+3+-+ +--R 3+-+ 2\|3 \|b x + a + \|3 \|a +-+3+-------+ +--R - 12b x\|a atan(--------------------------) + (9b x - 3a)\|3 \|b x + a +--R 3+-+ +--R 3\|a +--R / +--R +-+ +--R 3x\|3 +--R Type: Union(Expression(Integer),...) +--E 1993 + +--S 1994 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+-------+ 3+-+ +-+3+-+ 3+-------+ 3+-+ +--R 4b\|3 \|a log(\|b x + a - \|a ) - 4b\|3 \|a log(- \|b x + a + \|a ) +--R + +--R +-+3+-------+ +-+3+-+ 3+-------+ 3+-+ +--R 3+-+ 2\|3 \|b x + a + \|3 \|a 3+-+ 2\|b x + a + \|a +--R - 12b\|a atan(--------------------------) + 12b\|a atan(------------------) +--R 3+-+ +-+3+-+ +--R 3\|a \|3 \|a +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 1994 + +--S 1995 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1995 + +)clear all + +--S 1996 of 3330 +t0000:=(a+b*x)^(4/3)/x^3 +--R +--R +--R 3+-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1996 + +--S 1997 of 3330 +r0000:=-2/3*b*(a+b*x)^(1/3)/x-1/2*(a+b*x)^(4/3)/x^2+2/9*b^2*log(a^(1/3)-_ + (a+b*x)^(1/3))/a^(2/3)-1/9*b^2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))/a^(2/3)-2/3*b^2*atan((a^(1/3)+_ + 2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R 4b x \|3 log(- \|b x + a + \|a ) - 12b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R (- 21b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 +-+3+-+2 +--R 18x \|3 \|a +--R Type: Expression(Integer) +--E 1997 + +--S 1998 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+2 +--+ +--R 2 2 +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - 2b x \|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 2 2 +-+ 3| 2 3+-------+ +--R 4b x \|3 log(\|a \|b x + a - a) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 2 2 2\|3 \|a \|b x + a + a\|3 +--R - 12b x atan(----------------------------) +--R 3a +--R + +--R +--+ +--R +-+3| 2 3+-------+ +--R (- 21b x - 9a)\|3 \|a \|b x + a +--R / +--R +--+ +--R 2 +-+3| 2 +--R 18x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 1998 + +--S 1999 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+2 +--+ +--R 2 +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b \|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 2 +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R b \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--R 2 +-+3+-+2 3| 2 3+-------+ +--R 2b \|3 \|a log(\|a \|b x + a - a) +--R + +--R +--+ +--R 2 +-+3| 2 3+-------+ 3+-+ +--R - 2b \|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 2 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 6b \|a atan(----------------------------) +--R 3a +--R + +--R +--+ 3+-------+ 3+-+ +--R 2 3| 2 2\|b x + a + \|a +--R 6b \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 9\|3 \|a \|a +--R Type: Expression(Integer) +--E 1999 + +--S 2000 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2000 + +)clear all + +--S 2001 of 3330 +t0000:=x^3/(a+b*x)^(1/3) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2001 + +--S 2002 of 3330 +r0000:=-3/2*a^3*(a+b*x)^(2/3)/b^4+9/5*a^2*(a+b*x)^(5/3)/b^4-_ + 9/8*a*(a+b*x)^(8/3)/b^4+3/11*(a+b*x)^(11/3)/b^4 +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (120b x - 135a b x + 162a b x - 243a )\|b x + a +--R (2) --------------------------------------------------- +--R 4 +--R 440b +--R Type: Expression(Integer) +--E 2002 + +--S 2003 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (120b x - 135a b x + 162a b x - 243a )\|b x + a +--R (3) --------------------------------------------------- +--R 4 +--R 440b +--R Type: Union(Expression(Integer),...) +--E 2003 + +--S 2004 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2004 + +--S 2005 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2005 + +)clear all + +--S 2006 of 3330 +t0000:=x^2/(a+b*x)^(1/3) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2006 + +--S 2007 of 3330 +r0000:=3/2*a^2*(a+b*x)^(2/3)/b^3-6/5*a*(a+b*x)^(5/3)/b^3+3/8*(a+b*x)^(8/3)/b^3 +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x - 18a b x + 27a )\|b x + a +--R (2) ------------------------------------ +--R 3 +--R 40b +--R Type: Expression(Integer) +--E 2007 + +--S 2008 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x - 18a b x + 27a )\|b x + a +--R (3) ------------------------------------ +--R 3 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 2008 + +--S 2009 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2009 + +--S 2010 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2010 + +)clear all + +--S 2011 of 3330 +t0000:=x/(a+b*x)^(1/3) +--R +--R +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2011 + +--S 2012 of 3330 +r0000:=-3/2*a*(a+b*x)^(2/3)/b^2+3/5*(a+b*x)^(5/3)/b^2 +--R +--R +--R 3+-------+2 +--R (6b x - 9a)\|b x + a +--R (2) ---------------------- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 2012 + +--S 2013 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R (6b x - 9a)\|b x + a +--R (3) ---------------------- +--R 2 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 2013 + +--S 2014 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2014 + +--S 2015 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2015 + +)clear all + +--S 2016 of 3330 +t0000:=1/(a+b*x)^(1/3) +--R +--R +--R 1 +--R (1) ---------- +--R 3+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2016 + +--S 2017 of 3330 +r0000:=3/2*(a+b*x)^(2/3)/b +--R +--R +--R 3+-------+2 +--R 3\|b x + a +--R (2) ------------ +--R 2b +--R Type: Expression(Integer) +--E 2017 + +--S 2018 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R 3\|b x + a +--R (3) ------------ +--R 2b +--R Type: Union(Expression(Integer),...) +--E 2018 + +--S 2019 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2019 + +--S 2020 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2020 + +)clear all + +--S 2021 of 3330 +t0000:=1/(x*(a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ----------- +--R 3+-------+ +--R x\|b x + a +--R Type: Expression(Integer) +--E 2021 + +--S 2022 of 3330 +r0000:=log(a^(1/3)-(a+b*x)^(1/3))/a^(1/3)-1/2*log(a^(2/3)+_ + a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(1/3)+_ + atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3) +--R +--R +--R (2) +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-------+ 3+-+ +--R - log(\|b x + a + \|a \|b x + a + \|a ) + 2log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x + a + \|a +--R 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2\|a +--R Type: Expression(Integer) +--E 2022 + +--S 2023 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-+3+-------+2 3+-+2 3+-------+ 3+-+2 3+-------+ +--R - log(\|a \|b x + a + \|a \|b x + a + a) + 2log(\|a \|b x + a - a) +--R + +--R 3+-+2 3+-------+ +--R +-+ 2\|a \|b x + a + a +--R 2\|3 atan(--------------------) +--R +-+ +--R a\|3 +--R / +--R 3+-+ +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 2023 + +--S 2024 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+3+-------+2 3+-+2 3+-------+ +--R - log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-+2 3+-------+ +--R log(\|b x + a + \|a \|b x + a + \|a ) + 2log(\|a \|b x + a - a) +--R + +--R 3+-+2 3+-------+ +--R 3+-------+ 3+-+ +-+ 2\|a \|b x + a + a +--R - 2log(- \|b x + a + \|a ) + 2\|3 atan(--------------------) +--R +-+ +--R a\|3 +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x + a + \|a +--R - 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2\|a +--R Type: Expression(Integer) +--E 2024 + +--S 2025 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2025 + +)clear all + +--S 2026 of 3330 +t0000:=1/(x^2*(a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 3+-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 2026 + +--S 2027 of 3330 +r0000:=-(a+b*x)^(2/3)/(a*x)-1/3*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)+_ + 1/6*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(4/3)-_ + b*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x + a + \|a +--R - 2b x\|3 log(- \|b x + a + \|a ) - 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R - 6\|3 \|a \|b x + a +--R / +--R +-+3+-+ +--R 6a x\|3 \|a +--R Type: Expression(Integer) +--E 2027 + +--S 2028 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b x\|3 log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +-+ 3+---+2 3+-------+ +--R 2b x\|3 log(\|- a \|b x + a - a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2\|3 \|- a \|b x + a + a\|3 +-+3+---+3+-------+2 +--R 6b x atan(------------------------------) - 6\|3 \|- a \|b x + a +--R 3a +--R / +--R +-+3+---+ +--R 6a x\|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 2028 + +--S 2029 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b\|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+3+-+ 3+---+2 3+-------+ +--R 2b\|3 \|a log(\|- a \|b x + a - a) +--R + +--R +-+3+---+ 3+-------+ 3+-+ +--R 2b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 3+-+ 2\|3 \|- a \|b x + a + a\|3 +--R 6b\|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 3+---+ 2\|b x + a + \|a +--R 6b\|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+---+3+-+ +--R 6a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 2029 + +--S 2030 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2030 + +)clear all + +--S 2031 of 3330 +t0000:=1/(x^3*(a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 3+-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 2031 + +--S 2032 of 3330 +r0000:=-1/2*(a+b*x)^(2/3)/(a*x^2)+2/3*b*(a+b*x)^(2/3)/(a^2*x)+_ + 2/9*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(7/3)-1/9*b^2*log(a^(2/3)+_ + a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(7/3)+_ + 2/3*b^2*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R 4b x \|3 log(- \|b x + a + \|a ) + 12b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R (12b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 2 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 2032 + +--S 2033 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - 2b x \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 2 2 +-+ 3+-+2 3+-------+ +--R 4b x \|3 log(\|a \|b x + a - a) +--R + +--R +-+3+-+2 3+-------+ +-+ +--R 2 2 2\|3 \|a \|b x + a + a\|3 +-+3+-+3+-------+2 +--R 12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a +--R 3a +--R / +--R 2 2 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 2033 + +--S 2034 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - b \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 2 +-+ 3+-+2 3+-------+ 2 +-+ 3+-------+ 3+-+ +--R 2b \|3 log(\|a \|b x + a - a) - 2b \|3 log(- \|b x + a + \|a ) +--R + +--R +-+3+-+2 3+-------+ +-+ 3+-------+ 3+-+ +--R 2 2\|3 \|a \|b x + a + a\|3 2 2\|b x + a + \|a +--R 6b atan(----------------------------) - 6b atan(------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 2034 + +--S 2035 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2035 + +)clear all + +--S 2036 of 3330 +t0000:=x^3/(-a+b*x)^(1/3) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x - a +--R Type: Expression(Integer) +--E 2036 + +--S 2037 of 3330 +r0000:=3/2*a^3*(-a+b*x)^(2/3)/b^4+9/5*a^2*(-a+b*x)^(5/3)/b^4+_ + 9/8*a*(-a+b*x)^(8/3)/b^4+3/11*(-a+b*x)^(11/3)/b^4 +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (120b x + 135a b x + 162a b x + 243a )\|b x - a +--R (2) --------------------------------------------------- +--R 4 +--R 440b +--R Type: Expression(Integer) +--E 2037 + +--S 2038 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (120b x + 135a b x + 162a b x + 243a )\|b x - a +--R (3) --------------------------------------------------- +--R 4 +--R 440b +--R Type: Union(Expression(Integer),...) +--E 2038 + +--S 2039 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2039 + +--S 2040 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2040 + +)clear all + +--S 2041 of 3330 +t0000:=x^2/(-a+b*x)^(1/3) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x - a +--R Type: Expression(Integer) +--E 2041 + +--S 2042 of 3330 +r0000:=3/2*a^2*(-a+b*x)^(2/3)/b^3+6/5*a*(-a+b*x)^(5/3)/b^3+_ + 3/8*(-a+b*x)^(8/3)/b^3 +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x + 18a b x + 27a )\|b x - a +--R (2) ------------------------------------ +--R 3 +--R 40b +--R Type: Expression(Integer) +--E 2042 + +--S 2043 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x + 18a b x + 27a )\|b x - a +--R (3) ------------------------------------ +--R 3 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 2043 + +--S 2044 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2044 + +--S 2045 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2045 + +)clear all + +--S 2046 of 3330 +t0000:=x/(-a+b*x)^(1/3) +--R +--R +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x - a +--R Type: Expression(Integer) +--E 2046 + +--S 2047 of 3330 +r0000:=3/2*a*(-a+b*x)^(2/3)/b^2+3/5*(-a+b*x)^(5/3)/b^2 +--R +--R +--R 3+-------+2 +--R (6b x + 9a)\|b x - a +--R (2) ---------------------- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 2047 + +--S 2048 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R (6b x + 9a)\|b x - a +--R (3) ---------------------- +--R 2 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 2048 + +--S 2049 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2049 + +--S 2050 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2050 + +)clear all + +--S 2051 of 3330 +t0000:=1/(-a+b*x)^(1/3) +--R +--R +--R 1 +--R (1) ---------- +--R 3+-------+ +--R \|b x - a +--R Type: Expression(Integer) +--E 2051 + +--S 2052 of 3330 +r0000:=3/2*(-a+b*x)^(2/3)/b +--R +--R +--R 3+-------+2 +--R 3\|b x - a +--R (2) ------------ +--R 2b +--R Type: Expression(Integer) +--E 2052 + +--S 2053 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R 3\|b x - a +--R (3) ------------ +--R 2b +--R Type: Union(Expression(Integer),...) +--E 2053 + +--S 2054 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2054 + +--S 2055 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2055 + +)clear all + +--S 2056 of 3330 +t0000:=1/(x*(-a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ----------- +--R 3+-------+ +--R x\|b x - a +--R Type: Expression(Integer) +--E 2056 + +--S 2057 of 3330 +r0000:=-log(a^(1/3)+(-a+b*x)^(1/3))/a^(1/3)+1/2*log(a^(2/3)-_ + a^(1/3)*(-a+b*x)^(1/3)+(-a+b*x)^(2/3))/a^(1/3)-_ + atan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3) +--R +--R +--R (2) +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-------+ 3+-+ +--R log(\|b x - a - \|a \|b x - a + \|a ) - 2log(\|b x - a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x - a - \|a +--R 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2\|a +--R Type: Expression(Integer) +--E 2057 + +--S 2058 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+---+3+-------+2 3+---+2 3+-------+ +--R - log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R 3+---+2 3+-------+ +--R 3+---+2 3+-------+ +-+ 2\|- a \|b x - a - a +--R 2log(\|- a \|b x - a + a) - 2\|3 atan(----------------------) +--R +-+ +--R a\|3 +--R / +--R 3+---+ +--R 2\|- a +--R Type: Union(Expression(Integer),...) +--E 2058 + +--S 2059 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - \|a log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R 3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|- a log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R 3+-+ 3+---+2 3+-------+ 3+---+ 3+-------+ 3+-+ +--R 2\|a log(\|- a \|b x - a + a) + 2\|- a log(\|b x - a + \|a ) +--R + +--R 3+---+2 3+-------+ +--R +-+3+-+ 2\|- a \|b x - a - a +--R - 2\|3 \|a atan(----------------------) +--R +-+ +--R a\|3 +--R + +--R 3+-------+ 3+-+ +--R +-+3+---+ 2\|b x - a - \|a +--R - 2\|3 \|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+---+3+-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 2059 + +--S 2060 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2060 + +)clear all + +--S 2061 of 3330 +t0000:=1/(x^2*(-a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 3+-------+ +--R x \|b x - a +--R Type: Expression(Integer) +--E 2061 + +--S 2062 of 3330 +r0000:=(-a+b*x)^(2/3)/(a*x)-1/3*b*log(a^(1/3)+(-a+b*x)^(1/3))/a^(4/3)+_ + 1/6*b*log(a^(2/3)-a^(1/3)*(-a+b*x)^(1/3)+(-a+b*x)^(2/3))/a^(4/3)-_ + b*atan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x\|3 log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x - a - \|a +--R - 2b x\|3 log(\|b x - a + \|a ) + 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R 6\|3 \|a \|b x - a +--R / +--R +-+3+-+ +--R 6a x\|3 \|a +--R Type: Expression(Integer) +--E 2062 + +--S 2063 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b x\|3 log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R +-+ 3+---+2 3+-------+ +--R 2b x\|3 log(\|- a \|b x - a + a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2\|3 \|- a \|b x - a - a\|3 +-+3+---+3+-------+2 +--R - 6b x atan(------------------------------) + 6\|3 \|- a \|b x - a +--R 3a +--R / +--R +-+3+---+ +--R 6a x\|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 2063 + +--S 2064 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b\|3 \|a log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b\|3 \|- a log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R +-+3+-+ 3+---+2 3+-------+ +-+3+---+ 3+-------+ 3+-+ +--R 2b\|3 \|a log(\|- a \|b x - a + a) + 2b\|3 \|- a log(\|b x - a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 3+-+ 2\|3 \|- a \|b x - a - a\|3 +--R - 6b\|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 3+---+ 2\|b x - a - \|a +--R - 6b\|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+---+3+-+ +--R 6a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 2064 + +--S 2065 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2065 + +)clear all + +--S 2066 of 3330 +t0000:=1/(x^3*(-a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 3+-------+ +--R x \|b x - a +--R Type: Expression(Integer) +--E 2066 + +--S 2067 of 3330 +r0000:=1/2*(-a+b*x)^(2/3)/(a*x^2)+2/3*b*(-a+b*x)^(2/3)/(a^2*x)-_ + 2/9*b^2*log(a^(1/3)+(-a+b*x)^(1/3))/a^(7/3)+1/9*b^2*log(a^(2/3)-_ + a^(1/3)*(-a+b*x)^(1/3)+(-a+b*x)^(2/3))/a^(7/3)-_ + 2/3*b^2*atan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R 2b x \|3 log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x - a - \|a +--R - 4b x \|3 log(\|b x - a + \|a ) + 12b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R (12b x + 9a)\|3 \|a \|b x - a +--R / +--R 2 2 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 2067 + +--S 2068 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - 2b x \|3 log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R 2 2 +-+ 3+---+2 3+-------+ +--R 4b x \|3 log(\|- a \|b x - a + a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2 2 2\|3 \|- a \|b x - a - a\|3 +--R - 12b x atan(------------------------------) +--R 3a +--R + +--R +-+3+---+3+-------+2 +--R (12b x + 9a)\|3 \|- a \|b x - a +--R / +--R 2 2 +-+3+---+ +--R 18a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 2068 + +--S 2069 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b \|3 \|a log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R 2 +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b \|3 \|- a log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R 2 +-+3+-+ 3+---+2 3+-------+ +--R 2b \|3 \|a log(\|- a \|b x - a + a) +--R + +--R 2 +-+3+---+ 3+-------+ 3+-+ +--R 2b \|3 \|- a log(\|b x - a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2 3+-+ 2\|3 \|- a \|b x - a - a\|3 +--R - 6b \|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 2 3+---+ 2\|b x - a - \|a +--R - 6b \|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+---+3+-+ +--R 9a \|3 \|- a \|a +--R Type: Expression(Integer) +--E 2069 + +--S 2070 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2070 + +)clear all + +--S 2071 of 3330 +t0000:=x^3/(a+b*x)^(2/3) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R 3+-------+2 +--R \|b x + a +--R Type: Expression(Integer) +--E 2071 + +--S 2072 of 3330 +r0000:=-3*a^3*(a+b*x)^(1/3)/b^4+9/4*a^2*(a+b*x)^(4/3)/b^4-_ + 9/7*a*(a+b*x)^(7/3)/b^4+3/10*(a+b*x)^(10/3)/b^4 +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (42b x - 54a b x + 81a b x - 243a )\|b x + a +--R (2) ----------------------------------------------- +--R 4 +--R 140b +--R Type: Expression(Integer) +--E 2072 + +--S 2073 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (42b x - 54a b x + 81a b x - 243a )\|b x + a +--R (3) ----------------------------------------------- +--R 4 +--R 140b +--R Type: Union(Expression(Integer),...) +--E 2073 + +--S 2074 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2074 + +--S 2075 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2075 + +)clear all + +--S 2076 of 3330 +t0000:=x^2/(a+b*x)^(2/3) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R 3+-------+2 +--R \|b x + a +--R Type: Expression(Integer) +--E 2076 + +--S 2077 of 3330 +r0000:=3*a^2*(a+b*x)^(1/3)/b^3-3/2*a*(a+b*x)^(4/3)/b^3+3/7*(a+b*x)^(7/3)/b^3 +--R +--R +--R 2 2 2 3+-------+ +--R (6b x - 9a b x + 27a )\|b x + a +--R (2) --------------------------------- +--R 3 +--R 14b +--R Type: Expression(Integer) +--E 2077 + +--S 2078 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+ +--R (6b x - 9a b x + 27a )\|b x + a +--R (3) --------------------------------- +--R 3 +--R 14b +--R Type: Union(Expression(Integer),...) +--E 2078 + +--S 2079 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2079 + +--S 2080 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2080 + +)clear all + +--S 2081 of 3330 +t0000:=x/(a+b*x)^(2/3) +--R +--R +--R x +--R (1) ----------- +--R 3+-------+2 +--R \|b x + a +--R Type: Expression(Integer) +--E 2081 + +--S 2082 of 3330 +r0000:=-3*a*(a+b*x)^(1/3)/b^2+3/4*(a+b*x)^(4/3)/b^2 +--R +--R +--R 3+-------+ +--R (3b x - 9a)\|b x + a +--R (2) --------------------- +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 2082 + +--S 2083 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+ +--R (3b x - 9a)\|b x + a +--R (3) --------------------- +--R 2 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 2083 + +--S 2084 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2084 + +--S 2085 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2085 + +)clear all + +--S 2086 of 3330 +t0000:=1/(a+b*x)^(2/3) +--R +--R +--R 1 +--R (1) ----------- +--R 3+-------+2 +--R \|b x + a +--R Type: Expression(Integer) +--E 2086 + +--S 2087 of 3330 +r0000:=3*(a+b*x)^(1/3)/b +--R +--R +--R 3+-------+ +--R 3\|b x + a +--R (2) ----------- +--R b +--R Type: Expression(Integer) +--E 2087 + +--S 2088 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+ +--R 3\|b x + a +--R (3) ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 2088 + +--S 2089 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2089 + +--S 2090 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2090 + +)clear all + +--S 2091 of 3330 +t0000:=1/(x*(a+b*x)^(2/3)) +--R +--R +--R 1 +--R (1) ------------- +--R 3+-------+2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 2091 + +--S 2092 of 3330 +r0000:=log(a^(1/3)-(a+b*x)^(1/3))/a^(2/3)-1/2*log(a^(2/3)+_ + a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(2/3)-_ + atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(2/3) +--R +--R +--R (2) +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-------+ 3+-+ +--R - log(\|b x + a + \|a \|b x + a + \|a ) + 2log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x + a + \|a +--R - 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+2 +--R 2\|a +--R Type: Expression(Integer) +--E 2092 + +--S 2093 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+2 +--+ +--R 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R +--+ 3| 2 3+-------+ +--R 3| 2 3+-------+ +-+ 2\|a \|b x + a + a +--R 2log(\|a \|b x + a - a) - 2\|3 atan(--------------------) +--R +-+ +--R a\|3 +--R / +--R +--+ +--R 3| 2 +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 2093 + +--S 2094 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+2 +--+ +--R 3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--+ +--R 3+-+2 3| 2 3+-------+ 3| 2 3+-------+ 3+-+ +--R 2\|a log(\|a \|b x + a - a) - 2\|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--R 3| 2 3+-------+ +--+ 3+-------+ 3+-+ +--R +-+3+-+2 2\|a \|b x + a + a +-+3| 2 2\|b x + a + \|a +--R - 2\|3 \|a atan(--------------------) + 2\|3 \|a atan(------------------) +--R +-+ +-+3+-+ +--R a\|3 \|3 \|a +--R / +--R +--+ +--R 3+-+2 3| 2 +--R 2\|a \|a +--R Type: Expression(Integer) +--E 2094 + +--S 2095 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2095 + +)clear all + +--S 2096 of 3330 +t0000:=1/(x^2*(a+b*x)^(2/3)) +--R +--R +--R 1 +--R (1) ------------- +--R 2 3+-------+2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 2096 + +--S 2097 of 3330 +r0000:=-(a+b*x)^(1/3)/(a*x)-2/3*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(5/3)+_ + 1/3*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(5/3)+_ + 2*b*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x + a + \|a +--R - 2b x\|3 log(- \|b x + a + \|a ) + 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R - 3\|3 \|a \|b x + a +--R / +--R +-+3+-+2 +--R 3a x\|3 \|a +--R Type: Expression(Integer) +--E 2097 + +--S 2098 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +----+2 +----+ +--R +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b x\|3 log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--R +-+ 3| 2 3+-------+ +--R 2b x\|3 log(\|- a \|b x + a + a) +--R + +--R +----+ +--R +-+3| 2 3+-------+ +-+ +----+ +--R 2\|3 \|- a \|b x + a - a\|3 +-+3| 2 3+-------+ +--R 6b x atan(------------------------------) - 3\|3 \|- a \|b x + a +--R 3a +--R / +--R +----+ +--R +-+3| 2 +--R 3a x\|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 2098 + +--S 2099 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +----+2 +----+ +--R +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b\|3 \|a log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--R +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +----+ +--R +-+3+-+2 3| 2 3+-------+ +--R 2b\|3 \|a log(\|- a \|b x + a + a) +--R + +--R +----+ +--R +-+3| 2 3+-------+ 3+-+ +--R 2b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +----+ +--R +-+3| 2 3+-------+ +-+ +--R 3+-+2 2\|3 \|- a \|b x + a - a\|3 +--R 6b \|a atan(------------------------------) +--R 3a +--R + +--R +----+ 3+-------+ 3+-+ +--R 3| 2 2\|b x + a + \|a +--R - 6b\|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 3a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 2099 + +--S 2100 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2100 + +)clear all + +--S 2101 of 3330 +t0000:=1/(x^3*(a+b*x)^(2/3)) +--R +--R +--R 1 +--R (1) ------------- +--R 3 3+-------+2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 2101 + +--S 2102 of 3330 +r0000:=-1/2*(a+b*x)^(1/3)/(a*x^2)+5/6*b*(a+b*x)^(1/3)/(a^2*x)+_ + 5/9*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(8/3)-_ + 5/18*b^2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(8/3)-_ + 5/3*b^2*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 5b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R 10b x \|3 log(- \|b x + a + \|a ) - 30b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R (15b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 2 +-+3+-+2 +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 2102 + +--S 2103 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+2 +--+ +--R 2 2 +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - 5b x \|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 2 2 +-+ 3| 2 3+-------+ +--R 10b x \|3 log(\|a \|b x + a - a) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 2 2 2\|3 \|a \|b x + a + a\|3 +--R - 30b x atan(----------------------------) +--R 3a +--R + +--R +--+ +--R +-+3| 2 3+-------+ +--R (15b x - 9a)\|3 \|a \|b x + a +--R / +--R +--+ +--R 2 2 +-+3| 2 +--R 18a x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 2103 + +--S 2104 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+2 +--+ +--R 2 +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - 5b \|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 2 +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R 5b \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--R 2 +-+3+-+2 3| 2 3+-------+ +--R 10b \|3 \|a log(\|a \|b x + a - a) +--R + +--R +--+ +--R 2 +-+3| 2 3+-------+ 3+-+ +--R - 10b \|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 2 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 30b \|a atan(----------------------------) +--R 3a +--R + +--R +--+ 3+-------+ 3+-+ +--R 2 3| 2 2\|b x + a + \|a +--R 30b \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R 2 +-+3+-+2 3| 2 +--R 18a \|3 \|a \|a +--R Type: Expression(Integer) +--E 2104 + +--S 2105 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2105 + +)clear all + +--S 2106 of 3330 +t0000:=x^3/(a+b*x)^(4/3) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 3+-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2106 + +--S 2107 of 3330 +r0000:=3*a^3/(b^4*(a+b*x)^(1/3))+9/2*a^2*(a+b*x)^(2/3)/b^4-_ + 9/5*a*(a+b*x)^(5/3)/b^4+3/8*(a+b*x)^(8/3)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R 15b x - 27a b x + 81a b x + 243a +--R (2) ----------------------------------- +--R 4 3+-------+ +--R 40b \|b x + a +--R Type: Expression(Integer) +--E 2107 + +--S 2108 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 15b x - 27a b x + 81a b x + 243a +--R (3) ----------------------------------- +--R 4 3+-------+ +--R 40b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2108 + +--S 2109 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2109 + +--S 2110 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2110 + +)clear all + +--S 2111 of 3330 +t0000:=x^2/(a+b*x)^(4/3) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 3+-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2111 + +--S 2112 of 3330 +r0000:=-3*a^2/(b^3*(a+b*x)^(1/3))-3*a*(a+b*x)^(2/3)/b^3+3/5*(a+b*x)^(5/3)/b^3 +--R +--R +--R 2 2 2 +--R 3b x - 9a b x - 27a +--R (2) --------------------- +--R 3 3+-------+ +--R 5b \|b x + a +--R Type: Expression(Integer) +--E 2112 + +--S 2113 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 3b x - 9a b x - 27a +--R (3) --------------------- +--R 3 3+-------+ +--R 5b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2113 + +--S 2114 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2114 + +--S 2115 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2115 + +)clear all + +--S 2116 of 3330 +t0000:=x/(a+b*x)^(4/3) +--R +--R +--R x +--R (1) ------------------- +--R 3+-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2116 + +--S 2117 of 3330 +r0000:=3*a/(b^2*(a+b*x)^(1/3))+3/2*(a+b*x)^(2/3)/b^2 +--R +--R +--R 3b x + 9a +--R (2) ------------- +--R 2 3+-------+ +--R 2b \|b x + a +--R Type: Expression(Integer) +--E 2117 + +--S 2118 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3b x + 9a +--R (3) ------------- +--R 2 3+-------+ +--R 2b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2118 + +--S 2119 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2119 + +--S 2120 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2120 + +)clear all + +--S 2121 of 3330 +t0000:=1/(a+b*x)^(4/3) +--R +--R +--R 1 +--R (1) ------------------- +--R 3+-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2121 + +--S 2122 of 3330 +r0000:=(-3)/(b*(a+b*x)^(1/3)) +--R +--R +--R 3 +--R (2) - ----------- +--R 3+-------+ +--R b\|b x + a +--R Type: Expression(Integer) +--E 2122 + +--S 2123 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R (3) - ----------- +--R 3+-------+ +--R b\|b x + a +--R Type: Union(Expression(Integer),...) +--E 2123 + +--S 2124 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2124 + +--S 2125 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2125 + +)clear all + +--S 2126 of 3330 +t0000:=1/(x*(a+b*x)^(4/3)) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 3+-------+ +--R (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 2126 + +--S 2127 of 3330 +r0000:=3/(a*(a+b*x)^(1/3))+log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)-_ + 1/2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(4/3)+_ + atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(4/3) +--R +--R +--R (2) +--R 3+-------+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|b x + a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-------+ 3+-+ +--R 2\|b x + a log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+3+-------+ 2\|b x + a + \|a 3+-+ +--R 2\|3 \|b x + a atan(------------------) + 6\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+3+-------+ +--R 2a\|a \|b x + a +--R Type: Expression(Integer) +--E 2127 + +--S 2128 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-------+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - \|b x + a log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 3+-------+ 3+-+2 3+-------+ +--R 2\|b x + a log(\|a \|b x + a - a) +--R + +--R 3+-+2 3+-------+ +--R +-+3+-------+ 2\|a \|b x + a + a 3+-+ +--R 2\|3 \|b x + a atan(--------------------) + 6\|a +--R +-+ +--R a\|3 +--R / +--R 3+-+3+-------+ +--R 2a\|a \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2128 + +--S 2129 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+3+-------+2 3+-+2 3+-------+ +--R - log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-+2 3+-------+ +--R log(\|b x + a + \|a \|b x + a + \|a ) + 2log(\|a \|b x + a - a) +--R + +--R 3+-+2 3+-------+ +--R 3+-------+ 3+-+ +-+ 2\|a \|b x + a + a +--R - 2log(- \|b x + a + \|a ) + 2\|3 atan(--------------------) +--R +-+ +--R a\|3 +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x + a + \|a +--R - 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 2129 + +--S 2130 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2130 + +)clear all + +--S 2131 of 3330 +t0000:=1/(x^2*(a+b*x)^(4/3)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 3 2 3+-------+ +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 2131 + +--S 2132 of 3330 +r0000:=3/(a*x*(a+b*x)^(1/3))-4*(a+b*x)^(2/3)/(a^2*x)-4/3*b*log(a^(1/3)-_ + (a+b*x)^(1/3))/a^(7/3)+2/3*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))/a^(7/3)-4*b*atan((a^(1/3)+2*(a+b*x)^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-------+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R 2b x\|3 \|b x + a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+3+-------+ 3+-------+ 3+-+ +--R - 4b x\|3 \|b x + a log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-------+ 2\|b x + a + \|a +-+3+-+ +--R - 12b x\|b x + a atan(------------------) + (- 12b x - 3a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+3+-------+ +--R 3a x\|3 \|a \|b x + a +--R Type: Expression(Integer) +--E 2132 + +--S 2133 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+3+-------+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - 2b x\|3 \|b x + a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +-+3+-------+ 3+---+2 3+-------+ +--R 4b x\|3 \|b x + a log(\|- a \|b x + a - a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 3+-------+ 2\|3 \|- a \|b x + a + a\|3 +--R 12b x\|b x + a atan(------------------------------) +--R 3a +--R + +--R +-+3+---+ +--R (- 12b x - 3a)\|3 \|- a +--R / +--R 2 +-+3+---+3+-------+ +--R 3a x\|3 \|- a \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2133 + +--S 2134 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - 2b\|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+3+-+ 3+---+2 3+-------+ +--R 4b\|3 \|a log(\|- a \|b x + a - a) +--R + +--R +-+3+---+ 3+-------+ 3+-+ +--R 4b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 3+-+ 2\|3 \|- a \|b x + a + a\|3 +--R 12b\|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 3+---+ 2\|b x + a + \|a +--R 12b\|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+---+3+-+ +--R 3a \|3 \|- a \|a +--R Type: Expression(Integer) +--E 2134 + +--S 2135 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2135 + +)clear all + +--S 2136 of 3330 +t0000:=1/(x^3*(a+b*x)^(4/3)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 3 3+-------+ +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 2136 + +--S 2137 of 3330 +r0000:=3/(a*x^2*(a+b*x)^(1/3))-7/2*(a+b*x)^(2/3)/(a^2*x^2)+_ + 14/3*b*(a+b*x)^(2/3)/(a^3*x)+14/9*b^2*log(a^(1/3)-_ + (a+b*x)^(1/3))/a^(10/3)-7/9*b^2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))/a^(10/3)+14/3*b^2*atan((a^(1/3)+_ + 2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+3+-------+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 14b x \|3 \|b x + a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 2 2 +-+3+-------+ 3+-------+ 3+-+ +--R 28b x \|3 \|b x + a log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 3+-------+ 2\|b x + a + \|a 2 2 2 +-+3+-+ +--R 84b x \|b x + a atan(------------------ + (84b x + 21a b x - 9a )\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 +-+3+-+3+-------+ +--R 18a x \|3 \|a \|b x + a +--R Type: Expression(Integer) +--E 2137 + +--S 2138 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+3+-------+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - 14b x \|3 \|b x + a log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 2 2 +-+3+-------+ 3+-+2 3+-------+ +--R 28b x \|3 \|b x + a log(\|a \|b x + a - a) +--R + +--R +-+3+-+2 3+-------+ +-+ +--R 2 2 3+-------+ 2\|3 \|a \|b x + a + a\|3 +--R 84b x \|b x + a atan(----------------------------) +--R 3a +--R + +--R 2 2 2 +-+3+-+ +--R (84b x + 21a b x - 9a )\|3 \|a +--R / +--R 3 2 +-+3+-+3+-------+ +--R 18a x \|3 \|a \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2138 + +--S 2139 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - 7b \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R 7b \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 2 +-+ 3+-+2 3+-------+ 2 +-+ 3+-------+ 3+-+ +--R 14b \|3 log(\|a \|b x + a - a) - 14b \|3 log(- \|b x + a + \|a ) +--R + +--R +-+3+-+2 3+-------+ +-+ 3+-------+ 3+-+ +--R 2 2\|3 \|a \|b x + a + a\|3 2 2\|b x + a + \|a +--R 42b atan(----------------------------) - 42b atan(------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R 3 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 2139 + +--S 2140 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2140 + +)clear all + +--S 2141 of 3330 +t0000:=x^m*(a+b*x) +--R +--R +--R m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 2141 + +--S 2142 of 3330 +r0000:=a*x^(1+m)/(1+m)+b*x^(2+m)/(2+m) +--R +--R +--R m + 2 m + 1 +--R (b m + b)x + (a m + 2a)x +--R (2) ---------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Expression(Integer) +--E 2142 + +--S 2143 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 m log(x) +--R ((b m + b)x + (a m + 2a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Union(Expression(Integer),...) +--E 2143 + +--S 2144 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 m log(x) m + 2 +--R ((b m + b)x + (a m + 2a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 2a)x +--R / +--R 2 +--R m + 3m + 2 +--R Type: Expression(Integer) +--E 2144 + +--S 2145 of 3330 +d0000:=D(m0000,x) +--R +--R +--R m log(x) m + 1 m +--R (5) (b x + a)%e - b x - a x +--R Type: Expression(Integer) +--E 2145 + +)clear all + +--S 2146 of 3330 +t0000:=x^(5/2)*(a+b*x) +--R +--R +--R 3 2 +-+ +--R (1) (b x + a x )\|x +--R Type: Expression(Integer) +--E 2146 + +--S 2147 of 3330 +r0000:=2/7*a*x^(7/2)+2/9*b*x^(9/2) +--R +--R +--R 4 3 +-+ +--R (14b x + 18a x )\|x +--R (2) --------------------- +--R 63 +--R Type: Expression(Integer) +--E 2147 + +--S 2148 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 3 +-+ +--R (14b x + 18a x )\|x +--R (3) --------------------- +--R 63 +--R Type: Union(Expression(Integer),...) +--E 2148 + +--S 2149 of 3330 +m0000:=a0000.1 - r0000 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2149 + +--S 2150 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 2150 + +--S 2151 of 3330 +m0000:=a0000.2 - r0000 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2151 + +--S 2152 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Integer) +--E 2152 + +)clear all + +--S 2153 of 3330 +t0000:=x^(3/2)*(a+b*x) +--R +--R +--R 2 +-+ +--R (1) (b x + a x)\|x +--R Type: Expression(Integer) +--E 2153 + +--S 2154 of 3330 +r0000:=2/5*a*x^(5/2)+2/7*b*x^(7/2) +--R +--R +--R 3 2 +-+ +--R (10b x + 14a x )\|x +--R (2) --------------------- +--R 35 +--R Type: Expression(Integer) +--E 2154 + +--S 2155 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 +-+ +--R (10b x + 14a x )\|x +--R (3) --------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 2155 + +--S 2156 of 3330 +m0000:=a0000.1 - r0000 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2156 + +--S 2157 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 2157 + +--S 2158 of 3330 +m0000:=a0000.2 - r0000 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2158 + +--S 2159 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Integer) +--E 2159 + +)clear all + +--S 2160 of 3330 +t0000:=(a+b*x)*sqrt(x) +--R +--R +--R +-+ +--R (1) (b x + a)\|x +--R Type: Expression(Integer) +--E 2160 + +--S 2161 of 3330 +r0000:=2/3*a*x^(3/2)+2/5*b*x^(5/2) +--R +--R +--R 2 +-+ +--R (6b x + 10a x)\|x +--R (2) ------------------- +--R 15 +--R Type: Expression(Integer) +--E 2161 + +--S 2162 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-+ +--R (6b x + 10a x)\|x +--R (3) ------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 2162 + +--S 2163 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2163 + +--S 2164 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2164 + +)clear all + +--S 2165 of 3330 +t0000:=(a+b*x)/sqrt(x) +--R +--R +--R b x + a +--R (1) ------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2165 + +--S 2166 of 3330 +r0000:=2/3*b*x^(3/2)+2*a*sqrt(x) +--R +--R +--R +-+ +--R (2b x + 6a)\|x +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 2166 + +--S 2167 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R (2b x + 6a)\|x +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 2167 + +--S 2168 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2168 + +--S 2169 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2169 + +)clear all + +--S 2170 of 3330 +t0000:=(a+b*x)/x^(3/2) +--R +--R +--R b x + a +--R (1) ------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2170 + +--S 2171 of 3330 +r0000:=-2*a/sqrt(x)+2*b*sqrt(x) +--R +--R +--R 2b x - 2a +--R (2) --------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2171 + +--S 2172 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2b x - 2a +--R (3) --------- +--R +-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 2172 + +--S 2173 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2173 + +--S 2174 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2174 + +)clear all + +--S 2175 of 3330 +t0000:=(a+b*x)/x^(5/2) +--R +--R +--R b x + a +--R (1) ------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2175 + +--S 2176 of 3330 +r0000:=-2/3*a/x^(3/2)-2*b/sqrt(x) +--R +--R +--R - 6b x - 2a +--R (2) ----------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2176 + +--S 2177 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 6b x - 2a +--R (3) ----------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 2177 + +--S 2178 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2178 + +--S 2179 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2179 + +)clear all + +--S 2180 of 3330 +t0000:=x^m*(a+b*x)^2 +--R +--R +--R 2 2 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 2180 + +--S 2181 of 3330 +r0000:=a^2*x^(1+m)/(1+m)+2*a*b*x^(2+m)/(2+m)+b^2*x^(3+m)/(3+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 3 2 m + 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 5a m + 6a )x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 2181 + +--S 2182 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 3 2 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 +--R (a m + 5a m + 6a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Union(Expression(Integer),...) +--E 2182 + +--S 2183 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 2 2 3 2 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 +--R (a m + 5a m + 6a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 3 2 m + 2 +--R (- b m - 3b m - 2b )x + (- 2a b m - 8a b m - 6a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 5a m - 6a )x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 2183 + +--S 2184 of 3330 +d0000:=D(m0000,x) +--R +--R +--R 2 2 2 m log(x) 2 m + 2 m + 1 2 m +--R (5) (b x + 2a b x + a )%e - b x - 2a b x - a x +--R Type: Expression(Integer) +--E 2184 + +)clear all + +--S 2185 of 3330 +t0000:=x^(5/2)*(a+b*x)^2 +--R +--R +--R 2 4 3 2 2 +-+ +--R (1) (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 2185 + +--S 2186 of 3330 +r0000:=2/7*a^2*x^(7/2)+4/9*a*b*x^(9/2)+2/11*b^2*x^(11/2) +--R +--R +--R 2 5 4 2 3 +-+ +--R (126b x + 308a b x + 198a x )\|x +--R (2) ----------------------------------- +--R 693 +--R Type: Expression(Integer) +--E 2186 + +--S 2187 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 5 4 2 3 +-+ +--R (126b x + 308a b x + 198a x )\|x +--R (3) ----------------------------------- +--R 693 +--R Type: Union(Expression(Integer),...) +--E 2187 + +--S 2188 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2188 + +--S 2189 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2189 + +)clear all + +--S 2190 of 3330 +t0000:=x^(3/2)*(a+b*x)^2 +--R +--R +--R 2 3 2 2 +-+ +--R (1) (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 2190 + +--S 2191 of 3330 +r0000:=2/5*a^2*x^(5/2)+4/7*a*b*x^(7/2)+2/9*b^2*x^(9/2) +--R +--R +--R 2 4 3 2 2 +-+ +--R (70b x + 180a b x + 126a x )\|x +--R (2) ---------------------------------- +--R 315 +--R Type: Expression(Integer) +--E 2191 + +--S 2192 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 4 3 2 2 +-+ +--R (70b x + 180a b x + 126a x )\|x +--R (3) ---------------------------------- +--R 315 +--R Type: Union(Expression(Integer),...) +--E 2192 + +--S 2193 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2193 + +--S 2194 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2194 + +)clear all + +--S 2195 of 3330 +t0000:=(a+b*x)^2*sqrt(x) +--R +--R +--R 2 2 2 +-+ +--R (1) (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 2195 + +--S 2196 of 3330 +r0000:=2/3*a^2*x^(3/2)+4/5*a*b*x^(5/2)+2/7*b^2*x^(7/2) +--R +--R +--R 2 3 2 2 +-+ +--R (30b x + 84a b x + 70a x)\|x +--R (2) ------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 2196 + +--S 2197 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 2 2 +-+ +--R (30b x + 84a b x + 70a x)\|x +--R (3) ------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 2197 + +--S 2198 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2198 + +--S 2199 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2199 + +)clear all + +--S 2200 of 3330 +t0000:=(a+b*x)^2/sqrt(x) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2200 + +--S 2201 of 3330 +r0000:=4/3*a*b*x^(3/2)+2/5*b^2*x^(5/2)+2*a^2*sqrt(x) +--R +--R +--R 2 2 2 +-+ +--R (6b x + 20a b x + 30a )\|x +--R (2) ---------------------------- +--R 15 +--R Type: Expression(Integer) +--E 2201 + +--S 2202 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-+ +--R (6b x + 20a b x + 30a )\|x +--R (3) ---------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 2202 + +--S 2203 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2203 + +--S 2204 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2204 + +)clear all + +--S 2205 of 3330 +t0000:=(a+b*x)^2/x^(3/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2205 + +--S 2206 of 3330 +r0000:=2/3*b^2*x^(3/2)-2*a^2/sqrt(x)+4*a*b*sqrt(x) +--R +--R +--R 2 2 2 +--R 2b x + 12a b x - 6a +--R (2) --------------------- +--R +-+ +--R 3\|x +--R Type: Expression(Integer) +--E 2206 + +--S 2207 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2b x + 12a b x - 6a +--R (3) --------------------- +--R +-+ +--R 3\|x +--R Type: Union(Expression(Integer),...) +--E 2207 + +--S 2208 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2208 + +--S 2209 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2209 + +)clear all + +--S 2210 of 3330 +t0000:=(a+b*x)^2/x^(5/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2210 + +--S 2211 of 3330 +r0000:=-2/3*a^2/x^(3/2)-4*a*b/sqrt(x)+2*b^2*sqrt(x) +--R +--R +--R 2 2 2 +--R 6b x - 12a b x - 2a +--R (2) --------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2211 + +--S 2212 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 6b x - 12a b x - 2a +--R (3) --------------------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 2212 + +--S 2213 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2213 + +--S 2214 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2214 + +)clear all + +--S 2215 of 3330 +t0000:=x^m*(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 2215 + +--S 2216 of 3330 +r0000:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(2+m)/(2+m)+3*a*b^2*x^(3+m)/(3+m)+_ + b^3*x^(4+m)/(4+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (3a b m + 24a b m + 57a b m + 36a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 9a m + 26a m + 24a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 2216 + +--S 2217 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 3 3 +--R (3a b m + 24a b m + 57a b m + 36a b)x + (a m + 9a m + 26a m + 24a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Union(Expression(Integer),...) +--E 2217 + +--S 2218 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 3 3 2 3 3 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 2 +--R (3a b m + 24a b m + 57a b m + 36a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 9a m + 26a m + 24a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 4 +--R (- b m - 6b m - 11b m - 6b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (- 3a b m - 21a b m - 42a b m - 24a b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (- 3a b m - 24a b m - 57a b m - 36a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 9a m - 26a m - 24a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 2218 + +--S 2219 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 3 3 2 2 2 3 m log(x) 3 m + 3 2 m + 2 +--R (b x + 3a b x + 3a b x + a )%e - b x - 3a b x +--R + +--R 2 m + 1 3 m +--R - 3a b x - a x +--R Type: Expression(Integer) +--E 2219 + +)clear all + +--S 2220 of 3330 +t0000:=x^(5/2)*(a+b*x)^3 +--R +--R +--R 3 5 2 4 2 3 3 2 +-+ +--R (1) (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 2220 + +--S 2221 of 3330 +r0000:=2/7*a^3*x^(7/2)+2/3*a^2*b*x^(9/2)+6/11*a*b^2*x^(11/2)+2/13*b^3*x^(13/2) +--R +--R +--R 3 6 2 5 2 4 3 3 +-+ +--R (462b x + 1638a b x + 2002a b x + 858a x )\|x +--R (2) ------------------------------------------------- +--R 3003 +--R Type: Expression(Integer) +--E 2221 + +--S 2222 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 6 2 5 2 4 3 3 +-+ +--R (462b x + 1638a b x + 2002a b x + 858a x )\|x +--R (3) ------------------------------------------------- +--R 3003 +--R Type: Union(Expression(Integer),...) +--E 2222 + +--S 2223 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2223 + +--S 2224 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2224 + +)clear all + +--S 2225 of 3330 +t0000:=x^(3/2)*(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 2225 + +--S 2226 of 3330 +r0000:=2/5*a^3*x^(5/2)+6/7*a^2*b*x^(7/2)+2/3*a*b^2*x^(9/2)+2/11*b^3*x^(11/2) +--R +--R +--R 3 5 2 4 2 3 3 2 +-+ +--R (210b x + 770a b x + 990a b x + 462a x )\|x +--R (2) ----------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 2226 + +--S 2227 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 5 2 4 2 3 3 2 +-+ +--R (210b x + 770a b x + 990a b x + 462a x )\|x +--R (3) ----------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 2227 + +--S 2228 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2228 + +--S 2229 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2229 + +)clear all + +--S 2230 of 3330 +t0000:=(a+b*x)^3*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 2230 + +--S 2231 of 3330 +r0000:=2/3*a^3*x^(3/2)+6/5*a^2*b*x^(5/2)+6/7*a*b^2*x^(7/2)+2/9*b^3*x^(9/2) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (70b x + 270a b x + 378a b x + 210a x)\|x +--R (2) --------------------------------------------- +--R 315 +--R Type: Expression(Integer) +--E 2231 + +--S 2232 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (70b x + 270a b x + 378a b x + 210a x)\|x +--R (3) --------------------------------------------- +--R 315 +--R Type: Union(Expression(Integer),...) +--E 2232 + +--S 2233 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2233 + +--S 2234 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2234 + +)clear all + +--S 2235 of 3330 +t0000:=(a+b*x)^3/sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2235 + +--S 2236 of 3330 +r0000:=2*a^2*b*x^(3/2)+6/5*a*b^2*x^(5/2)+2/7*b^3*x^(7/2)+2*a^3*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (10b x + 42a b x + 70a b x + 70a )\|x +--R (2) ---------------------------------------- +--R 35 +--R Type: Expression(Integer) +--E 2236 + +--S 2237 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (10b x + 42a b x + 70a b x + 70a )\|x +--R (3) ---------------------------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 2237 + +--S 2238 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2238 + +--S 2239 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2239 + +)clear all + +--S 2240 of 3330 +t0000:=(a+b*x)^3/x^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2240 + +--S 2241 of 3330 +r0000:=2*a*b^2*x^(3/2)+2/5*b^3*x^(5/2)-2*a^3/sqrt(x)+6*a^2*b*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 10a b x + 30a b x - 10a +--R (2) --------------------------------- +--R +-+ +--R 5\|x +--R Type: Expression(Integer) +--E 2241 + +--S 2242 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 10a b x + 30a b x - 10a +--R (3) --------------------------------- +--R +-+ +--R 5\|x +--R Type: Union(Expression(Integer),...) +--E 2242 + +--S 2243 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2243 + +--S 2244 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2244 + +)clear all + +--S 2245 of 3330 +t0000:=(a+b*x)^3/x^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2245 + +--S 2246 of 3330 +r0000:=-2/3*a^3/x^(3/2)+2/3*b^3*x^(3/2)-6*a^2*b/sqrt(x)+6*a*b^2*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 18a b x - 18a b x - 2a +--R (2) -------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2246 + +--S 2247 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 18a b x - 18a b x - 2a +--R (3) -------------------------------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 2247 + +--S 2248 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2248 + +--S 2249 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2249 + +)clear all + +--S 2250 of 3330 +t0000:=x^(5/2)/(a+b*x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 2250 + +--S 2251 of 3330 +r0000:=-2/3*a*x^(3/2)/b^2+2/5*x^(5/2)/b-_ + 2*a^(5/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+2*a^2*sqrt(x)/b^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R - 30a \|a atan(--------) + (6b x - 10a b x + 30a )\|b \|x +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------- +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 2251 + +--S 2252 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +--R 2 | a \| b 2 2 2 +-+ +--R 15a |- - log(------------------------) + (6b x - 10a b x + 30a )\|x +--R \| b b x + a +--R [----------------------------------------------------------------------, +--R 3 +--R 15b +--R +-+ +-+ +--R 2 |a \|x 2 2 2 +-+ +--R - 30a |- atan(----) + (6b x - 10a b x + 30a )\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R ---------------------------------------------------] +--R 3 +--R 15b +--R Type: Union(List(Expression(Integer)),...) +--E 2252 + +--S 2253 of 3330 +m0000:=a0000 - r0000 +--R +--R There are 12 exposed and 3 unexposed library operations named - +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op - +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named - +--R with argument type(s) +--R List(Expression(Integer)) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2253 + +--S 2254 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 2254 + +)clear all + +--S 2255 of 3330 +t0000:=x^(3/2)/(a+b*x) +--R +--R +--R +-+ +--R x\|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 2255 + +--S 2256 of 3330 +r0000:=2/3*x^(3/2)/b+2*a^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/b^(5/2)-_ + 2*a*sqrt(x)/b^2 +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R 6a\|a atan(--------) + (2b x - 6a)\|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 2256 + +--S 2257 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +--R | a \| b +-+ +--R 3a |- - log(----------------------) + (2b x - 6a)\|x +--R \| b b x + a +--R [-----------------------------------------------------, +--R 2 +--R 3b +--R +-+ +-+ +--R |a \|x +-+ +--R 6a |- atan(----) + (2b x - 6a)\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R ----------------------------------] +--R 2 +--R 3b +--R Type: Union(List(Expression(Integer)),...) +--E 2257 + +--S 2258 of 3330 +m0000:=a0000 - r0000 +--R +--R There are 12 exposed and 3 unexposed library operations named - +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op - +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named - +--R with argument type(s) +--R List(Expression(Integer)) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2258 + +--S 2259 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 2259 + +)clear all + +--S 2260 of 3330 +t0000:=sqrt(x)/(a+b*x) +--R +--R +--R +-+ +--R \|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 2260 + +--S 2261 of 3330 +r0000:=-2*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(3/2)+2*sqrt(x)/b +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R - 2\|a atan(--------) + 2\|b \|x +--R +-+ +--R \|a +--R (2) --------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2261 + +--S 2262 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +---+ |a \|x +-+ +--R | a +-+ - 2 |- atan(---- + 2\|x +--R +---+ - 2b |- - \|x + b x - a \|b +-+ +--R | a \| b +-+ |a +--R |- - log(------------------------) + 2\|x |- +--R \| b b x + a \|b +--R [-------------------------------------------,-------------------------] +--R b b +--R Type: Union(List(Expression(Integer)),...) +--E 2262 + +--S 2263 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R |- - \|b log(------------------------) + 2\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2263 + +--S 2264 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2264 + +--S 2265 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R 2\|a atan(--------) - 2 |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) ----------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2265 + +--S 2266 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2266 + +)clear all + +--S 2267 of 3330 +t0000:=1/((a+b*x)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +--R (b x + a)\|x +--R Type: Expression(Integer) +--E 2267 + +--S 2268 of 3330 +r0000:=2*atan(sqrt(b)*sqrt(x)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atan(--------) +--R +-+ +--R \|a +--R (2) --------------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 2268 + +--S 2269 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-----+ +---+ +-+ +--R 2a b\|x + (b x - a)\|- a b \|a b \|x +--R log(----------------------------) 2atan(----------) +--R b x + a a +--R (3) [---------------------------------,-----------------] +--R +-----+ +---+ +--R \|- a b \|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2269 + +--S 2270 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2270 + +--S 2271 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2271 + +--S 2272 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R 2\|a \|b atan(----------) - 2\|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 2272 + +--S 2273 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2273 + +)clear all + +--S 2274 of 3330 +t0000:=1/(x^(3/2)*(a+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 +-+ +--R (b x + a x)\|x +--R Type: Expression(Integer) +--E 2274 + +--S 2275 of 3330 +r0000:=-2*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(3/2)+(-2)/(a*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R - 2\|b \|x atan(--------) - 2\|a +--R +-+ +--R \|a +--R (2) --------------------------------- +--R +-+ +-+ +--R a\|a \|x +--R Type: Expression(Integer) +--E 2275 + +--S 2276 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +---+ |b +-+ b\|x +--R | b +-+ - 2 |- \|x atan(----- - 2 +--R +---+ - 2a |- - \|x + b x - a \|a +-+ +--R | b +-+ \| a |b +--R |- - \|x log(------------------------) - 2 a |- +--R \| a b x + a \|a +--R [-------------------------------------------,--------------------------] +--R +-+ +-+ +--R a\|x a\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2276 + +--S 2277 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R |- - \|a log(------------------------) + 2\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 2277 + +--S 2278 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2278 + +--S 2279 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R 2\|b atan(--------) - 2\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ------------------------------------------ +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 2279 + +--S 2280 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2280 + +)clear all + +--S 2281 of 3330 +t0000:=1/(x^(5/2)*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 3 2 +-+ +--R (b x + a x )\|x +--R Type: Expression(Integer) +--E 2281 + +--S 2282 of 3330 +r0000:=(-2/3)/(a*x^(3/2))+2*b^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/a^(5/2)+_ + 2*b/(a^2*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R 6b x\|b \|x atan(--------) + (6b x - 2a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------- +--R 2 +-+ +-+ +--R 3a x\|a \|x +--R Type: Expression(Integer) +--E 2282 + +--S 2283 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +--R | b +-+ \| a +--R 3b x |- - \|x log(----------------------) + 6b x - 2a +--R \| a b x + a +--R [-----------------------------------------------------, +--R 2 +-+ +--R 3a x\|x +--R +-+ +-+ +--R |b +-+ b\|x +--R 6b x |- \|x atan(-----) + 6b x - 2a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R -----------------------------------] +--R 2 +-+ +--R 3a x\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2283 + +--S 2284 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R b |- - \|a log(----------------------) - 2b\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2284 + +--S 2285 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2285 + +--S 2286 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R - 2b\|b atan(--------) + 2b\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ---------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2286 + +--S 2287 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2287 + +)clear all + +--S 2288 of 3330 +t0000:=1/(x^(7/2)*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 3 +-+ +--R (b x + a x )\|x +--R Type: Expression(Integer) +--E 2288 + +--S 2289 of 3330 +r0000:=(-2/5)/(a*x^(5/2))+2/3*b/(a^2*x^(3/2))-_ + 2*b^(5/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)-2*b^2/(a^3*sqrt(x)) +--R +--R +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R - 30b x \|b \|x atan(--------) + (- 30b x + 10a b x - 6a )\|a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 3 2 +-+ +-+ +--R 15a x \|a \|x +--R Type: Expression(Integer) +--E 2289 + +--S 2290 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +--R 2 2 | b +-+ \| a 2 2 2 +--R 15b x |- - \|x log(------------------------) - 30b x + 10a b x - 6a +--R \| a b x + a +--R [----------------------------------------------------------------------, +--R 3 2 +-+ +--R 15a x \|x +--R +-+ +-+ +--R 2 2 |b +-+ b\|x 2 2 2 +--R - 30b x |- \|x atan(-----) - 30b x + 10a b x - 6a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R ----------------------------------------------------] +--R 3 2 +-+ +--R 15a x \|x +--R Type: Union(List(Expression(Integer)),...) +--E 2290 + +--S 2291 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +-+ +-+ +--R 2 | b +-+ \| a 2 +-+ \|b \|x +--R b |- - \|a log(------------------------) + 2b \|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2291 + +--S 2292 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2292 + +--S 2293 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 +-+ \|b \|x 2 +-+ |b b\|x +--R 2b \|b atan(--------) - 2b \|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ---------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2293 + +--S 2294 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2294 + +)clear all + +--S 2295 of 3330 +t0000:=x^(5/2)/(a+b*x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 2295 + +--S 2296 of 3330 +r0000:=5/3*x^(3/2)/b^2-x^(5/2)/(b*(a+b*x))+_ + 5*a^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)-5*a*sqrt(x)/b^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R (15a b x + 15a )\|a atan(--------) + (2b x - 10a b x - 15a )\|b \|x +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------------- +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 2296 + +--S 2297 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +--R 2 | a \| b +--R (15a b x + 15a ) |- - log(----------------------) +--R \| b b x + a +--R + +--R 2 2 2 +-+ +--R (4b x - 20a b x - 30a )\|x +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +-+ +-+ +--R 2 |a \|x 2 2 2 +-+ +--R (15a b x + 15a ) |- atan(----) + (2b x - 10a b x - 15a )\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R -------------------------------------------------------------] +--R 4 3 +--R 3b x + 3a b +--R Type: Union(List(Expression(Integer)),...) +--E 2297 + +--S 2298 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R 5a |- - \|b log(----------------------) - 10a\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 2298 + +--S 2299 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2299 + +--S 2300 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R - 5a\|a atan(--------) + 5a |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) --------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2300 + +--S 2301 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2301 + +)clear all + +--S 2302 of 3330 +t0000:=x^(3/2)/(a+b*x)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 2302 + +--S 2303 of 3330 +r0000:=-x^(3/2)/(b*(a+b*x))-3*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(5/2)+_ + 3*sqrt(x)/b^2 +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R (- 3b x - 3a)\|a atan(--------) + (2b x + 3a)\|b \|x +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 3 2 +-+ +--R (b x + a b )\|b +--R Type: Expression(Integer) +--E 2303 + +--S 2304 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +--R | a \| b +-+ +--R (3b x + 3a) |- - log(------------------------) + (4b x + 6a)\|x +--R \| b b x + a +--R [----------------------------------------------------------------, +--R 3 2 +--R 2b x + 2a b +--R +-+ +-+ +--R |a \|x +-+ +--R (- 3b x - 3a) |- atan(----) + (2b x + 3a)\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R ---------------------------------------------] +--R 3 2 +--R b x + a b +--R Type: Union(List(Expression(Integer)),...) +--E 2304 + +--S 2305 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R 3 |- - \|b log(------------------------ + 6\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 2305 + +--S 2306 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2306 + +--S 2307 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R 3\|a atan(--------) - 3 |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) ----------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2307 + +--S 2308 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2308 + +)clear all + +--S 2309 of 3330 +t0000:=sqrt(x)/(a+b*x)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 2309 + +--S 2310 of 3330 +r0000:=atan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(3/2)*sqrt(a))-sqrt(x)/(b*(a+b*x)) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (b x + a)atan(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R 2 +-+ +-+ +--R (b x + a b)\|a \|b +--R Type: Expression(Integer) +--E 2310 + +--S 2311 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-----+ +--R 2a b\|x + (b x - a)\|- a b +-----+ +-+ +--R (b x + a)log(----------------------------) - 2\|- a b \|x +--R b x + a +--R [----------------------------------------------------------, +--R 2 +-----+ +--R (2b x + 2a b)\|- a b +--R +---+ +-+ +--R \|a b \|x +---+ +-+ +--R (b x + a)atan(----------) - \|a b \|x +--R a +--R --------------------------------------] +--R 2 +---+ +--R (b x + a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2311 + +--S 2312 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2312 + +--S 2313 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2313 + +--S 2314 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R b\|a \|b \|a b +--R Type: Expression(Integer) +--E 2314 + +--S 2315 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2315 + +)clear all + +--S 2316 of 3330 +t0000:=1/((a+b*x)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 2316 + +--S 2317 of 3330 +r0000:=atan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*sqrt(b))+sqrt(x)/(a*(a+b*x)) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (b x + a)atan(--------) + \|a \|b \|x +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R Type: Expression(Integer) +--E 2317 + +--S 2318 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-----+ +--R 2a b\|x + (b x - a)\|- a b +-----+ +-+ +--R (b x + a)log(----------------------------) + 2\|- a b \|x +--R b x + a +--R [----------------------------------------------------------, +--R 2 +-----+ +--R (2a b x + 2a )\|- a b +--R +---+ +-+ +--R \|a b \|x +---+ +-+ +--R (b x + a)atan(----------) + \|a b \|x +--R a +--R --------------------------------------] +--R 2 +---+ +--R (a b x + a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2318 + +--S 2319 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2319 + +--S 2320 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2320 + +--S 2321 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R a\|a \|b \|a b +--R Type: Expression(Integer) +--E 2321 + +--S 2322 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2322 + +)clear all + +--S 2323 of 3330 +t0000:=1/(x^(3/2)*(a+b*x)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 3 2 2 +-+ +--R (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 2323 + +--S 2324 of 3330 +r0000:=-3*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(5/2)+_ + (-3)/(a^2*sqrt(x))+1/(a*(a+b*x)*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R (- 3b x - 3a)\|b \|x atan(--------) + (- 3b x - 2a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 2 3 +-+ +-+ +--R (a b x + a )\|a \|x +--R Type: Expression(Integer) +--E 2324 + +--S 2325 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +--R | b +-+ \| a +--R (3b x + 3a) |- - \|x log(------------------------) - 6b x - 4a +--R \| a b x + a +--R [--------------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x + 2a )\|x +--R +-+ +-+ +--R |b +-+ b\|x +--R (- 3b x - 3a) |- \|x atan(-----) - 3b x - 2a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R --------------------------------------------] +--R 2 3 +-+ +--R (a b x + a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2325 + +--S 2326 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R 3 |- - \|a log(------------------------ + 6\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 2326 + +--S 2327 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2327 + +--S 2328 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R 3\|b atan(--------) - 3\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ------------------------------------------ +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2328 + +--S 2329 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2329 + +)clear all + +--S 2330 of 3330 +t0000:=1/(x^(5/2)*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 4 3 2 2 +-+ +--R (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 2330 + +--S 2331 of 3330 +r0000:=(-5/3)/(a^2*x^(3/2))+1/(a*x^(3/2)*(a+b*x))+_ + 5*b^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)+5*b/(a^3*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R (15b x + 15a b x)\|b \|x atan(--------) + (15b x + 10a b x - 2a )\|a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x + 3a x)\|a \|x +--R Type: Expression(Integer) +--E 2331 + +--S 2332 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +--R 2 2 | b +-+ \| a 2 2 +--R (15b x + 15a b x) |- - \|x log(----------------------) + 30b x +--R \| a b x + a +--R + +--R 2 +--R 20a b x - 4a +--R / +--R 3 2 4 +-+ +--R (6a b x + 6a x)\|x +--R , +--R +-+ +-+ +--R 2 2 |b +-+ b\|x 2 2 2 +--R (15b x + 15a b x) |- \|x atan(-----) + 15b x + 10a b x - 2a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R --------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x + 3a x)\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2332 + +--S 2333 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R 5b |- - \|a log(----------------------) - 10b\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 2333 + +--S 2334 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2334 + +--S 2335 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R - 5b\|b atan(--------) + 5b\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ---------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2335 + +--S 2336 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2336 + +)clear all + +--S 2337 of 3330 +t0000:=x^(7/2)/(a+b*x)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2337 + +--S 2338 of 3330 +r0000:=35/12*x^(3/2)/b^3-1/2*x^(7/2)/(b*(a+b*x)^2)-_ + 7/4*x^(5/2)/(b^2*(a+b*x))+35/4*a^(3/2)*_ + atan(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)-35/4*a*sqrt(x)/b^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 3 +-+ \|b \|x +--R (105a b x + 210a b x + 105a )\|a atan(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (8b x - 56a b x - 175a b x - 105a )\|b \|x +--R / +--R 6 2 5 2 4 +-+ +--R (12b x + 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 2338 + +--S 2339 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +--R 2 2 2 3 | a \| b +--R (105a b x + 210a b x + 105a ) |- - log(----------------------) +--R \| b b x + a +--R + +--R 3 3 2 2 2 3 +-+ +--R (16b x - 112a b x - 350a b x - 210a )\|x +--R / +--R 6 2 5 2 4 +--R 24b x + 48a b x + 24a b +--R , +--R +--R +-+ +-+ +--R 2 2 2 3 |a \|x +--R (105a b x + 210a b x + 105a ) |- atan(----) +--R \|b +-+ +--R |a +--R |- +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (8b x - 56a b x - 175a b x - 105a )\|x +--R / +--R 6 2 5 2 4 +--R 12b x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2339 + +--S 2340 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R 35a |- - \|b log(----------------------) - 70a\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2340 + +--S 2341 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2341 + +--S 2342 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R - 35a\|a atan(--------) + 35a |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) ----------------------------------------------- +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2342 + +--S 2343 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2343 + +)clear all + +--S 2344 of 3330 +t0000:=x^(5/2)/(a+b*x)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2344 + +--S 2345 of 3330 +r0000:=-1/2*x^(5/2)/(b*(a+b*x)^2)-5/4*x^(3/2)/(b^2*(a+b*x))-_ + 15/4*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(7/2)+15/4*sqrt(x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ \|b \|x +--R (- 15b x - 30a b x - 15a )\|a atan(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +-+ +--R (8b x + 25a b x + 15a )\|b \|x +--R / +--R 5 2 4 2 3 +-+ +--R (4b x + 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 2345 + +--S 2346 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +--R 2 2 2 | a \| b +--R (15b x + 30a b x + 15a ) |- - log(------------------------) +--R \| b b x + a +--R + +--R 2 2 2 +-+ +--R (16b x + 50a b x + 30a )\|x +--R / +--R 5 2 4 2 3 +--R 8b x + 16a b x + 8a b +--R , +--R +-+ +-+ +--R 2 2 2 |a \|x 2 2 2 +-+ +--R (- 15b x - 30a b x - 15a ) |- atan(----) + (8b x + 25a b x + 15a )\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R ------------------------------------------------------------------------] +--R 5 2 4 2 3 +--R 4b x + 8a b x + 4a b +--R Type: Union(List(Expression(Integer)),...) +--E 2346 + +--S 2347 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R 15 |- - \|b log(------------------------ + 30\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2347 + +--S 2348 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2348 + +--S 2349 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R 15\|a atan(--------) - 15 |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) ------------------------------------------- +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2349 + +--S 2350 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2350 + +)clear all + +--S 2351 of 3330 +t0000:=x^(3/2)/(a+b*x)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2351 + +--S 2352 of 3330 +r0000:=-1/2*x^(3/2)/(b*(a+b*x)^2)+_ + 3/4*atan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(5/2)*sqrt(a))-_ + 3/4*sqrt(x)/(b^2*(a+b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (3b x + 6a b x + 3a )atan(--------) + (- 5b x - 3a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4b x + 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 2352 + +--S 2353 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (b x - a)\|- a b +--R (3b x + 6a b x + 3a )log(----------------------------) +--R b x + a +--R + +--R +-----+ +-+ +--R (- 10b x - 6a)\|- a b \|x +--R / +--R 4 2 3 2 2 +-----+ +--R (8b x + 16a b x + 8a b )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (3b x + 6a b x + 3a )atan(----------) + (- 5b x - 3a)\|a b \|x +--R a +--R ----------------------------------------------------------------] +--R 4 2 3 2 2 +---+ +--R (4b x + 8a b x + 4a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2353 + +--S 2354 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2354 + +--S 2355 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2355 + +--S 2356 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R 3\|a \|b atan(----------) - 3\|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 4b \|a \|b \|a b +--R Type: Expression(Integer) +--E 2356 + +--S 2357 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2357 + +)clear all + +--S 2358 of 3330 +t0000:=sqrt(x)/(a+b*x)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2358 + +--S 2359 of 3330 +r0000:=1/4*atan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(3/2))-_ + 1/2*sqrt(x)/(b*(a+b*x)^2)+1/4*sqrt(x)/(a*b*(a+b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (b x + 2a b x + a )atan(--------) + (b x - a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x + 8a b x + 4a b)\|a \|b +--R Type: Expression(Integer) +--E 2359 + +--S 2360 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (b x - a)\|- a b +--R (b x + 2a b x + a )log(----------------------------) +--R b x + a +--R + +--R +-----+ +-+ +--R (2b x - 2a)\|- a b \|x +--R / +--R 3 2 2 2 3 +-----+ +--R (8a b x + 16a b x + 8a b)\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (b x + 2a b x + a )atan(----------) + (b x - a)\|a b \|x +--R a +--R ----------------------------------------------------------] +--R 3 2 2 2 3 +---+ +--R (4a b x + 8a b x + 4a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2360 + +--S 2361 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2361 + +--S 2362 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2362 + +--S 2363 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R 4a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 2363 + +--S 2364 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2364 + +)clear all + +--S 2365 of 3330 +t0000:=1/((a+b*x)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 2365 + +--S 2366 of 3330 +r0000:=3/4*atan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*sqrt(b))+_ + 1/2*sqrt(x)/(a*(a+b*x)^2)+3/4*sqrt(x)/(a^2*(a+b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (3b x + 6a b x + 3a )atan(--------) + (3b x + 5a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R 2 2 2 3 4 +-+ +-+ +--R (4a b x + 8a b x + 4a )\|a \|b +--R Type: Expression(Integer) +--E 2366 + +--S 2367 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (b x - a)\|- a b +--R (3b x + 6a b x + 3a )log(----------------------------) +--R b x + a +--R + +--R +-----+ +-+ +--R (6b x + 10a)\|- a b \|x +--R / +--R 2 2 2 3 4 +-----+ +--R (8a b x + 16a b x + 8a )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (3b x + 6a b x + 3a )atan(----------) + (3b x + 5a)\|a b \|x +--R a +--R --------------------------------------------------------------] +--R 2 2 2 3 4 +---+ +--R (4a b x + 8a b x + 4a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2367 + +--S 2368 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2368 + +--S 2369 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2369 + +--S 2370 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R 3\|a \|b atan(----------) - 3\|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 4a \|a \|b \|a b +--R Type: Expression(Integer) +--E 2370 + +--S 2371 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2371 + +)clear all + +--S 2372 of 3330 +t0000:=1/(x^(3/2)*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 2372 + +--S 2373 of 3330 +r0000:=-15/4*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(7/2)+_ + (-15/4)/(a^3*sqrt(x))+1/2/(a*(a+b*x)^2*sqrt(x))+_ + 5/4/(a^2*(a+b*x)*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|b \|x +--R (- 15b x - 30a b x - 15a )\|b \|x atan(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (- 15b x - 25a b x - 8a )\|a +--R / +--R 3 2 2 4 5 +-+ +-+ +--R (4a b x + 8a b x + 4a )\|a \|x +--R Type: Expression(Integer) +--E 2373 + +--S 2374 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +--R 2 2 2 | b +-+ \| a +--R (15b x + 30a b x + 15a ) |- - \|x log(------------------------) +--R \| a b x + a +--R + +--R 2 2 2 +--R - 30b x - 50a b x - 16a +--R / +--R 3 2 2 4 5 +-+ +--R (8a b x + 16a b x + 8a )\|x +--R , +--R +-+ +-+ +--R 2 2 2 |b +-+ b\|x 2 2 2 +--R (- 15b x - 30a b x - 15a ) |- \|x atan(-----) - 15b x - 25a b x - 8a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R -----------------------------------------------------------------------] +--R 3 2 2 4 5 +-+ +--R (4a b x + 8a b x + 4a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2374 + +--S 2375 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R 15 |- - \|a log(------------------------ + 30\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 2375 + +--S 2376 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2376 + +--S 2377 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R 15\|b atan(--------) - 15\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) -------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 2377 + +--S 2378 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2378 + +)clear all + +--S 2379 of 3330 +t0000:=1/(x^(5/2)*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 2379 + +--S 2380 of 3330 +r0000:=(-35/12)/(a^3*x^(3/2))+1/2/(a*x^(3/2)*(a+b*x)^2)+_ + 7/4/(a^2*x^(3/2)*(a+b*x))+35/4*b^(3/2)*_ + atan(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)+35/4*b/(a^4*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|b \|x +--R (105b x + 210a b x + 105a b x)\|b \|x atan(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x + 175a b x + 56a b x - 8a )\|a +--R / +--R 4 2 3 5 2 6 +-+ +-+ +--R (12a b x + 24a b x + 12a x)\|a \|x +--R Type: Expression(Integer) +--E 2380 + +--S 2381 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +--R 3 3 2 2 2 | b +-+ \| a +--R (105b x + 210a b x + 105a b x) |- - \|x log(----------------------) +--R \| a b x + a +--R + +--R 3 3 2 2 2 3 +--R 210b x + 350a b x + 112a b x - 16a +--R / +--R 4 2 3 5 2 6 +-+ +--R (24a b x + 48a b x + 24a x)\|x +--R , +--R +--R +-+ +-+ +--R 3 3 2 2 2 |b +-+ b\|x 3 3 +--R (105b x + 210a b x + 105a b x) |- \|x atan(-----) + 105b x +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R + +--R 2 2 2 3 +--R 175a b x + 56a b x - 8a +--R / +--R 4 2 3 5 2 6 +-+ +--R (12a b x + 24a b x + 12a x)\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2381 + +--S 2382 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R 35b |- - \|a log(----------------------) - 70b\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 2382 + +--S 2383 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2383 + +--S 2384 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R - 35b\|b atan(--------) + 35b\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ------------------------------------------------ +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 2384 + +--S 2385 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2385 + +)clear all + +--S 2386 of 3330 +t0000:=x^(5/2)/(-a+b*x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------- +--R b x - a +--R Type: Expression(Integer) +--E 2386 + +--S 2387 of 3330 +r0000:=2/3*a*x^(3/2)/b^2+2/5*x^(5/2)/b-_ + 2*a^(5/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+2*a^2*sqrt(x)/b^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R - 30a \|a atanh(--------) + (6b x + 10a b x + 30a )\|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------ +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 2387 + +--S 2388 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 |a \|b 2 2 2 +-+ +--R 15a |- log(----------------------) + (6b x + 10a b x + 30a )\|x +--R \|b b x - a +--R [------------------------------------------------------------------, +--R 3 +--R 15b +--R +---+ +-+ +--R 2 | a \|x 2 2 2 +-+ +--R - 30a |- - atan(------) + (6b x + 10a b x + 30a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------------] +--R 3 +--R 15b +--R Type: Union(List(Expression(Integer)),...) +--E 2388 + +--S 2389 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R 2 |a +-+ \|b 2 +-+ \|b \|x +--R a |- \|b log(----------------------) + 2a \|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2389 + +--S 2390 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2390 + +--S 2391 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R 2 +-+ \|b \|x 2 | a +-+ \|x +--R 2a \|a atanh(--------) - 2a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) -------------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2391 + +--S 2392 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2392 + +)clear all + +--S 2393 of 3330 +t0000:=x^(3/2)/(-a+b*x) +--R +--R +--R +-+ +--R x\|x +--R (1) ------- +--R b x - a +--R Type: Expression(Integer) +--E 2393 + +--S 2394 of 3330 +r0000:=2/3*x^(3/2)/b-2*a^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(5/2)+_ + 2*a*sqrt(x)/b^2 +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R - 6a\|a atanh(--------) + (2b x + 6a)\|b \|x +--R +-+ +--R \|a +--R (2) --------------------------------------------- +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 2394 + +--S 2395 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R |a \|b +-+ +--R 3a |- log(----------------------) + (2b x + 6a)\|x +--R \|b b x - a +--R [---------------------------------------------------, +--R 2 +--R 3b +--R +---+ +-+ +--R | a \|x +-+ +--R - 6a |- - atan(------) + (2b x + 6a)\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R ----------------------------------------] +--R 2 +--R 3b +--R Type: Union(List(Expression(Integer)),...) +--E 2395 + +--S 2396 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R a |- \|b log(----------------------) + 2a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------ +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2396 + +--S 2397 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2397 + +--S 2398 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 2a\|a atanh(--------) - 2a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ------------------------------------------------ +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2398 + +--S 2399 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2399 + +)clear all + +--S 2400 of 3330 +t0000:=sqrt(x)/(-a+b*x) +--R +--R +--R +-+ +--R \|x +--R (1) ------- +--R b x - a +--R Type: Expression(Integer) +--E 2400 + +--S 2401 of 3330 +r0000:=-2*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(3/2)+2*sqrt(x)/b +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R - 2\|a atanh(--------) + 2\|b \|x +--R +-+ +--R \|a +--R (2) ---------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2401 + +--S 2402 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-+ +--R +-+ | a \|x +-+ +--R |a +-+ - 2 |- - atan(------ + 2\|x +--R +-+ - 2b |- \|x + b x + a \| b +---+ +--R |a \|b +-+ | a +--R |- log(----------------------) + 2\|x |- - +--R \|b b x - a \| b +--R [---------------------------------------,-----------------------------] +--R b b +--R Type: Union(List(Expression(Integer)),...) +--E 2402 + +--S 2403 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R |- \|b log(----------------------) + 2\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) ---------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2403 + +--S 2404 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2404 + +--S 2405 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 2\|a atanh(--------) - 2 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ---------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2405 + +--S 2406 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2406 + +)clear all + +--S 2407 of 3330 +t0000:=1/((-a+b*x)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +--R (b x - a)\|x +--R Type: Expression(Integer) +--E 2407 + +--S 2408 of 3330 +r0000:=-2*atanh(sqrt(b)*sqrt(x)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atanh(--------) +--R +-+ +--R \|a +--R (2) - ---------------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 2408 + +--S 2409 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +---+ +-----+ +-+ +--R - 2a b\|x + (b x + a)\|a b \|- a b \|x +--R log(----------------------------) 2atan(------------) +--R b x - a a +--R (3) [---------------------------------,- -------------------] +--R +---+ +-----+ +--R \|a b \|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2409 + +--S 2410 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 2410 + +--S 2411 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2411 + +--S 2412 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 2\|- a b atanh(--------) - 2\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2412 + +--S 2413 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2413 + +)clear all + +--S 2414 of 3330 +t0000:=1/(x^(3/2)*(-a+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 +-+ +--R (b x - a x)\|x +--R Type: Expression(Integer) +--E 2414 + +--S 2415 of 3330 +r0000:=-2*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(3/2)+2/(a*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R - 2\|b \|x atanh(--------) + 2\|a +--R +-+ +--R \|a +--R (2) ---------------------------------- +--R +-+ +-+ +--R a\|a \|x +--R Type: Expression(Integer) +--E 2415 + +--S 2416 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-+ +--R +-+ | b +-+ b\|x +--R |b +-+ - 2 |- - \|x atan(------- + 2 +--R +-+ - 2a |- \|x + b x + a \| a +---+ +--R |b +-+ \|a | b +--R |- \|x log(----------------------) + 2 a |- - +--R \|a b x - a \| a +--R [---------------------------------------,------------------------------] +--R +-+ +-+ +--R a\|x a\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2416 + +--S 2417 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R \|a |- log(----------------------) + 2\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) ---------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 2417 + +--S 2418 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2418 + +--S 2419 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 2\|b atanh(--------) - 2 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) ----------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 2419 + +--S 2420 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2420 + +)clear all + +--S 2421 of 3330 +t0000:=1/(x^(5/2)*(-a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 3 2 +-+ +--R (b x - a x )\|x +--R Type: Expression(Integer) +--E 2421 + +--S 2422 of 3330 +r0000:=2/3/(a*x^(3/2))-2*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(5/2)+_ + 2*b/(a^2*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R - 6b x\|b \|x atanh(--------) + (6b x + 2a)\|a +--R +-+ +--R \|a +--R (2) ----------------------------------------------- +--R 2 +-+ +-+ +--R 3a x\|a \|x +--R Type: Expression(Integer) +--E 2422 + +--S 2423 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R |b +-+ \|a +--R 3b x |- \|x log(----------------------) + 6b x + 2a +--R \|a b x - a +--R [---------------------------------------------------, +--R 2 +-+ +--R 3a x\|x +--R +---+ +-+ +--R | b +-+ b\|x +--R - 6b x |- - \|x atan(-------) + 6b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R -----------------------------------------] +--R 2 +-+ +--R 3a x\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2423 + +--S 2424 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R b\|a |- log(----------------------) + 2b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------ +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2424 + +--S 2425 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2425 + +--S 2426 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 2b\|b atanh(--------) - 2b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) ------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2426 + +--S 2427 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2427 + +)clear all + +--S 2428 of 3330 +t0000:=1/(x^(7/2)*(-a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 3 +-+ +--R (b x - a x )\|x +--R Type: Expression(Integer) +--E 2428 + +--S 2429 of 3330 +r0000:=2/5/(a*x^(5/2))+2/3*b/(a^2*x^(3/2))-_ + 2*b^(5/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)+2*b^2/(a^3*sqrt(x)) +--R +--R +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R - 30b x \|b \|x atanh(--------) + (30b x + 10a b x + 6a )\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R 3 2 +-+ +-+ +--R 15a x \|a \|x +--R Type: Expression(Integer) +--E 2429 + +--S 2430 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 2 2 |b +-+ \|a 2 2 2 +--R 15b x |- \|x log(----------------------) + 30b x + 10a b x + 6a +--R \|a b x - a +--R [------------------------------------------------------------------, +--R 3 2 +-+ +--R 15a x \|x +--R +---+ +-+ +--R 2 2 | b +-+ b\|x 2 2 2 +--R - 30b x |- - \|x atan(-------) + 30b x + 10a b x + 6a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R --------------------------------------------------------] +--R 3 2 +-+ +--R 15a x \|x +--R Type: Union(List(Expression(Integer)),...) +--E 2430 + +--S 2431 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R 2 +-+ |b \|a 2 +-+ \|b \|x +--R b \|a |- log(----------------------) + 2b \|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2431 + +--S 2432 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2432 + +--S 2433 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R 2 +-+ \|b \|x 2 | b +-+ b\|x +--R 2b \|b atanh(--------) - 2b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) --------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2433 + +--S 2434 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2434 + +)clear all + +--S 2435 of 3330 +t0000:=x^(5/2)/(-a+b*x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 2435 + +--S 2436 of 3330 +r0000:=5/3*x^(3/2)/b^2+x^(5/2)/(b*(a-b*x))-_ + 5*a^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+5*a*sqrt(x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R (- 15a b x + 15a )\|a atanh(--------) + (2b x + 10a b x - 15a )\|b \|x +--R +-+ +--R \|a +--R ------------------------------------------------------------------------ +--R 4 3 +-+ +--R (3b x - 3a b )\|b +--R Type: Expression(Integer) +--E 2436 + +--S 2437 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 |a \|b +--R (15a b x - 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (4b x + 20a b x - 30a )\|x +--R / +--R 4 3 +--R 6b x - 6a b +--R , +--R +---+ +-+ +--R 2 | a \|x 2 2 2 +-+ +--R (- 15a b x + 15a ) |- - atan(------) + (2b x + 10a b x - 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------------------------] +--R 4 3 +--R 3b x - 3a b +--R Type: Union(List(Expression(Integer)),...) +--E 2437 + +--S 2438 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 5a |- \|b log(----------------------) + 10a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 2438 + +--S 2439 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2439 + +--S 2440 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 5a\|a atanh(--------) - 5a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ------------------------------------------------ +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2440 + +--S 2441 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2441 + +)clear all + +--S 2442 of 3330 +t0000:=x^(3/2)/(-a+b*x)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 2442 + +--S 2443 of 3330 +r0000:=x^(3/2)/(b*(a-b*x))-3*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(5/2)+_ + 3*sqrt(x)/b^2 +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R (- 3b x + 3a)\|a atanh(--------) + (2b x - 3a)\|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 3 2 +-+ +--R (b x - a b )\|b +--R Type: Expression(Integer) +--E 2443 + +--S 2444 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R |a \|b +-+ +--R (3b x - 3a) |- log(----------------------) + (4b x - 6a)\|x +--R \|b b x - a +--R [------------------------------------------------------------, +--R 3 2 +--R 2b x - 2a b +--R +---+ +-+ +--R | a \|x +-+ +--R (- 3b x + 3a) |- - atan(------) + (2b x - 3a)\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------] +--R 3 2 +--R b x - a b +--R Type: Union(List(Expression(Integer)),...) +--E 2444 + +--S 2445 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 3 |- \|b log(---------------------- + 6\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) ----------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 2445 + +--S 2446 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2446 + +--S 2447 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 3\|a atanh(--------) - 3 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ---------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2447 + +--S 2448 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2448 + +)clear all + +--S 2449 of 3330 +t0000:=sqrt(x)/(-a+b*x)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 2449 + +--S 2450 of 3330 +r0000:=-atanh(sqrt(b)*sqrt(x)/sqrt(a))/(b^(3/2)*sqrt(a))+sqrt(x)/(b*(a-b*x)) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (- b x + a)atanh(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (2) ----------------------------------------- +--R 2 +-+ +-+ +--R (b x - a b)\|a \|b +--R Type: Expression(Integer) +--E 2450 + +--S 2451 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +---+ +--R - 2a b\|x + (b x + a)\|a b +---+ +-+ +--R (b x - a)log(----------------------------) - 2\|a b \|x +--R b x - a +--R [--------------------------------------------------------, +--R 2 +---+ +--R (2b x - 2a b)\|a b +--R +-----+ +-+ +--R \|- a b \|x +-----+ +-+ +--R (- b x + a)atan(------------) - \|- a b \|x +--R a +--R --------------------------------------------] +--R 2 +-----+ +--R (b x - a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2451 + +--S 2452 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 2452 + +--S 2453 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2453 + +--S 2454 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R \|- a b atanh(--------) - \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------- +--R +-----+ +-+ +-+ +--R b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2454 + +--S 2455 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2455 + +)clear all + +--S 2456 of 3330 +t0000:=1/((-a+b*x)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (b x - 2a b x + a )\|x +--R Type: Expression(Integer) +--E 2456 + +--S 2457 of 3330 +r0000:=atanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*sqrt(b))+sqrt(x)/(a*(a-b*x)) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (b x - a)atanh(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (2) --------------------------------------- +--R 2 +-+ +-+ +--R (a b x - a )\|a \|b +--R Type: Expression(Integer) +--E 2457 + +--S 2458 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +---+ +--R 2a b\|x + (b x + a)\|a b +---+ +-+ +--R (b x - a)log(--------------------------) - 2\|a b \|x +--R b x - a +--R [------------------------------------------------------, +--R 2 +---+ +--R (2a b x - 2a )\|a b +--R +-----+ +-+ +--R \|- a b \|x +-----+ +-+ +--R (b x - a)atan(------------) - \|- a b \|x +--R a +--R ------------------------------------------] +--R 2 +-----+ +--R (a b x - a )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2458 + +--S 2459 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(--------------------------) - 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R +-+ +-+ +---+ +--R 2a\|a \|b \|a b +--R Type: Expression(Integer) +--E 2459 + +--S 2460 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2460 + +--S 2461 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R - \|- a b atanh(--------) + \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2461 + +--S 2462 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2462 + +)clear all + +--S 2463 of 3330 +t0000:=1/(x^(3/2)*(-a+b*x)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 3 2 2 +-+ +--R (b x - 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 2463 + +--S 2464 of 3330 +r0000:=3*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(5/2)+_ + (-3)/(a^2*sqrt(x))+1/(a*(a-b*x)*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R (3b x - 3a)\|b \|x atanh(--------) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 3 +-+ +-+ +--R (a b x - a )\|a \|x +--R Type: Expression(Integer) +--E 2464 + +--S 2465 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R |b +-+ \|a +--R (3b x - 3a) |- \|x log(--------------------) - 6b x + 4a +--R \|a b x - a +--R [--------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x - 2a )\|x +--R +---+ +-+ +--R | b +-+ b\|x +--R (3b x - 3a) |- - \|x atan(-------) - 3b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ----------------------------------------------] +--R 2 3 +-+ +--R (a b x - a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2465 + +--S 2466 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 3\|a |- log(--------------------) - 6\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 2466 + +--S 2467 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2467 + +--S 2468 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 3\|b atanh(--------) + 3 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) ------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2468 + +--S 2469 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2469 + +)clear all + +--S 2470 of 3330 +t0000:=1/(x^(5/2)*(-a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 4 3 2 2 +-+ +--R (b x - 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 2470 + +--S 2471 of 3330 +r0000:=(-5/3)/(a^2*x^(3/2))+1/(a*x^(3/2)*(a-b*x))+_ + 5*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)-5*b/(a^3*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R (15b x - 15a b x)\|b \|x atanh(--------) + (- 15b x + 10a b x + 2a )\|a +--R +-+ +--R \|a +--R -------------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x - 3a x)\|a \|x +--R Type: Expression(Integer) +--E 2471 + +--S 2472 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R 2 2 |b +-+ \|a 2 2 2 +--R (15b x - 15a b x) |- \|x log(--------------------) - 30b x + 20a b x + 4a +--R \|a b x - a +--R [---------------------------------------------------------------------------- +--R 3 2 4 +-+ +--R (6a b x - 6a x)\|x +--R , +--R +---+ +-+ +--R 2 2 | b +-+ b\|x 2 2 2 +--R (15b x - 15a b x) |- - \|x atan(-------) - 15b x + 10a b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ------------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x - 3a x)\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2472 + +--S 2473 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 5b\|a |- log(--------------------) - 10b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 2473 + +--S 2474 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2474 + +--S 2475 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 5b\|b atanh(--------) + 5b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) --------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2475 + +--S 2476 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2476 + +)clear all + +--S 2477 of 3330 +t0000:=x^(7/2)/(-a+b*x)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 2477 + +--S 2478 of 3330 +r0000:=35/12*x^(3/2)/b^3-1/2*x^(7/2)/(b*(a-b*x)^2)+_ + 7/4*x^(5/2)/(b^2*(a-b*x))-_ + 35/4*a^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)+35/4*a*sqrt(x)/b^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 3 +-+ \|b \|x +--R (- 105a b x + 210a b x - 105a )\|a atanh(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (8b x + 56a b x - 175a b x + 105a )\|b \|x +--R / +--R 6 2 5 2 4 +-+ +--R (12b x - 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 2478 + +--S 2479 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 2 2 3 |a \|b +--R (105a b x - 210a b x + 105a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 3 3 2 2 2 3 +-+ +--R (16b x + 112a b x - 350a b x + 210a )\|x +--R / +--R 6 2 5 2 4 +--R 24b x - 48a b x + 24a b +--R , +--R +--R +---+ +-+ +--R 2 2 2 3 | a \|x +--R (- 105a b x + 210a b x - 105a ) |- - atan(------) +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R + +--R 3 3 2 2 2 3 +-+ +--R (8b x + 56a b x - 175a b x + 105a )\|x +--R / +--R 6 2 5 2 4 +--R 12b x - 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2479 + +--S 2480 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 35a |- \|b log(----------------------) + 70a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2480 + +--S 2481 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2481 + +--S 2482 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 35a\|a atanh(--------) - 35a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) -------------------------------------------------- +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2482 + +--S 2483 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2483 + +)clear all + +--S 2484 of 3330 +t0000:=x^(5/2)/(-a+b*x)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 2484 + +--S 2485 of 3330 +r0000:=-1/2*x^(5/2)/(b*(a-b*x)^2)+5/4*x^(3/2)/(b^2*(a-b*x))-_ + 15/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(7/2)+15/4*sqrt(x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|a atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +-+ +--R (8b x - 25a b x + 15a )\|b \|x +--R / +--R 5 2 4 2 3 +-+ +--R (4b x - 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 2485 + +--S 2486 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 2 2 |a \|b +--R (15b x - 30a b x + 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (16b x - 50a b x + 30a )\|x +--R / +--R 5 2 4 2 3 +--R 8b x - 16a b x + 8a b +--R , +--R +---+ +-+ +--R 2 2 2 | a \|x 2 2 2 +-+ +--R (- 15b x + 30a b x - 15a ) |- - atan(------) + (8b x - 25a b x + 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R ---------------------------------------------------------------------------- +--R 5 2 4 2 3 +--R 4b x - 8a b x + 4a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2486 + +--S 2487 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 15 |- \|b log(---------------------- + 30\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2487 + +--S 2488 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2488 + +--S 2489 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 15\|a atanh(--------) - 15 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ------------------------------------------------ +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2489 + +--S 2490 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2490 + +)clear all + +--S 2491 of 3330 +t0000:=x^(3/2)/(-a+b*x)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 2491 + +--S 2492 of 3330 +r0000:=-1/2*x^(3/2)/(b*(a-b*x)^2)-_ + 3/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))/(b^(5/2)*sqrt(a))+_ + 3/4*sqrt(x)/(b^2*(a-b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (- 3b x + 6a b x - 3a )atanh(--------) + (- 5b x + 3a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4b x - 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 2492 + +--S 2493 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +---+ +--R 2 2 2 - 2a b\|x + (b x + a)\|a b +--R (3b x - 6a b x + 3a )log(----------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 10b x + 6a)\|a b \|x +--R / +--R 4 2 3 2 2 +---+ +--R (8b x - 16a b x + 8a b )\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (- 3b x + 6a b x - 3a )atan(------------) + (- 5b x + 3a)\|- a b \|x +--R a +--R ----------------------------------------------------------------------] +--R 4 2 3 2 2 +-----+ +--R (4b x - 8a b x + 4a b )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2493 + +--S 2494 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R 3\|a \|b log(----------------------------) + 6\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression(Integer) +--E 2494 + +--S 2495 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2495 + +--S 2496 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 3\|- a b atanh(--------) - 3\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 4b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2496 + +--S 2497 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2497 + +)clear all + +--S 2498 of 3330 +t0000:=sqrt(x)/(-a+b*x)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 2498 + +--S 2499 of 3330 +r0000:=1/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(3/2))-_ + 1/2*sqrt(x)/(b*(a-b*x)^2)+1/4*sqrt(x)/(a*b*(a-b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (b x - 2a b x + a )atanh(--------) + (- b x - a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x - 8a b x + 4a b)\|a \|b +--R Type: Expression(Integer) +--E 2499 + +--S 2500 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +---+ +--R 2 2 2 2a b\|x + (b x + a)\|a b +--R (b x - 2a b x + a )log(--------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 2b x - 2a)\|a b \|x +--R / +--R 3 2 2 2 3 +---+ +--R (8a b x - 16a b x + 8a b)\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (b x - 2a b x + a )atan(------------) + (- b x - a)\|- a b \|x +--R a +--R ----------------------------------------------------------------] +--R 3 2 2 2 3 +-----+ +--R (4a b x - 8a b x + 4a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2500 + +--S 2501 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(--------------------------) - 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 2501 + +--S 2502 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2502 + +--S 2503 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R - \|- a b atanh(--------) + \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R 4a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2503 + +--S 2504 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2504 + +)clear all + +--S 2505 of 3330 +t0000:=1/((-a+b*x)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (b x - 3a b x + 3a b x - a )\|x +--R Type: Expression(Integer) +--E 2505 + +--S 2506 of 3330 +r0000:=-3/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*sqrt(b))-_ + 1/2*sqrt(x)/(a*(a-b*x)^2)-3/4*sqrt(x)/(a^2*(a-b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (- 3b x + 6a b x - 3a )atanh(--------) + (3b x - 5a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------------- +--R 2 2 2 3 4 +-+ +-+ +--R (4a b x - 8a b x + 4a )\|a \|b +--R Type: Expression(Integer) +--E 2506 + +--S 2507 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +---+ +--R 2 2 2 - 2a b\|x + (b x + a)\|a b +--R (3b x - 6a b x + 3a )log(----------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (6b x - 10a)\|a b \|x +--R / +--R 2 2 2 3 4 +---+ +--R (8a b x - 16a b x + 8a )\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (- 3b x + 6a b x - 3a )atan(------------) + (3b x - 5a)\|- a b \|x +--R a +--R --------------------------------------------------------------------] +--R 2 2 2 3 4 +-----+ +--R (4a b x - 8a b x + 4a )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2507 + +--S 2508 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R 3\|a \|b log(----------------------------) + 6\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a \|a \|b \|a b +--R Type: Expression(Integer) +--E 2508 + +--S 2509 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2509 + +--S 2510 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 3\|- a b atanh(--------) - 3\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 4a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2510 + +--S 2511 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2511 + +)clear all + +--S 2512 of 3330 +t0000:=1/(x^(3/2)*(-a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (b x - 3a b x + 3a b x - a x)\|x +--R Type: Expression(Integer) +--E 2512 + +--S 2513 of 3330 +r0000:=-15/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(7/2)+_ + 15/4/(a^3*sqrt(x))+(-1/2)/(a*(a-b*x)^2*sqrt(x))+_ + (-5/4)/(a^2*(a-b*x)*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (15b x - 25a b x + 8a )\|a +--R / +--R 3 2 2 4 5 +-+ +-+ +--R (4a b x - 8a b x + 4a )\|a \|x +--R Type: Expression(Integer) +--E 2513 + +--S 2514 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 2 2 2 |b +-+ \|a 2 2 +--R (15b x - 30a b x + 15a ) |- \|x log(----------------------) + 30b x +--R \|a b x - a +--R + +--R 2 +--R - 50a b x + 16a +--R / +--R 3 2 2 4 5 +-+ +--R (8a b x - 16a b x + 8a )\|x +--R , +--R +---+ +-+ +--R 2 2 2 | b +-+ b\|x 2 2 2 +--R (- 15b x + 30a b x - 15a ) |- - \|x atan(-------) + 15b x - 25a b x + 8a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ---------------------------------------------------------------------------] +--R 3 2 2 4 5 +-+ +--R (4a b x - 8a b x + 4a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2514 + +--S 2515 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 15\|a |- log(----------------------) + 30\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 2515 + +--S 2516 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2516 + +--S 2517 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 15\|b atanh(--------) - 15 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) ------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 2517 + +--S 2518 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2518 + +)clear all + +--S 2519 of 3330 +t0000:=1/(x^(5/2)*(-a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (b x - 3a b x + 3a b x - a x )\|x +--R Type: Expression(Integer) +--E 2519 + +--S 2520 of 3330 +r0000:=35/12/(a^3*x^(3/2))+(-1/2)/(a*x^(3/2)*(a-b*x)^2)+_ + (-7/4)/(a^2*x^(3/2)*(a-b*x))-_ + 35/4*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)+35/4*b/(a^4*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|b \|x +--R (- 105b x + 210a b x - 105a b x)\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 175a b x + 56a b x + 8a )\|a +--R / +--R 4 2 3 5 2 6 +-+ +-+ +--R (12a b x - 24a b x + 12a x)\|a \|x +--R Type: Expression(Integer) +--E 2520 + +--S 2521 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 3 3 2 2 2 |b +-+ \|a +--R (105b x - 210a b x + 105a b x) |- \|x log(----------------------) +--R \|a b x - a +--R + +--R 3 3 2 2 2 3 +--R 210b x - 350a b x + 112a b x + 16a +--R / +--R 4 2 3 5 2 6 +-+ +--R (24a b x - 48a b x + 24a x)\|x +--R , +--R +--R +---+ +-+ +--R 3 3 2 2 2 | b +-+ b\|x 3 3 +--R (- 105b x + 210a b x - 105a b x) |- - \|x atan(-------) + 105b x +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R + +--R 2 2 2 3 +--R - 175a b x + 56a b x + 8a +--R / +--R 4 2 3 5 2 6 +-+ +--R (12a b x - 24a b x + 12a x)\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2521 + +--S 2522 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 35b\|a |- log(----------------------) + 70b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 2522 + +--S 2523 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2523 + +--S 2524 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 35b\|b atanh(--------) - 35b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) --------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 2524 + +--S 2525 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2525 + +)clear all + +--S 2526 of 3330 +t0000:=x^(5/2)*sqrt(a+b*x) +--R +--R +--R 2 +-+ +-------+ +--R (1) x \|x \|b x + a +--R Type: Expression(Integer) +--E 2526 + +--S 2527 of 3330 +r0000:=-5/64*a^4*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-_ + 5/96*a^2*x^(3/2)*sqrt(a+b*x)/b^2+_ + 1/24*a*x^(5/2)*sqrt(a+b*x)/b+1/4*x^(7/2)*sqrt(a+b*x)+_ + 5/64*a^3*sqrt(x)*sqrt(a+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x +--R - 15a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +-------+ +--R (48b x + 8a b x - 10a b x + 15a )\|b \|x \|b x + a +--R / +--R 3 +-+ +--R 192b \|b +--R Type: Expression(Integer) +--E 2527 + +--S 2528 of 3330 +--a0000:=integrate(t0000,x) +--E 2528 + +--S 2529 of 3330 +--m0000:=a0000 - r0000 +--E 2529 + +--S 2530 of 3330 +--d0000:=D(m0000,x) +--E 2530 + +)clear all + +--S 2531 of 3330 +t0000:=x^(3/2)*sqrt(a+b*x) +--R +--R +--R +-+ +-------+ +--R (1) x\|x \|b x + a +--R Type: Expression(Integer) +--E 2531 + +--S 2532 of 3330 +r0000:=1/8*a^3*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+_ + 1/12*a*x^(3/2)*sqrt(a+b*x)/b+1/3*x^(5/2)*sqrt(a+b*x)-_ + 1/8*a^2*sqrt(x)*sqrt(a+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 3a atanh(----------) + (8b x + 2a b x - 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) --------------------------------------------------------------- +--R 2 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2532 + +--S 2533 of 3330 +--a0000:=integrate(t0000,x) +--E 2533 + +--S 2534 of 3330 +--m0000:=a0000 - r0000 +--E 2534 + +--S 2535 of 3330 +--d0000:=D(m0000,x) +--E 2535 + +)clear all + +--S 2536 of 3330 +t0000:=sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-------+ +--R (1) \|x \|b x + a +--R Type: Expression(Integer) +--E 2536 + +--S 2537 of 3330 +r0000:=-1/4*a^2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+_ + 1/2*x^(3/2)*sqrt(a+b*x)+1/4*a*sqrt(x)*sqrt(a+b*x)/b +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + (2b x + a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression(Integer) +--E 2537 + +--S 2538 of 3330 +--a0000:=integrate(t0000,x) +--E 2538 + +--S 2539 of 3330 +--m0000:=a0000 - r0000 +--E 2539 + +--S 2540 of 3330 +--d0000:=D(m0000,x) +--E 2540 + +)clear all + +--S 2541 of 3330 +t0000:=sqrt(a+b*x)/sqrt(x) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2541 + +--S 2542 of 3330 +r0000:=a*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)+sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2542 + +--S 2543 of 3330 +--a0000:=integrate(t0000,x) +--E 2543 + +--S 2544 of 3330 +--m0000:=a0000 - r0000 +--E 2544 + +--S 2545 of 3330 +--d0000:=D(m0000,x) +--E 2545 + +)clear all + +--S 2546 of 3330 +t0000:=sqrt(a+b*x)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2546 + +--S 2547 of 3330 +r0000:=2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-2*sqrt(a+b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 2\|b \|x atanh(----------) - 2\|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2547 + +--S 2548 of 3330 +--a0000:=integrate(t0000,x) +--E 2548 + +--S 2549 of 3330 +--m0000:=a0000 - r0000 +--E 2549 + +--S 2550 of 3330 +--d0000:=D(m0000,x) +--E 2550 + +)clear all + +--S 2551 of 3330 +t0000:=sqrt(a+b*x)/x^(5/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2551 + +--S 2552 of 3330 +r0000:=-2/3*(a+b*x)^(3/2)/(a*x^(3/2)) +--R +--R +--R +-------+ +--R (- 2b x - 2a)\|b x + a +--R (2) ----------------------- +--R +-+ +--R 3a x\|x +--R Type: Expression(Integer) +--E 2552 + +--S 2553 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ 2 2 2 +--R (- 4b x - 4a)\|x \|b x + a + (- b + (- 2a - 4)b - a - 4a)x +--R (3) -------------------------------------------------------------- +--R 2 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 2553 + +--S 2554 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R - b + (- 2a - 4)b - a - 4a +--R (4) ---------------------------- +--R 6a +--R Type: Expression(Integer) +--E 2554 + +--S 2555 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2555 + +)clear all + +--S 2556 of 3330 +t0000:=sqrt(a+b*x)/x^(7/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2556 + +--S 2557 of 3330 +r0000:=-2/5*(a+b*x)^(3/2)/(a*x^(5/2))+4/15*b*(a+b*x)^(3/2)/(a^2*x^(3/2)) +--R +--R +--R 2 2 2 +-------+ +--R (4b x - 2a b x - 6a )\|b x + a +--R (2) -------------------------------- +--R 2 2 +-+ +--R 15a x \|x +--R Type: Expression(Integer) +--E 2557 + +--S 2558 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +-+ +-------+ +--R (4b x - 2a b x - 6a )\|x \|b x + a +--R + +--R 3 2 2 3 2 3 +--R (2b + (a + 2)b + (- 4a - a)b - 3a - 3a )x +--R / +--R 2 3 +--R 15a x +--R Type: Union(Expression(Integer),...) +--E 2558 + +--S 2559 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R 2b + (a + 2)b + (- 4a - a)b - 3a - 3a +--R (4) ------------------------------------------ +--R 2 +--R 15a +--R Type: Expression(Integer) +--E 2559 + +--S 2560 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2560 + +)clear all + +--S 2561 of 3330 +t0000:=sqrt(a+b*x)/x^(9/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2561 + +--S 2562 of 3330 +r0000:=-2/7*(a+b*x)^(3/2)/(a*x^(7/2))+8/35*b*(a+b*x)^(3/2)/(a^2*x^(5/2))-_ + 16/105*b^2*(a+b*x)^(3/2)/(a^3*x^(3/2)) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (- 16b x + 8a b x - 6a b x - 30a )\|b x + a +--R (2) ---------------------------------------------- +--R 3 3 +-+ +--R 105a x \|x +--R Type: Expression(Integer) +--E 2562 + +--S 2563 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +-------+ +--R (- 80b x + 40a b x - 30a b x - 150a )\|x \|b x + a +--R + +--R 4 3 2 2 3 2 4 +--R - 8b + (- 4a - 200)b + (a + 100a)b + (- 18a - 75a )b - 15a +--R + +--R 3 +--R - 375a +--R * +--R 4 +--R x +--R / +--R 3 4 +--R 525a x +--R Type: Union(Expression(Integer),...) +--E 2563 + +--S 2564 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 3 2 2 3 2 4 3 +--R - 8b + (- 4a - 200)b + (a + 100a)b + (- 18a - 75a )b - 15a - 375a +--R ------------------------------------------------------------------------ +--R 3 +--R 525a +--R Type: Expression(Integer) +--E 2564 + +--S 2565 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2565 + +)clear all + +--S 2566 of 3330 +t0000:=x^(5/2)*sqrt(a-b*x) +--R +--R +--R 2 +---------+ +-+ +--R (1) x \|- b x + a \|x +--R Type: Expression(Integer) +--E 2566 + +--S 2567 of 3330 +r0000:=5/64*a^4*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-_ + 5/96*a^2*x^(3/2)*sqrt(a-b*x)/b^2-1/24*a*x^(5/2)*sqrt(a-b*x)/b+_ + 1/4*x^(7/2)*sqrt(a-b*x)-5/64*a^3*sqrt(x)*sqrt(a-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x +--R 15a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 3 3 2 2 2 3 +---------+ +-+ +-+ +--R (48b x - 8a b x - 10a b x - 15a )\|- b x + a \|b \|x +--R / +--R 3 +-+ +--R 192b \|b +--R Type: Expression(Integer) +--E 2567 + +--S 2568 of 3330 +--a0000:=integrate(t0000,x) +--E 2568 + +--S 2569 of 3330 +--m0000:=a0000 - r0000 +--E 2569 + +--S 2570 of 3330 +--d0000:=D(m0000,x) +--E 2570 + +)clear all + +--S 2571 of 3330 +t0000:=x^(3/2)*sqrt(a-b*x) +--R +--R +--R +---------+ +-+ +--R (1) x\|- b x + a \|x +--R Type: Expression(Integer) +--E 2571 + +--S 2572 of 3330 +r0000:=1/8*a^3*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-_ + 1/12*a*x^(3/2)*sqrt(a-b*x)/b+1/3*x^(5/2)*sqrt(a-b*x)-_ + 1/8*a^2*sqrt(x)*sqrt(a-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +---------+ +-+ +-+ +--R 3a atan(------------) + (8b x - 2a b x - 3a )\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) ------------------------------------------------------------------ +--R 2 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2572 + +--S 2573 of 3330 +--a0000:=integrate(t0000,x) +--E 2573 + +--S 2574 of 3330 +--m0000:=a0000 - r0000 +--E 2574 + +--S 2575 of 3330 +--d0000:=D(m0000,x) +--E 2575 + +)clear all + +--S 2576 of 3330 +t0000:=sqrt(x)*sqrt(a-b*x) +--R +--R +--R +---------+ +-+ +--R (1) \|- b x + a \|x +--R Type: Expression(Integer) +--E 2576 + +--S 2577 of 3330 +r0000:=1/4*a^2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+_ + 1/2*x^(3/2)*sqrt(a-b*x)-1/4*a*sqrt(x)*sqrt(a-b*x)/b +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + (2b x - a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) ----------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression(Integer) +--E 2577 + +--S 2578 of 3330 +--a0000:=integrate(t0000,x) +--E 2578 + +--S 2579 of 3330 +--m0000:=a0000 - r0000 +--E 2579 + +--S 2580 of 3330 +--d0000:=D(m0000,x) +--E 2580 + +)clear all + +--S 2581 of 3330 +t0000:=sqrt(a-b*x)/sqrt(x) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2581 + +--S 2582 of 3330 +r0000:=a*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)+sqrt(x)*sqrt(a-b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) ------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2582 + +--S 2583 of 3330 +--a0000:=integrate(t0000,x) +--E 2583 + +--S 2584 of 3330 +--m0000:=a0000 - r0000 +--E 2584 + +--S 2585 of 3330 +--d0000:=D(m0000,x) +--E 2585 + +)clear all + +--S 2586 of 3330 +t0000:=sqrt(a-b*x)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2586 + +--S 2587 of 3330 +r0000:=-2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))*sqrt(b)-2*sqrt(a-b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 2\|b \|x atan(------------) - 2\|- b x + a +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2587 + +--S 2588 of 3330 +--a0000:=integrate(t0000,x) +--E 2588 + +--S 2589 of 3330 +--m0000:=a0000 - r0000 +--E 2589 + +--S 2590 of 3330 +--d0000:=D(m0000,x) +--E 2590 + +)clear all + +--S 2591 of 3330 +t0000:=sqrt(a-b*x)/x^(5/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2591 + +--S 2592 of 3330 +r0000:=-2/3*(a-b*x)^(3/2)/(a*x^(3/2)) +--R +--R +--R +---------+ +--R (2b x - 2a)\|- b x + a +--R (2) ----------------------- +--R +-+ +--R 3a x\|x +--R Type: Expression(Integer) +--E 2592 + +--S 2593 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ 2 2 2 +--R (10b x - 10a)\|- b x + a \|x + (25b + (- 50a - 1)b + 25a + a)x +--R (3) ------------------------------------------------------------------ +--R 2 +--R 15a x +--R Type: Union(Expression(Integer),...) +--E 2593 + +--S 2594 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R 25b + (- 50a - 1)b + 25a + a +--R (4) ------------------------------ +--R 15a +--R Type: Expression(Integer) +--E 2594 + +--S 2595 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2595 + +)clear all + +--S 2596 of 3330 +t0000:=sqrt(a-b*x)/x^(7/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2596 + +--S 2597 of 3330 +r0000:=-2/5*(a-b*x)^(3/2)/(a*x^(5/2))-4/15*b*(a-b*x)^(3/2)/(a^2*x^(3/2)) +--R +--R +--R 2 2 2 +---------+ +--R (4b x + 2a b x - 6a )\|- b x + a +--R (2) ---------------------------------- +--R 2 2 +-+ +--R 15a x \|x +--R Type: Expression(Integer) +--E 2597 + +--S 2598 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +---------+ +-+ +--R (8b x + 4a b x - 12a )\|- b x + a \|x +--R + +--R 3 2 2 3 2 3 +--R (8b + (- 4a - 2)b + (- 16a - a)b + 12a + 3a )x +--R / +--R 2 3 +--R 30a x +--R Type: Union(Expression(Integer),...) +--E 2598 + +--S 2599 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R 8b + (- 4a - 2)b + (- 16a - a)b + 12a + 3a +--R (4) ----------------------------------------------- +--R 2 +--R 30a +--R Type: Expression(Integer) +--E 2599 + +--S 2600 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2600 + +)clear all + +--S 2601 of 3330 +t0000:=sqrt(a-b*x)/x^(9/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2601 + +--S 2602 of 3330 +r0000:=-2/7*(a-b*x)^(3/2)/(a*x^(7/2))-8/35*b*(a-b*x)^(3/2)/(a^2*x^(5/2))-_ + 16/105*b^2*(a-b*x)^(3/2)/(a^3*x^(3/2)) +--R +--R +--R 3 3 2 2 2 3 +---------+ +--R (16b x + 8a b x + 6a b x - 30a )\|- b x + a +--R (2) ---------------------------------------------- +--R 3 3 +-+ +--R 105a x \|x +--R Type: Expression(Integer) +--E 2602 + +--S 2603 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +---------+ +-+ +--R (48b x + 24a b x + 18a b x - 90a )\|- b x + a \|x +--R + +--R 4 3 2 2 3 2 4 3 4 +--R (72b + (- 36a - 8)b + (- 9a - 4a)b + (- 162a - 3a )b + 135a + 15a )x +--R / +--R 3 4 +--R 315a x +--R Type: Union(Expression(Integer),...) +--E 2603 + +--S 2604 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 3 2 2 3 2 4 3 +--R 72b + (- 36a - 8)b + (- 9a - 4a)b + (- 162a - 3a )b + 135a + 15a +--R ----------------------------------------------------------------------- +--R 3 +--R 315a +--R Type: Expression(Integer) +--E 2604 + +--S 2605 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2605 + +)clear all + +--S 2606 of 3330 +t0000:=x^(5/2)*sqrt(2+b*x) +--R +--R +--R 2 +-+ +-------+ +--R (1) x \|x \|b x + 2 +--R Type: Expression(Integer) +--E 2606 + +--S 2607 of 3330 +r0000:=-5/4*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 5/24*x^(3/2)*sqrt(2+b*x)/b^2+1/12*x^(5/2)*sqrt(2+b*x)/b+_ + 1/4*x^(7/2)*sqrt(2+b*x)+5/8*sqrt(x)*sqrt(2+b*x)/b^3 +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +-+ +-+ +-------+ +--R - 30asinh(--------) + (6b x + 2b x - 5b x + 15)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------------- +--R 3 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2607 + +--S 2608 of 3330 +--a0000:=integrate(t0000,x) +--E 2608 + +--S 2609 of 3330 +--m0000:=a0000 - r0000 +--E 2609 + +--S 2610 of 3330 +--d0000:=D(m0000,x) +--E 2610 + +)clear all + +--S 2611 of 3330 +t0000:=x^(3/2)*sqrt(2+b*x) +--R +--R +--R +-+ +-------+ +--R (1) x\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2611 + +--S 2612 of 3330 +r0000:=asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+1/6*x^(3/2)*sqrt(2+b*x)/b+_ + 1/3*x^(5/2)*sqrt(2+b*x)-1/2*sqrt(x)*sqrt(2+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +-+ +-+ +-------+ +--R 6asinh(--------) + (2b x + b x - 3)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------ +--R 2 +-+ +--R 6b \|b +--R Type: Expression(Integer) +--E 2612 + +--S 2613 of 3330 +--a0000:=integrate(t0000,x) +--E 2613 + +--S 2614 of 3330 +--m0000:=a0000 - r0000 +--E 2614 + +--S 2615 of 3330 +--d0000:=D(m0000,x) +--E 2615 + +)clear all + +--S 2616 of 3330 +t0000:=sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-------+ +--R (1) \|x \|b x + 2 +--R Type: Expression(Integer) +--E 2616 + +--S 2617 of 3330 +r0000:=-asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+1/2*x^(3/2)*sqrt(2+b*x)+_ + 1/2*sqrt(x)*sqrt(2+b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R - 2asinh(--------) + (b x + 1)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------ +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 2617 + +--S 2618 of 3330 +--a0000:=integrate(t0000,x) +--E 2618 + +--S 2619 of 3330 +--m0000:=a0000 - r0000 +--E 2619 + +--S 2620 of 3330 +--d0000:=D(m0000,x) +--E 2620 + +)clear all + +--S 2621 of 3330 +t0000:=sqrt(2+b*x)/sqrt(x) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2621 + +--S 2622 of 3330 +r0000:=2*asinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R 2asinh(--------) + \|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2622 + +--S 2623 of 3330 +--a0000:=integrate(t0000,x) +--E 2623 + +--S 2624 of 3330 +--m0000:=a0000 - r0000 +--E 2624 + +--S 2625 of 3330 +--d0000:=D(m0000,x) +--E 2625 + +)clear all + +--S 2626 of 3330 +t0000:=sqrt(2+b*x)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2626 + +--S 2627 of 3330 +r0000:=2*asinh(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*sqrt(2+b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 2\|b \|x asinh(--------) - 2\|b x + 2 +--R +-+ +--R \|2 +--R (2) -------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2627 + +--S 2628 of 3330 +--a0000:=integrate(t0000,x) +--E 2628 + +--S 2629 of 3330 +--m0000:=a0000 - r0000 +--E 2629 + +--S 2630 of 3330 +--d0000:=D(m0000,x) +--E 2630 + +)clear all + +--S 2631 of 3330 +t0000:=sqrt(2+b*x)/x^(5/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2631 + +--S 2632 of 3330 +r0000:=-1/3*(2+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (- b x - 2)\|b x + 2 +--R (2) --------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2632 + +--S 2633 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ 2 2 +--R (- 8b x - 16)\|x \|b x + 2 + (- b - 20b - 36)x +--R (3) ------------------------------------------------- +--R 2 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 2633 + +--S 2634 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - b - 20b - 36 +--R (4) --------------- +--R 24 +--R Type: Expression(Integer) +--E 2634 + +--S 2635 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2635 + +)clear all + +--S 2636 of 3330 +t0000:=sqrt(2+b*x)/x^(7/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2636 + +--S 2637 of 3330 +r0000:=-1/5*(2+b*x)^(3/2)/x^(5/2)+1/15*b*(2+b*x)^(3/2)/x^(3/2) +--R +--R +--R 2 2 +-------+ +--R (b x - b x - 6)\|b x + 2 +--R (2) -------------------------- +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 2637 + +--S 2638 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +-+ +-------+ 3 2 3 +--R (2b x - 2b x - 12)\|x \|b x + 2 + (b + 2b - 9b - 18)x +--R (3) ---------------------------------------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 2638 + +--S 2639 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R b + 2b - 9b - 18 +--R (4) ------------------ +--R 30 +--R Type: Expression(Integer) +--E 2639 + +--S 2640 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2640 + +)clear all + +--S 2641 of 3330 +t0000:=sqrt(2+b*x)/x^(9/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2641 + +--S 2642 of 3330 +r0000:=-1/7*(2+b*x)^(3/2)/x^(7/2)+2/35*b*(2+b*x)^(3/2)/x^(5/2)-_ + 2/105*b^2*(2+b*x)^(3/2)/x^(3/2) +--R +--R +--R 3 3 2 2 +-------+ +--R (- 2b x + 2b x - 3b x - 30)\|b x + 2 +--R (2) --------------------------------------- +--R 3 +-+ +--R 105x \|x +--R Type: Expression(Integer) +--E 2642 + +--S 2643 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 +-+ +-------+ +--R (- 12b x + 12b x - 18b x - 180)\|x \|b x + 2 +--R + +--R 4 3 2 4 +--R (- 2b - 20b + 19b - 63b - 330)x +--R / +--R 4 +--R 630x +--R Type: Union(Expression(Integer),...) +--E 2643 + +--S 2644 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 +--R - 2b - 20b + 19b - 63b - 330 +--R (4) ------------------------------- +--R 630 +--R Type: Expression(Integer) +--E 2644 + +--S 2645 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2645 + +)clear all + +--S 2646 of 3330 +t0000:=x^(5/2)*sqrt(2-b*x) +--R +--R +--R 2 +---------+ +-+ +--R (1) x \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2646 + +--S 2647 of 3330 +r0000:=5/4*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 5/24*x^(3/2)*sqrt(2-b*x)/b^2-1/12*x^(5/2)*sqrt(2-b*x)/b+_ + 1/4*x^(7/2)*sqrt(2-b*x)-5/8*sqrt(x)*sqrt(2-b*x)/b^3 +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +---------+ +-+ +-+ +--R 30asin(--------) + (6b x - 2b x - 5b x - 15)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------------ +--R 3 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2647 + +--S 2648 of 3330 +--a0000:=integrate(t0000,x) +--E 2648 + +--S 2649 of 3330 +--m0000:=a0000 - r0000 +--E 2649 + +--S 2650 of 3330 +--d0000:=D(m0000,x) +--E 2650 + +)clear all + +--S 2651 of 3330 +t0000:=x^(3/2)*sqrt(2-b*x) +--R +--R +--R +---------+ +-+ +--R (1) x\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2651 + +--S 2652 of 3330 +r0000:=asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-_ + 1/6*x^(3/2)*sqrt(2-b*x)/b+1/3*x^(5/2)*sqrt(2-b*x)-_ + 1/2*sqrt(x)*sqrt(2-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +---------+ +-+ +-+ +--R 6asin(--------) + (2b x - b x - 3)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------- +--R 2 +-+ +--R 6b \|b +--R Type: Expression(Integer) +--E 2652 + +--S 2653 of 3330 +--a0000:=integrate(t0000,x) +--E 2653 + +--S 2654 of 3330 +--m0000:=a0000 - r0000 +--E 2654 + +--S 2655 of 3330 +--d0000:=D(m0000,x) +--E 2655 + +)clear all + +--S 2656 of 3330 +t0000:=sqrt(x)*sqrt(2-b*x) +--R +--R +--R +---------+ +-+ +--R (1) \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2656 + +--S 2657 of 3330 +r0000:=asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+1/2*x^(3/2)*sqrt(2-b*x)-_ + 1/2*sqrt(x)*sqrt(2-b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R 2asin(--------) + (b x - 1)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ----------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 2657 + +--S 2658 of 3330 +--a0000:=integrate(t0000,x) +--E 2658 + +--S 2659 of 3330 +--m0000:=a0000 - r0000 +--E 2659 + +--S 2660 of 3330 +--d0000:=D(m0000,x) +--E 2660 + +)clear all + +--S 2661 of 3330 +t0000:=sqrt(2-b*x)/sqrt(x) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2661 + +--S 2662 of 3330 +r0000:=2*asin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+sqrt(x)*sqrt(2-b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R 2asin(--------) + \|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) -------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2662 + +--S 2663 of 3330 +--a0000:=integrate(t0000,x) +--E 2663 + +--S 2664 of 3330 +--m0000:=a0000 - r0000 +--E 2664 + +--S 2665 of 3330 +--d0000:=D(m0000,x) +--E 2665 + +)clear all + +--S 2666 of 3330 +t0000:=sqrt(2-b*x)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2666 + +--S 2667 of 3330 +r0000:=-2*asin(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*sqrt(2-b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 2\|b \|x asin(--------) - 2\|- b x + 2 +--R +-+ +--R \|2 +--R (2) ----------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2667 + +--S 2668 of 3330 +--a0000:=integrate(t0000,x) +--E 2668 + +--S 2669 of 3330 +--m0000:=a0000 - r0000 +--E 2669 + +--S 2670 of 3330 +--d0000:=D(m0000,x) +--E 2670 + +)clear all + +--S 2671 of 3330 +t0000:=sqrt(2-b*x)/x^(5/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2671 + +--S 2672 of 3330 +r0000:=-1/3*(2-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R (2) --------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2672 + +--S 2673 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ 2 2 +--R (8b x - 16)\|- b x + 2 \|x + (- 16b + 65b - 66)x +--R (3) --------------------------------------------------- +--R 2 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 2673 + +--S 2674 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - 16b + 65b - 66 +--R (4) ----------------- +--R 24 +--R Type: Expression(Integer) +--E 2674 + +--S 2675 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2675 + +)clear all + +--S 2676 of 3330 +t0000:=sqrt(2-b*x)/x^(7/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2676 + +--S 2677 of 3330 +r0000:=-1/5*(2-b*x)^(3/2)/x^(5/2)-1/15*b*(2-b*x)^(3/2)/x^(3/2) +--R +--R +--R 2 2 +---------+ +--R (b x + b x - 6)\|- b x + 2 +--R (2) ---------------------------- +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 2677 + +--S 2678 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +---------+ +-+ 3 2 3 +--R (2b x + 2b x - 12)\|- b x + 2 \|x + (- b + 2b + 9b - 18)x +--R (3) -------------------------------------------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 2678 + +--S 2679 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R - b + 2b + 9b - 18 +--R (4) -------------------- +--R 30 +--R Type: Expression(Integer) +--E 2679 + +--S 2680 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2680 + +)clear all + +--S 2681 of 3330 +t0000:=sqrt(2-b*x)/x^(9/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2681 + +--S 2682 of 3330 +r0000:=-1/7*(2-b*x)^(3/2)/x^(7/2)-2/35*b*(2-b*x)^(3/2)/x^(5/2)-_ + 2/105*b^2*(2-b*x)^(3/2)/x^(3/2) +--R +--R +--R 3 3 2 2 +---------+ +--R (2b x + 2b x + 3b x - 30)\|- b x + 2 +--R (2) --------------------------------------- +--R 3 +-+ +--R 105x \|x +--R Type: Expression(Integer) +--E 2682 + +--S 2683 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 +---------+ +-+ 4 3 2 4 +--R (4b x + 4b x + 6b x - 60)\|- b x + 2 \|x + (2b - 4b - 3b - 39b + 90)x +--R ---------------------------------------------------------------------------- +--R 4 +--R 210x +--R Type: Union(Expression(Integer),...) +--E 2683 + +--S 2684 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 +--R 2b - 4b - 3b - 39b + 90 +--R (4) -------------------------- +--R 210 +--R Type: Expression(Integer) +--E 2684 + +--S 2685 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2685 + +)clear all + +--S 2686 of 3330 +t0000:=x^(5/2)*(a+b*x)^(3/2) +--R +--R +--R 3 2 +-+ +-------+ +--R (1) (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 2686 + +--S 2687 of 3330 +r0000:=1/5*x^(7/2)*(a+b*x)^(3/2)-_ + 3/128*a^5*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-_ + 1/64*a^3*x^(3/2)*sqrt(a+b*x)/b^2+1/80*a^2*x^(5/2)*sqrt(a+b*x)/b+_ + 3/40*a*x^(7/2)*sqrt(a+b*x)+3/128*a^4*sqrt(x)*sqrt(a+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 5 \|b \|x +--R - 15a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-+ +-------+ +--R (128b x + 176a b x + 8a b x - 10a b x + 15a )\|b \|x \|b x + a +--R / +--R 3 +-+ +--R 640b \|b +--R Type: Expression(Integer) +--E 2687 + +--S 2688 of 3330 +--a0000:=integrate(t0000,x) +--E 2688 + +--S 2689 of 3330 +--m0000:=a0000 - r0000 +--E 2689 + +--S 2690 of 3330 +--d0000:=D(m0000,x) +--E 2690 + +)clear all + +--S 2691 of 3330 +t0000:=x^(3/2)*(a+b*x)^(3/2) +--R +--R +--R 2 +-+ +-------+ +--R (1) (b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 2691 + +--S 2692 of 3330 +r0000:=1/4*x^(5/2)*(a+b*x)^(3/2)+_ + 3/64*a^4*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+_ + 1/32*a^2*x^(3/2)*sqrt(a+b*x)/b+1/8*a*x^(5/2)*sqrt(a+b*x)-_ + 3/64*a^3*sqrt(x)*sqrt(a+b*x)/b^2 +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x 3 3 2 2 2 3 +-+ +-+ +-------+ +--R 3a atanh(----------) + (16b x + 24a b x + 2a b x - 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +-+ +--R 64b \|b +--R Type: Expression(Integer) +--E 2692 + +--S 2693 of 3330 +--a0000:=integrate(t0000,x) +--E 2693 + +--S 2694 of 3330 +--m0000:=a0000 - r0000 +--E 2694 + +--S 2695 of 3330 +--d0000:=D(m0000,x) +--E 2695 + +)clear all + +--S 2696 of 3330 +t0000:=(a+b*x)^(3/2)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R (1) (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 2696 + +--S 2697 of 3330 +r0000:=1/3*x^(3/2)*(a+b*x)^(3/2)-_ + 1/8*a^3*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+_ + 1/4*a*x^(3/2)*sqrt(a+b*x)+1/8*a^2*sqrt(x)*sqrt(a+b*x)/b +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 3a atanh(----------) + (8b x + 14a b x + 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ------------------------------------------------------------------ +--R +-+ +--R 24b\|b +--R Type: Expression(Integer) +--E 2697 + +--S 2698 of 3330 +--a0000:=integrate(t0000,x) +--E 2698 + +--S 2699 of 3330 +--m0000:=a0000 - r0000 +--E 2699 + +--S 2700 of 3330 +--d0000:=D(m0000,x) +--E 2700 + +)clear all + +--S 2701 of 3330 +t0000:=(a+b*x)^(3/2)/sqrt(x) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2701 + +--S 2702 of 3330 +r0000:=3/4*a^2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)+_ + 1/2*(a+b*x)^(3/2)*sqrt(x)+3/4*a*sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x + 5a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 2702 + +--S 2703 of 3330 +--a0000:=integrate(t0000,x) +--E 2703 + +--S 2704 of 3330 +--m0000:=a0000 - r0000 +--E 2704 + +--S 2705 of 3330 +--d0000:=D(m0000,x) +--E 2705 + +)clear all + +--S 2706 of 3330 +t0000:=(a+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2706 + +--S 2707 of 3330 +r0000:=3*a*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-_ + 2*(a+b*x)^(3/2)/sqrt(x)+3*b*sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 3a\|b \|x atanh(----------) + (b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (2) -------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2707 + +--S 2708 of 3330 +--a0000:=integrate(t0000,x) +--E 2708 + +--S 2709 of 3330 +--m0000:=a0000 - r0000 +--E 2709 + +--S 2710 of 3330 +--d0000:=D(m0000,x) +--E 2710 + +)clear all + +--S 2711 of 3330 +t0000:=(a+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2711 + +--S 2712 of 3330 +r0000:=-2/3*(a+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))-2*b*sqrt(a+b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 6b x\|b \|x atanh(----------) + (- 8b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (2) ------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2712 + +--S 2713 of 3330 +--a0000:=integrate(t0000,x) +--E 2713 + +--S 2714 of 3330 +--m0000:=a0000 - r0000 +--E 2714 + +--S 2715 of 3330 +--d0000:=D(m0000,x) +--E 2715 + +)clear all + +--S 2716 of 3330 +t0000:=x^(5/2)*(a-b*x)^(3/2) +--R +--R +--R 3 2 +---------+ +-+ +--R (1) (- b x + a x )\|- b x + a \|x +--R Type: Expression(Integer) +--E 2716 + +--S 2717 of 3330 +r0000:=1/5*x^(7/2)*(a-b*x)^(3/2)+_ + 3/128*a^5*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-_ + 1/64*a^3*x^(3/2)*sqrt(a-b*x)/b^2-1/80*a^2*x^(5/2)*sqrt(a-b*x)/b+_ + 3/40*a*x^(7/2)*sqrt(a-b*x)-3/128*a^4*sqrt(x)*sqrt(a-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 5 \|b \|x +--R 15a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +---------+ +-+ +-+ +--R (- 128b x + 176a b x - 8a b x - 10a b x - 15a )\|- b x + a \|b \|x +--R / +--R 3 +-+ +--R 640b \|b +--R Type: Expression(Integer) +--E 2717 + +--S 2718 of 3330 +--a0000:=integrate(t0000,x) +--E 2718 + +--S 2719 of 3330 +--m0000:=a0000 - r0000 +--E 2719 + +--S 2720 of 3330 +--d0000:=D(m0000,x) +--E 2720 + +)clear all + +--S 2721 of 3330 +t0000:=x^(3/2)*(a-b*x)^(3/2) +--R +--R +--R 2 +---------+ +-+ +--R (1) (- b x + a x)\|- b x + a \|x +--R Type: Expression(Integer) +--E 2721 + +--S 2722 of 3330 +r0000:=1/4*x^(5/2)*(a-b*x)^(3/2)+_ + 3/64*a^4*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-_ + 1/32*a^2*x^(3/2)*sqrt(a-b*x)/b+1/8*a*x^(5/2)*sqrt(a-b*x)-_ + 3/64*a^3*sqrt(x)*sqrt(a-b*x)/b^2 +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x +--R 3a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 3 3 2 2 2 3 +---------+ +-+ +-+ +--R (- 16b x + 24a b x - 2a b x - 3a )\|- b x + a \|b \|x +--R / +--R 2 +-+ +--R 64b \|b +--R Type: Expression(Integer) +--E 2722 + +--S 2723 of 3330 +--a0000:=integrate(t0000,x) +--E 2723 + +--S 2724 of 3330 +--m0000:=a0000 - r0000 +--E 2724 + +--S 2725 of 3330 +--d0000:=D(m0000,x) +--E 2725 + +)clear all + +--S 2726 of 3330 +t0000:=(a-b*x)^(3/2)*sqrt(x) +--R +--R +--R +---------+ +-+ +--R (1) (- b x + a)\|- b x + a \|x +--R Type: Expression(Integer) +--E 2726 + +--S 2727 of 3330 +r0000:=1/3*x^(3/2)*(a-b*x)^(3/2)+_ + 1/8*a^3*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+_ + 1/4*a*x^(3/2)*sqrt(a-b*x)-1/8*a^2*sqrt(x)*sqrt(a-b*x)/b +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +---------+ +-+ +-+ +--R 3a atan(------------) + (- 8b x + 14a b x - 3a )\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------------------- +--R +-+ +--R 24b\|b +--R Type: Expression(Integer) +--E 2727 + +--S 2728 of 3330 +--a0000:=integrate(t0000,x) +--E 2728 + +--S 2729 of 3330 +--m0000:=a0000 - r0000 +--E 2729 + +--S 2730 of 3330 +--d0000:=D(m0000,x) +--E 2730 + +)clear all + +--S 2731 of 3330 +t0000:=(a-b*x)^(3/2)/sqrt(x) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (1) ----------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2731 + +--S 2732 of 3330 +r0000:=3/4*a^2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)+_ + 1/2*(a-b*x)^(3/2)*sqrt(x)+3/4*a*sqrt(x)*sqrt(a-b*x) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R 3a atan(------------) + (- 2b x + 5a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 2732 + +--S 2733 of 3330 +--a0000:=integrate(t0000,x) +--E 2733 + +--S 2734 of 3330 +--m0000:=a0000 - r0000 +--E 2734 + +--S 2735 of 3330 +--d0000:=D(m0000,x) +--E 2735 + +)clear all + +--S 2736 of 3330 +t0000:=(a-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (1) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2736 + +--S 2737 of 3330 +r0000:=-3*a*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))*sqrt(b)-2*(a-b*x)^(3/2)/sqrt(x)-_ + 3*b*sqrt(x)*sqrt(a-b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 3a\|b \|x atan(------------) + (- b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2737 + +--S 2738 of 3330 +--a0000:=integrate(t0000,x) +--E 2738 + +--S 2739 of 3330 +--m0000:=a0000 - r0000 +--E 2739 + +--S 2740 of 3330 +--d0000:=D(m0000,x) +--E 2740 + +)clear all + +--S 2741 of 3330 +t0000:=(a-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (1) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2741 + +--S 2742 of 3330 +r0000:=-2/3*(a-b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))+2*b*sqrt(a-b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R 6b x\|b \|x atan(------------) + (8b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (2) -------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2742 + +--S 2743 of 3330 +--a0000:=integrate(t0000,x) +--E 2743 + +--S 2744 of 3330 +--m0000:=a0000 - r0000 +--E 2744 + +--S 2745 of 3330 +--d0000:=D(m0000,x) +--E 2745 + +)clear all + +--S 2746 of 3330 +t0000:=x^(5/2)*(2+b*x)^(3/2) +--R +--R +--R 3 2 +-+ +-------+ +--R (1) (b x + 2x )\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2746 + +--S 2747 of 3330 +r0000:=1/5*x^(7/2)*(2+b*x)^(3/2)-_ + 3/4*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 1/8*x^(3/2)*sqrt(2+b*x)/b^2+1/20*x^(5/2)*sqrt(2+b*x)/b+_ + 3/20*x^(7/2)*sqrt(2+b*x)+3/8*sqrt(x)*sqrt(2+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R \|b \|x 4 4 3 3 2 2 +-+ +-+ +-------+ +--R - 30asinh(--------) + (8b x + 22b x + 2b x - 5b x + 15)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R ---------------------------------------------------------------------------- +--R 3 +-+ +--R 40b \|b +--R Type: Expression(Integer) +--E 2747 + +--S 2748 of 3330 +--a0000:=integrate(t0000,x) +--E 2748 + +--S 2749 of 3330 +--m0000:=a0000 - r0000 +--E 2749 + +--S 2750 of 3330 +--d0000:=D(m0000,x) +--E 2750 + +)clear all + +--S 2751 of 3330 +t0000:=x^(3/2)*(2+b*x)^(3/2) +--R +--R +--R 2 +-+ +-------+ +--R (1) (b x + 2x)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2751 + +--S 2752 of 3330 +r0000:=1/4*x^(5/2)*(2+b*x)^(3/2)+_ + 3/4*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+_ + 1/8*x^(3/2)*sqrt(2+b*x)/b+1/4*x^(5/2)*sqrt(2+b*x)-_ + 3/8*sqrt(x)*sqrt(2+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +-+ +-+ +-------+ +--R 6asinh(--------) + (2b x + 6b x + b x - 3)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------------- +--R 2 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2752 + +--S 2753 of 3330 +--a0000:=integrate(t0000,x) +--E 2753 + +--S 2754 of 3330 +--m0000:=a0000 - r0000 +--E 2754 + +--S 2755 of 3330 +--d0000:=D(m0000,x) +--E 2755 + +)clear all + +--S 2756 of 3330 +t0000:=(2+b*x)^(3/2)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R (1) (b x + 2)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2756 + +--S 2757 of 3330 +r0000:=1/3*x^(3/2)*(2+b*x)^(3/2)-asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+_ + 1/2*x^(3/2)*sqrt(2+b*x)+1/2*sqrt(x)*sqrt(2+b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +-+ +-+ +-------+ +--R - 6asinh(--------) + (2b x + 7b x + 3)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) --------------------------------------------------------- +--R +-+ +--R 6b\|b +--R Type: Expression(Integer) +--E 2757 + +--S 2758 of 3330 +--a0000:=integrate(t