diff --git a/changelog b/changelog index 13bb346..5584d83 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20130720 tpd src/axiom-website/patches.html 20130720.01.tpd.patch +20130720 tpd src/input/rich2.input +20130720 tpd src/input/Makefile 20130719 tpd src/axiom-website/patches.html 20130719.01.tpd.patch 20130719 tpd src/axiom-website/CATS/index.html 20130719 tpd src/axiom-website/CATS/rich1a.input diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 15bf897..5e3b362 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4238,6 +4238,8 @@ CATS updated with txt, charlwood src/input/rich1a, rich1b 20130719.01.tpd.patch src/axiom-website/CATS/index.html, rich1a, rich1b +20130720.01.tpd.patch +src/input/rich2.input diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 0a5cccd..c366df6 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -432,7 +432,7 @@ CATSTESTS= \ These long-running tests have been split into a different group so we can run them in parallel. <>= -NEWRICHTESTS = rich1a.regress rich1b.regress +NEWRICHTESTS = rich1a.regress rich1b.regress rich2.regress RICHTESTS= \ richalgebraic000-099.regress \ @@ -786,7 +786,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/poly1.input ${OUT}/psgenfcn.input \ ${OUT}/quat.input ${OUT}/quat1.input ${OUT}/ribbon.input \ ${OUT}/ribbons.input ${OUT}/ribbonsnew.input \ - ${OUT}/rich1a.input ${OUT}/rich1b.input \ + ${OUT}/rich1a.input ${OUT}/rich1b.input ${OUT}/rich2.input \ ${OUT}/rk4draw.input \ ${OUT}/r20abugs.input \ ${OUT}/r20bugs.input ${OUT}/r21bugsbig.input \ @@ -871,7 +871,7 @@ FILES2=${OUT}/arith.input ${OUT}/bugs.input \ ${OUT}/spadprof.input \ ${OUT}/synonym2.input ${OUT}/torus.input -NEWRICHINPUT= ${OUT}/rich1a.input ${OUT}/rich1b.input +NEWRICHINPUT= ${OUT}/rich1a.input ${OUT}/rich1b.input ${OUT}/rich2.input RICHINPUT= \ ${OUT}/richalgebraic000-099.input \ @@ -1190,7 +1190,7 @@ 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}/rich1a.input.dvi ${DOC}/rich2.input.dvi \ ${DOC}/rich1b.input.dvi \ ${DOC}/richalgebraic000-099.input.dvi \ ${DOC}/richalgebraic100-199.input.dvi \ diff --git a/src/input/rich2.input.pamphlet b/src/input/rich2.input.pamphlet new file mode 100644 index 0000000..1aeae06 --- /dev/null +++ b/src/input/rich2.input.pamphlet @@ -0,0 +1,36137 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich2.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +2.1.2 (a+b x)^m (A+B x) (d+e x)^p +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich2.output +)spool rich2.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1293 +t0:=x^m*(a+b*x)*(A+B*x) +--R +--R +--R 2 m +--R (1) (B b x + (A b + B a)x + A a)x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1293 +r0:=a*A*x^(1+m)/(1+m)+(A*b+a*B)*x^(2+m)/(2+m)+b*B*x^(3+m)/(3+m) +--R +--R +--R (2) +--R 2 m + 3 +--R (B b m + 3B b m + 2B b)x +--R + +--R 2 m + 2 +--R ((A b + B a)m + (4A b + 4B a)m + 3A b + 3B a)x +--R + +--R 2 m + 1 +--R (A a m + 5A a m + 6A a)x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 +--R (B b m + 3B b m + 2B b)x +--R + +--R 2 2 +--R ((A b + B a)m + (4A b + 4B a)m + 3A b + 3B a)x +--R + +--R 2 +--R (A a m + 5A a m + 6A a)x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 +--R (B b m + 3B b m + 2B b)x +--R + +--R 2 2 +--R ((A b + B a)m + (4A b + 4B a)m + 3A b + 3B a)x +--R + +--R 2 +--R (A a m + 5A a m + 6A a)x +--R * +--R m log(x) +--R %e +--R + +--R 2 m + 3 +--R (- B b m - 3B b m - 2B b)x +--R + +--R 2 m + 2 +--R ((- A b - B a)m + (- 4A b - 4B a)m - 3A b - 3B a)x +--R + +--R 2 m + 1 +--R (- A a m - 5A a m - 6A a)x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 m log(x) m + 2 m + 1 +--R (B b x + (A b + B a)x + A a)%e - B b x + (- A b - B a)x +--R + +--R m +--R - A a x +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1293 +t0:=x^4*(a+b*x)*(A+B*x) +--R +--R +--R 6 5 4 +--R (6) B b x + (A b + B a)x + A a x +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 1293 +r0:=1/5*a*A*x^5+1/6*(A*b+a*B)*x^6+1/7*b*B*x^7 +--R +--R +--R 1 7 1 1 6 1 5 +--R (7) - B b x + (- A b + - B a)x + - A a x +--R 7 6 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 7 + +--S 8 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 7 1 1 6 1 5 +--R (8) - B b x + (- A b + - B a)x + - A a x +--R 7 6 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 1293 +m0:=a0-r0 +--R +--R +--R (9) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 9 + +--S 10 of 1293 +d0:=D(m0,x) +--R +--R +--R (10) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 10 + +--S 11 of 1293 +t0:=x^3*(a+b*x)*(A+B*x) +--R +--R +--R 5 4 3 +--R (11) B b x + (A b + B a)x + A a x +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 1293 +r0:=1/4*a*A*x^4+1/5*(A*b+a*B)*x^5+1/6*b*B*x^6 +--R +--R +--R 1 6 1 1 5 1 4 +--R (12) - B b x + (- A b + - B a)x + - A a x +--R 6 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 12 + +--S 13 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 6 1 1 5 1 4 +--R (13) - B b x + (- A b + - B a)x + - A a x +--R 6 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 1293 +m0:=a0-r0 +--R +--R +--R (14) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 of 1293 +d0:=D(m0,x) +--R +--R +--R (15) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +--S 16 of 1293 +t0:=x^2*(a+b*x)*(A+B*x) +--R +--R +--R 4 3 2 +--R (16) B b x + (A b + B a)x + A a x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 1293 +r0:=1/3*a*A*x^3+1/4*(A*b+a*B)*x^4+1/5*b*B*x^5 +--R +--R +--R 1 5 1 1 4 1 3 +--R (17) - B b x + (- A b + - B a)x + - A a x +--R 5 4 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 5 1 1 4 1 3 +--R (18) - B b x + (- A b + - B a)x + - A a x +--R 5 4 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 1293 +m0:=a0-r0 +--R +--R +--R (19) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 1293 +d0:=D(m0,x) +--R +--R +--R (20) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +--S 21 of 1293 +t0:=x*(a+b*x)*(A+B*x) +--R +--R +--R 3 2 +--R (21) B b x + (A b + B a)x + A a x +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 1293 +r0:=1/2*a*A*x^2+1/3*(A*b+a*B)*x^3+1/4*b*B*x^4 +--R +--R +--R 1 4 1 1 3 1 2 +--R (22) - B b x + (- A b + - B a)x + - A a x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 1 3 1 2 +--R (23) - B b x + (- A b + - B a)x + - A a x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 1293 +m0:=a0-r0 +--R +--R +--R (24) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 1293 +d0:=D(m0,x) +--R +--R +--R (25) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +--S 26 of 1293 +t0:=(a+b*x)*(A+B*x) +--R +--R +--R 2 +--R (26) B b x + (A b + B a)x + A a +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1293 +r0:=a*A*x+1/2*(A*b+a*B)*x^2+1/3*b*B*x^3 +--R +--R +--R 1 3 1 1 2 +--R (27) - B b x + (- A b + - B a)x + A a x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 3 1 1 2 +--R (28) - B b x + (- A b + - B a)x + A a x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1293 +m0:=a0-r0 +--R +--R +--R (29) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1293 +d0:=D(m0,x) +--R +--R +--R (30) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +--S 31 of 1293 +t0:=(a+b*x)*(A+B*x)/x +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (31) --------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 1293 +r0:=a*B*x+1/2*b*(A+B*x)^2/B+a*A*log(x) +--R +--R +--R 2 2 2 2 +--R 2A B a log(x) + B b x + (2A B b + 2B a)x + A b +--R (32) ----------------------------------------------- +--R 2B +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2A a log(x) + B b x + (2A b + 2B a)x +--R (33) ------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1293 +m0:=a0-r0 +--R +--R +--R 2 +--R A b +--R (34) - --- +--R 2B +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1293 +d0:=D(m0,x) +--R +--R +--R (35) 0 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1293 +t0:=(a+b*x)*(A+B*x)/x^2 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (36) --------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1293 +r0:=-a*A/x+b*B*x+(A*b+a*B)*log(x) +--R +--R +--R 2 +--R (A b + B a)x log(x) + B b x - A a +--R (37) ---------------------------------- +--R x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (A b + B a)x log(x) + B b x - A a +--R (38) ---------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1293 +m0:=a0-r0 +--R +--R +--R (39) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1293 +d0:=D(m0,x) +--R +--R +--R (40) 0 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1293 +t0:=(a+b*x)*(A+B*x)/x^3 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (41) --------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1293 +r0:=-1/2*a*A/x^2+(-A*b-a*B)/x+b*B*log(x) +--R +--R +--R 2 +--R 2B b x log(x) + (- 2A b - 2B a)x - A a +--R (42) -------------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2B b x log(x) + (- 2A b - 2B a)x - A a +--R (43) -------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1293 +m0:=a0-r0 +--R +--R +--R (44) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1293 +d0:=D(m0,x) +--R +--R +--R (45) 0 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 1293 +t0:=(a+b*x)*(A+B*x)/x^4 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (46) --------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1293 +r0:=-1/3*a*A/x^3+1/2*(-A*b-a*B)/x^2-b*B/x +--R +--R +--R 2 1 1 1 +--R - B b x + (- - A b - - B a)x - - A a +--R 2 2 3 +--R (47) ------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 6B b x + (- 3A b - 3B a)x - 2A a +--R (48) ----------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1293 +m0:=a0-r0 +--R +--R +--R (49) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1293 +d0:=D(m0,x) +--R +--R +--R (50) 0 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1293 +t0:=(a+b*x)*(A+B*x)/x^5 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (51) --------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1293 +r0:=-1/4*a*A/x^4+1/3*(-A*b-a*B)/x^3-1/2*b*B/x^2 +--R +--R +--R 1 2 1 1 1 +--R - - B b x + (- - A b - - B a)x - - A a +--R 2 3 3 4 +--R (52) --------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 52 + +--S 53 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 6B b x + (- 4A b - 4B a)x - 3A a +--R (53) ----------------------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1293 +m0:=a0-r0 +--R +--R +--R (54) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1293 +d0:=D(m0,x) +--R +--R +--R (55) 0 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1293 +t0:=(a+b*x)*(A+B*x)/x^6 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (56) --------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1293 +r0:=-1/5*a*A/x^5+1/4*(-A*b-a*B)/x^4-1/3*b*B/x^3 +--R +--R +--R 1 2 1 1 1 +--R - - B b x + (- - A b - - B a)x - - A a +--R 3 4 4 5 +--R (57) --------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 57 + +--S 58 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 20B b x + (- 15A b - 15B a)x - 12A a +--R (58) --------------------------------------- +--R 5 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1293 +m0:=a0-r0 +--R +--R +--R (59) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1293 +d0:=D(m0,x) +--R +--R +--R (60) 0 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1293 +t0:=x^m*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 3 2 2 2 2 m +--R (61) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1293 +r0:=a^2*A*x^(1+m)/(1+m)+a*(2*A*b+a*B)*x^(2+m)/(2+m)+_ + b*(A*b+2*a*B)*x^(3+m)/(3+m)+b^2*B*x^(4+m)/(4+m) +--R +--R +--R (62) +--R 2 3 2 2 2 2 m + 4 +--R (B b m + 6B b m + 11B b m + 6B b )x +--R + +--R 2 3 2 2 2 2 +--R (A b + 2B a b)m + (7A b + 14B a b)m + (14A b + 28B a b)m + 8A b +--R + +--R 16B a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 2 2 2 +--R (2A a b + B a )m + (16A a b + 8B a )m + (38A a b + 19B a )m +--R + +--R 2 +--R 24A a b + 12B a +--R * +--R m + 2 +--R x +--R + +--R 2 3 2 2 2 2 m + 1 +--R (A a m + 9A a m + 26A a m + 24A a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (63) +--R 2 3 2 2 2 2 4 +--R (B b m + 6B b m + 11B b m + 6B b )x +--R + +--R 2 3 2 2 2 +--R (A b + 2B a b)m + (7A b + 14B a b)m + (14A b + 28B a b)m +--R + +--R 2 +--R 8A b + 16B a b +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 2 +--R (2A a b + B a )m + (16A a b + 8B a )m + (38A a b + 19B a )m +--R + +--R 2 +--R 24A a b + 12B a +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R (A a m + 9A a m + 26A a m + 24A a )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 63 + +--S 64 of 1293 +m0:=a0-r0 +--R +--R +--R (64) +--R 2 3 2 2 2 2 4 +--R (B b m + 6B b m + 11B b m + 6B b )x +--R + +--R 2 3 2 2 2 +--R (A b + 2B a b)m + (7A b + 14B a b)m + (14A b + 28B a b)m +--R + +--R 2 +--R 8A b + 16B a b +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 2 +--R (2A a b + B a )m + (16A a b + 8B a )m + (38A a b + 19B a )m +--R + +--R 2 +--R 24A a b + 12B a +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R (A a m + 9A a m + 26A a m + 24A a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 3 2 2 2 2 m + 4 +--R (- B b m - 6B b m - 11B b m - 6B b )x +--R + +--R 2 3 2 2 2 +--R (- A b - 2B a b)m + (- 7A b - 14B a b)m + (- 14A b - 28B a b)m +--R + +--R 2 +--R - 8A b - 16B a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 2 2 2 +--R (- 2A a b - B a )m + (- 16A a b - 8B a )m + (- 38A a b - 19B a )m +--R + +--R 2 +--R - 24A a b - 12B a +--R * +--R m + 2 +--R x +--R + +--R 2 3 2 2 2 2 m + 1 +--R (- A a m - 9A a m - 26A a m - 24A a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1293 +d0:=D(m0,x) +--R +--R +--R (65) +--R 2 3 2 2 2 2 m log(x) +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )%e +--R + +--R 2 m + 3 2 m + 2 2 m + 1 2 m +--R - B b x + (- A b - 2B a b)x + (- 2A a b - B a )x - A a x +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1293 +t0:=x^4*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 7 2 6 2 5 2 4 +--R (66) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 66 + +--S 67 of 1293 +r0:=1/5*a^2*A*x^5+1/6*a*(2*A*b+a*B)*x^6+1/7*b*(A*b+2*a*B)*x^7+1/8*b^2*B*x^8 +--R +--R +--R 1 2 8 1 2 2 7 1 1 2 6 1 2 5 +--R (67) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 8 7 7 3 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 67 + +--S 68 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 8 1 2 2 7 1 1 2 6 1 2 5 +--R (68) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 8 7 7 3 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 68 + +--S 69 of 1293 +m0:=a0-r0 +--R +--R +--R (69) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 69 + +--S 70 of 1293 +d0:=D(m0,x) +--R +--R +--R (70) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 70 + +--S 71 of 1293 +t0:=x^3*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 6 2 5 2 4 2 3 +--R (71) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 71 + +--S 72 of 1293 +r0:=1/4*a^2*A*x^4+1/5*a*(2*A*b+a*B)*x^5+1/6*b*(A*b+2*a*B)*x^6+1/7*b^2*B*x^7 +--R +--R +--R 1 2 7 1 2 1 6 2 1 2 5 1 2 4 +--R (72) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 7 6 3 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 72 + +--S 73 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 7 1 2 1 6 2 1 2 5 1 2 4 +--R (73) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 7 6 3 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 1293 +m0:=a0-r0 +--R +--R +--R (74) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 1293 +d0:=D(m0,x) +--R +--R +--R (75) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +--S 76 of 1293 +t0:=x^2*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R (76) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1293 +r0:=1/3*a^2*A*x^3+1/4*a*(2*A*b+a*B)*x^4+1/5*b*(A*b+2*a*B)*x^5+1/6*b^2*B*x^6 +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (77) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (78) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1293 +m0:=a0-r0 +--R +--R +--R (79) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 79 + +--S 80 of 1293 +d0:=D(m0,x) +--R +--R +--R (80) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +--S 81 of 1293 +t0:=x*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 4 2 3 2 2 2 +--R (81) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1293 +r0:=1/2*a^2*A*x^2+1/3*a*(2*A*b+a*B)*x^3+1/4*b*(A*b+2*a*B)*x^4+1/5*b^2*B*x^5 +--R +--R +--R 1 2 5 1 2 1 4 2 1 2 3 1 2 2 +--R (82) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 5 4 2 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 5 1 2 1 4 2 1 2 3 1 2 2 +--R (83) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 5 4 2 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1293 +m0:=a0-r0 +--R +--R +--R (84) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1293 +d0:=D(m0,x) +--R +--R +--R (85) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +--S 86 of 1293 +t0:=(a+b*x)^2*(A+B*x) +--R +--R +--R 2 3 2 2 2 2 +--R (86) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 1293 +r0:=1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2 +--R +--R +--R (87) +--R 1 4 4 1 4 2 3 3 3 1 2 2 2 2 2 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x + A a b x +--R 4 3 3 2 +--R + +--R 1 3 1 4 +--R - A a b - -- B a +--R 3 12 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 4 1 2 2 3 1 2 2 2 +--R (88) - B b x + (- A b + - B a b)x + (A a b + - B a )x + A a x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1293 +m0:=a0-r0 +--R +--R +--R 1 3 1 4 +--R - - A a b + -- B a +--R 3 12 +--R (89) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 1293 +d0:=D(m0,x) +--R +--R +--R (90) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 90 + +--S 91 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (91) ---------------------------------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 1293 +r0:=2*a*A*b*x+1/2*A*b^2*x^2+1/3*B*(a+b*x)^3/b+a^2*A*log(x) +--R +--R +--R (92) +--R 2 3 3 3 2 2 2 2 3 +--R 6A a b log(x) + 2B b x + (3A b + 6B a b )x + (12A a b + 6B a b)x + 2B a +--R ---------------------------------------------------------------------------- +--R 6b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 2 2 2 +--R 6A a log(x) + 2B b x + (3A b + 6B a b)x + (12A a b + 6B a )x +--R (93) --------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1293 +m0:=a0-r0 +--R +--R +--R 3 +--R B a +--R (94) - ---- +--R 3b +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1293 +d0:=D(m0,x) +--R +--R +--R (95) 0 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^2 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (96) ---------------------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 1293 +r0:=-a^2*A/x+b*(A*b+2*a*B)*x+1/2*b^2*B*x^2+a*(2*A*b+a*B)*log(x) +--R +--R +--R 2 2 3 2 2 2 +--R (4A a b + 2B a )x log(x) + B b x + (2A b + 4B a b)x - 2A a +--R (97) -------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 2 2 2 +--R (4A a b + 2B a )x log(x) + B b x + (2A b + 4B a b)x - 2A a +--R (98) -------------------------------------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1293 +m0:=a0-r0 +--R +--R +--R (99) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1293 +d0:=D(m0,x) +--R +--R +--R (100) 0 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^3 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (101) ---------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1293 +r0:=-1/2*a^2*A/x^2-a*(2*A*b+a*B)/x+b^2*B*x+b*(A*b+2*a*B)*log(x) +--R +--R +--R 2 2 2 3 2 2 +--R (2A b + 4B a b)x log(x) + 2B b x + (- 4A a b - 2B a )x - A a +--R (102) --------------------------------------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 3 2 2 +--R (2A b + 4B a b)x log(x) + 2B b x + (- 4A a b - 2B a )x - A a +--R (103) --------------------------------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1293 +m0:=a0-r0 +--R +--R +--R (104) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1293 +d0:=D(m0,x) +--R +--R +--R (105) 0 +--R Type: Expression(Integer) +--E 105 + +--S 106 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^4 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (106) ---------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1293 +r0:=-1/3*a^2*A/x^3-1/2*a*(2*A*b+a*B)/x^2-b*(A*b+2*a*B)/x+b^2*B*log(x) +--R +--R +--R 2 3 2 2 2 2 +--R 6B b x log(x) + (- 6A b - 12B a b)x + (- 6A a b - 3B a )x - 2A a +--R (107) ------------------------------------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 2 2 +--R 6B b x log(x) + (- 6A b - 12B a b)x + (- 6A a b - 3B a )x - 2A a +--R (108) ------------------------------------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1293 +m0:=a0-r0 +--R +--R +--R (109) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1293 +d0:=D(m0,x) +--R +--R +--R (110) 0 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^5 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (111) ---------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 1293 +r0:=-1/4*a^2*A/x^4-1/3*a*(2*A*b+a*B)/x^3-1/2*b*(A*b+2*a*B)/x^2-b^2*B/x +--R +--R +--R 2 3 1 2 2 2 1 2 1 2 +--R - B b x + (- - A b - B a b)x + (- - A a b - - B a )x - - A a +--R 2 3 3 4 +--R (112) ---------------------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 2 2 +--R - 12B b x + (- 6A b - 12B a b)x + (- 8A a b - 4B a )x - 3A a +--R (113) ---------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1293 +m0:=a0-r0 +--R +--R +--R (114) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1293 +d0:=D(m0,x) +--R +--R +--R (115) 0 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^6 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (116) ---------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1293 +r0:=-1/5*a^2*A/x^5-1/4*a*(2*A*b+a*B)/x^4-1/3*b*(A*b+2*a*B)/x^3-1/2*b^2*B/x^2 +--R +--R +--R 1 2 3 1 2 2 2 1 1 2 1 2 +--R - - B b x + (- - A b - - B a b)x + (- - A a b - - B a )x - - A a +--R 2 3 3 2 4 5 +--R (117) -------------------------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 117 + +--S 118 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 2 2 +--R - 30B b x + (- 20A b - 40B a b)x + (- 30A a b - 15B a )x - 12A a +--R (118) -------------------------------------------------------------------- +--R 5 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1293 +m0:=a0-r0 +--R +--R +--R (119) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1293 +d0:=D(m0,x) +--R +--R +--R (120) 0 +--R Type: Expression(Integer) +--E 120 + +--S 121 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^7 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (121) ---------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 1293 +r0:=-1/6*a^2*A/x^6-1/5*a*(2*A*b+a*B)/x^5-1/4*b*(A*b+2*a*B)/x^4-1/3*b^2*B/x^3 +--R +--R +--R 1 2 3 1 2 1 2 2 1 2 1 2 +--R - - B b x + (- - A b - - B a b)x + (- - A a b - - B a )x - - A a +--R 3 4 2 5 5 6 +--R (122) -------------------------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 122 + +--S 123 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 2 2 +--R - 20B b x + (- 15A b - 30B a b)x + (- 24A a b - 12B a )x - 10A a +--R (123) -------------------------------------------------------------------- +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1293 +m0:=a0-r0 +--R +--R +--R (124) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1293 +d0:=D(m0,x) +--R +--R +--R (125) 0 +--R Type: Expression(Integer) +--E 125 + +--S 126 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^8 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (126) ---------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 1293 +r0:=-1/7*a^2*A/x^7-1/6*a*(2*A*b+a*B)/x^6-1/5*b*(A*b+2*a*B)/x^5-1/4*b^2*B/x^4 +--R +--R +--R 1 2 3 1 2 2 2 1 1 2 1 2 +--R - - B b x + (- - A b - - B a b)x + (- - A a b - - B a )x - - A a +--R 4 5 5 3 6 7 +--R (127) -------------------------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 127 + +--S 128 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (128) +--R 2 3 2 2 2 2 +--R - 105B b x + (- 84A b - 168B a b)x + (- 140A a b - 70B a )x - 60A a +--R ----------------------------------------------------------------------- +--R 7 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1293 +m0:=a0-r0 +--R +--R +--R (129) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1293 +d0:=D(m0,x) +--R +--R +--R (130) 0 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 1293 +t0:=x^m*(a+b*x)^3*(A+B*x) +--R +--R +--R (131) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1293 +r0:=a^3*A*x^(1+m)/(1+m)+a^2*(3*A*b+a*B)*x^(2+m)/(2+m)+_ + 3*a*b*(A*b+a*B)*x^(3+m)/(3+m)+b^2*(A*b+3*a*B)*x^(4+m)/(4+m)+_ + b^3*B*x^(5+m)/(5+m) +--R +--R +--R (132) +--R 3 4 3 3 3 2 3 3 m + 5 +--R (B b m + 10B b m + 35B b m + 50B b m + 24B b )x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (A b + 3B a b )m + (11A b + 33B a b )m + (41A b + 123B a b )m +--R + +--R 3 2 3 2 +--R (61A b + 183B a b )m + 30A b + 90B a b +--R * +--R m + 4 +--R x +--R + +--R 2 2 4 2 2 3 +--R (3A a b + 3B a b)m + (36A a b + 36B a b)m +--R + +--R 2 2 2 2 2 2 +--R (147A a b + 147B a b)m + (234A a b + 234B a b)m + 120A a b +--R + +--R 2 +--R 120B a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 4 2 3 3 2 3 2 +--R (3A a b + B a )m + (39A a b + 13B a )m + (177A a b + 59B a )m +--R + +--R 2 3 2 3 +--R (321A a b + 107B a )m + 180A a b + 60B a +--R * +--R m + 2 +--R x +--R + +--R 3 4 3 3 3 2 3 3 m + 1 +--R (A a m + 14A a m + 71A a m + 154A a m + 120A a )x +--R / +--R 5 4 3 2 +--R m + 15m + 85m + 225m + 274m + 120 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (133) +--R 3 4 3 3 3 2 3 3 5 +--R (B b m + 10B b m + 35B b m + 50B b m + 24B b )x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (A b + 3B a b )m + (11A b + 33B a b )m + (41A b + 123B a b )m +--R + +--R 3 2 3 2 +--R (61A b + 183B a b )m + 30A b + 90B a b +--R * +--R 4 +--R x +--R + +--R 2 2 4 2 2 3 +--R (3A a b + 3B a b)m + (36A a b + 36B a b)m +--R + +--R 2 2 2 2 2 2 +--R (147A a b + 147B a b)m + (234A a b + 234B a b)m + 120A a b +--R + +--R 2 +--R 120B a b +--R * +--R 3 +--R x +--R + +--R 2 3 4 2 3 3 2 3 2 +--R (3A a b + B a )m + (39A a b + 13B a )m + (177A a b + 59B a )m +--R + +--R 2 3 2 3 +--R (321A a b + 107B a )m + 180A a b + 60B a +--R * +--R 2 +--R x +--R + +--R 3 4 3 3 3 2 3 3 +--R (A a m + 14A a m + 71A a m + 154A a m + 120A a )x +--R * +--R m log(x) +--R %e +--R / +--R 5 4 3 2 +--R m + 15m + 85m + 225m + 274m + 120 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1293 +m0:=a0-r0 +--R +--R +--R (134) +--R 3 4 3 3 3 2 3 3 5 +--R (B b m + 10B b m + 35B b m + 50B b m + 24B b )x +--R + +--R 3 2 4 3 2 3 +--R (A b + 3B a b )m + (11A b + 33B a b )m +--R + +--R 3 2 2 3 2 3 2 +--R (41A b + 123B a b )m + (61A b + 183B a b )m + 30A b + 90B a b +--R * +--R 4 +--R x +--R + +--R 2 2 4 2 2 3 +--R (3A a b + 3B a b)m + (36A a b + 36B a b)m +--R + +--R 2 2 2 2 2 2 +--R (147A a b + 147B a b)m + (234A a b + 234B a b)m + 120A a b +--R + +--R 2 +--R 120B a b +--R * +--R 3 +--R x +--R + +--R 2 3 4 2 3 3 2 3 2 +--R (3A a b + B a )m + (39A a b + 13B a )m + (177A a b + 59B a )m +--R + +--R 2 3 2 3 +--R (321A a b + 107B a )m + 180A a b + 60B a +--R * +--R 2 +--R x +--R + +--R 3 4 3 3 3 2 3 3 +--R (A a m + 14A a m + 71A a m + 154A a m + 120A a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 4 3 3 3 2 3 3 m + 5 +--R (- B b m - 10B b m - 35B b m - 50B b m - 24B b )x +--R + +--R 3 2 4 3 2 3 +--R (- A b - 3B a b )m + (- 11A b - 33B a b )m +--R + +--R 3 2 2 3 2 3 2 +--R (- 41A b - 123B a b )m + (- 61A b - 183B a b )m - 30A b - 90B a b +--R * +--R m + 4 +--R x +--R + +--R 2 2 4 2 2 3 +--R (- 3A a b - 3B a b)m + (- 36A a b - 36B a b)m +--R + +--R 2 2 2 2 2 2 +--R (- 147A a b - 147B a b)m + (- 234A a b - 234B a b)m - 120A a b +--R + +--R 2 +--R - 120B a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 4 2 3 3 +--R (- 3A a b - B a )m + (- 39A a b - 13B a )m +--R + +--R 2 3 2 2 3 2 3 +--R (- 177A a b - 59B a )m + (- 321A a b - 107B a )m - 180A a b - 60B a +--R * +--R m + 2 +--R x +--R + +--R 3 4 3 3 3 2 3 3 m + 1 +--R (- A a m - 14A a m - 71A a m - 154A a m - 120A a )x +--R / +--R 5 4 3 2 +--R m + 15m + 85m + 225m + 274m + 120 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1293 +d0:=D(m0,x) +--R +--R +--R (135) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R m log(x) +--R %e +--R + +--R 3 m + 4 3 2 m + 3 2 2 m + 2 +--R - B b x + (- A b - 3B a b )x + (- 3A a b - 3B a b)x +--R + +--R 2 3 m + 1 3 m +--R (- 3A a b - B a )x - A a x +--R Type: Expression(Integer) +--E 135 + +--S 136 of 1293 +t0:=x^4*(a+b*x)^3*(A+B*x) +--R +--R +--R (136) +--R 3 8 3 2 7 2 2 6 2 3 5 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 4 +--R A a x +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 1293 +r0:=1/5*a^3*A*x^5+1/6*a^2*(3*A*b+a*B)*x^6+3/7*a*b*(A*b+a*B)*x^7+_ + 1/8*b^2*(A*b+3*a*B)*x^8+1/9*b^3*B*x^9 +--R +--R +--R (137) +--R 1 3 9 1 3 3 2 8 3 2 3 2 7 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 3 6 1 3 5 +--R (- A a b + - B a )x + - A a x +--R 2 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (138) +--R 1 3 9 1 3 3 2 8 3 2 3 2 7 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 3 6 1 3 5 +--R (- A a b + - B a )x + - A a x +--R 2 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 1293 +m0:=a0-r0 +--R +--R +--R (139) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 1293 +d0:=D(m0,x) +--R +--R +--R (140) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +--S 141 of 1293 +t0:=x^3*(a+b*x)^3*(A+B*x) +--R +--R +--R (141) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 3 +--R A a x +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 1293 +r0:=1/4*a^3*A*x^4+1/5*a^2*(3*A*b+a*B)*x^5+1/2*a*b*(A*b+a*B)*x^6+_ + 1/7*b^2*(A*b+3*a*B)*x^7+1/8*b^3*B*x^8 +--R +--R +--R (142) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A a b + - B a )x + - A a x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 142 + +--S 143 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (143) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A a b + - B a )x + - A a x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 1293 +m0:=a0-r0 +--R +--R +--R (144) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 144 + +--S 145 of 1293 +d0:=D(m0,x) +--R +--R +--R (145) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 145 + +--S 146 of 1293 +t0:=x^2*(a+b*x)^3*(A+B*x) +--R +--R +--R (146) +--R 3 6 3 2 5 2 2 4 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 2 +--R A a x +--R Type: Polynomial(Integer) +--E 146 + +--S 147 of 1293 +r0:=1/3*a^3*A*x^3+1/4*a^2*(3*A*b+a*B)*x^4+3/5*a*b*(A*b+a*B)*x^5+_ + 1/6*b^2*(A*b+3*a*B)*x^6+1/7*b^3*B*x^7 +--R +--R +--R (147) +--R 1 3 7 1 3 1 2 6 3 2 3 2 5 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 7 6 2 5 5 +--R + +--R 3 2 1 3 4 1 3 3 +--R (- A a b + - B a )x + - A a x +--R 4 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 147 + +--S 148 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (148) +--R 1 3 7 1 3 1 2 6 3 2 3 2 5 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 7 6 2 5 5 +--R + +--R 3 2 1 3 4 1 3 3 +--R (- A a b + - B a )x + - A a x +--R 4 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 148 + +--S 149 of 1293 +m0:=a0-r0 +--R +--R +--R (149) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 149 + +--S 150 of 1293 +d0:=D(m0,x) +--R +--R +--R (150) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 150 + +--S 151 of 1293 +t0:=x*(a+b*x)^3*(A+B*x) +--R +--R +--R (151) +--R 3 5 3 2 4 2 2 3 2 3 2 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a x +--R Type: Polynomial(Integer) +--E 151 + +--S 152 of 1293 +r0:=-1/4*a*(A*b-a*B)*(a+b*x)^4/b^3+1/5*(A*b-2*a*B)*(a+b*x)^5/b^3+_ + 1/6*B*(a+b*x)^6/b^3 +--R +--R +--R (152) +--R 1 6 6 1 6 3 5 5 3 5 3 2 4 4 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 6 5 5 4 4 +--R + +--R 2 4 1 3 3 3 1 3 3 2 1 5 1 6 +--R (A a b + - B a b )x + - A a b x - -- A a b + -- B a +--R 3 2 20 60 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 152 + +--S 153 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (153) +--R 1 3 6 1 3 3 2 5 3 2 3 2 4 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 6 5 5 4 4 +--R + +--R 2 1 3 3 1 3 2 +--R (A a b + - B a )x + - A a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 153 + +--S 154 of 1293 +m0:=a0-r0 +--R +--R +--R 1 5 1 6 +--R -- A a b - -- B a +--R 20 60 +--R (154) ------------------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 154 + +--S 155 of 1293 +d0:=D(m0,x) +--R +--R +--R (155) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 155 + +--S 156 of 1293 +t0:=(a+b*x)^3*(A+B*x) +--R +--R +--R (156) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 156 + +--S 157 of 1293 +r0:=1/4*(A*b-a*B)*(a+b*x)^4/b^2+1/5*B*(a+b*x)^5/b^2 +--R +--R +--R (157) +--R 1 5 5 1 5 3 4 4 4 2 3 3 +--R - B b x + (- A b + - B a b )x + (A a b + B a b )x +--R 5 4 4 +--R + +--R 3 2 3 1 3 2 2 3 2 1 4 1 5 +--R (- A a b + - B a b )x + A a b x + - A a b - -- B a +--R 2 2 4 20 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +--S 158 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (158) +--R 1 3 5 1 3 3 2 4 2 2 3 +--R - B b x + (- A b + - B a b )x + (A a b + B a b)x +--R 5 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- A a b + - B a )x + A a x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 158 + +--S 159 of 1293 +m0:=a0-r0 +--R +--R +--R 1 4 1 5 +--R - - A a b + -- B a +--R 4 20 +--R (159) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 159 + +--S 160 of 1293 +d0:=D(m0,x) +--R +--R +--R (160) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 160 + +--S 161 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x +--R +--R +--R (161) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1293 +r0:=3*a^2*A*b*x+3/2*a*A*b^2*x^2+1/3*A*b^3*x^3+1/4*B*(a+b*x)^4/b+a^3*A*log(x) +--R +--R +--R (162) +--R 3 4 4 4 3 3 3 2 2 2 +--R 12A a b log(x) + 3B b x + (4A b + 12B a b )x + (18A a b + 18B a b )x +--R + +--R 2 2 3 4 +--R (36A a b + 12B a b)x + 3B a +--R / +--R 12b +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (163) +--R 3 3 4 3 2 3 2 2 2 +--R 12A a log(x) + 3B b x + (4A b + 12B a b )x + (18A a b + 18B a b)x +--R + +--R 2 3 +--R (36A a b + 12B a )x +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1293 +m0:=a0-r0 +--R +--R +--R 4 +--R B a +--R (164) - ---- +--R 4b +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1293 +d0:=D(m0,x) +--R +--R +--R (165) 0 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^2 +--R +--R +--R (166) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1293 +r0:=-a^3*A/x+3*a*b*(A*b+a*B)*x+1/2*b^2*(A*b+3*a*B)*x^2+1/3*b^3*B*x^3+_ + a^2*(3*A*b+a*B)*log(x) +--R +--R +--R (167) +--R 2 3 3 4 3 2 3 +--R (18A a b + 6B a )x log(x) + 2B b x + (3A b + 9B a b )x +--R + +--R 2 2 2 3 +--R (18A a b + 18B a b)x - 6A a +--R / +--R 6x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (168) +--R 2 3 3 4 3 2 3 +--R (18A a b + 6B a )x log(x) + 2B b x + (3A b + 9B a b )x +--R + +--R 2 2 2 3 +--R (18A a b + 18B a b)x - 6A a +--R / +--R 6x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1293 +m0:=a0-r0 +--R +--R +--R (169) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1293 +d0:=D(m0,x) +--R +--R +--R (170) 0 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^3 +--R +--R +--R (171) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1293 +r0:=-1/2*a^3*A/x^2-a^2*(3*A*b+a*B)/x+b^2*(A*b+3*a*B)*x+1/2*b^3*B*x^2+_ + 3*a*b*(A*b+a*B)*log(x) +--R +--R +--R (172) +--R 2 2 2 3 4 3 2 3 +--R (6A a b + 6B a b)x log(x) + B b x + (2A b + 6B a b )x +--R + +--R 2 3 3 +--R (- 6A a b - 2B a )x - A a +--R / +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (173) +--R 2 2 2 3 4 3 2 3 +--R (6A a b + 6B a b)x log(x) + B b x + (2A b + 6B a b )x +--R + +--R 2 3 3 +--R (- 6A a b - 2B a )x - A a +--R / +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1293 +m0:=a0-r0 +--R +--R +--R (174) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1293 +d0:=D(m0,x) +--R +--R +--R (175) 0 +--R Type: Expression(Integer) +--E 175 + +--S 176 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^4 +--R +--R +--R (176) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1293 +r0:=-1/3*a^3*A/x^3-1/2*a^2*(3*A*b+a*B)/x^2-3*a*b*(A*b+a*B)/x+_ + b^3*B*x+b^2*(A*b+3*a*B)*log(x) +--R +--R +--R (177) +--R 3 2 3 3 4 2 2 2 +--R (6A b + 18B a b )x log(x) + 6B b x + (- 18A a b - 18B a b)x +--R + +--R 2 3 3 +--R (- 9A a b - 3B a )x - 2A a +--R / +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (178) +--R 3 2 3 3 4 2 2 2 +--R (6A b + 18B a b )x log(x) + 6B b x + (- 18A a b - 18B a b)x +--R + +--R 2 3 3 +--R (- 9A a b - 3B a )x - 2A a +--R / +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1293 +m0:=a0-r0 +--R +--R +--R (179) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1293 +d0:=D(m0,x) +--R +--R +--R (180) 0 +--R Type: Expression(Integer) +--E 180 + +--S 181 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^5 +--R +--R +--R (181) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1293 +r0:=-1/3*a^3*B/x^3-3/2*a^2*b*B/x^2-3*a*b^2*B/x-1/4*A*(a+b*x)^4/(a*x^4)+_ + b^3*B*log(x) +--R +--R +--R (182) +--R 3 4 4 4 3 2 2 3 +--R 12B a b x log(x) - 3A b x + (- 12A a b - 36B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 18A a b - 18B a b)x + (- 12A a b - 4B a )x - 3A a +--R / +--R 4 +--R 12a x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (183) +--R 3 4 3 2 3 2 2 2 +--R 12B b x log(x) + (- 12A b - 36B a b )x + (- 18A a b - 18B a b)x +--R + +--R 2 3 3 +--R (- 12A a b - 4B a )x - 3A a +--R / +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1293 +m0:=a0-r0 +--R +--R +--R 4 +--R A b +--R (184) ---- +--R 4a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1293 +d0:=D(m0,x) +--R +--R +--R (185) 0 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^6 +--R +--R +--R (186) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1293 +r0:=-1/5*a^3*A/x^5-1/4*a^2*(3*A*b+a*B)/x^4-a*b*(A*b+a*B)/x^3-_ + 1/2*b^2*(A*b+3*a*B)/x^2-b^3*B/x +--R +--R +--R (187) +--R 3 4 1 3 3 2 3 2 2 2 +--R - B b x + (- - A b - - B a b )x + (- A a b - B a b)x +--R 2 2 +--R + +--R 3 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 4 4 5 +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 187 + +--S 188 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (188) +--R 3 4 3 2 3 2 2 2 +--R - 20B b x + (- 10A b - 30B a b )x + (- 20A a b - 20B a b)x +--R + +--R 2 3 3 +--R (- 15A a b - 5B a )x - 4A a +--R / +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1293 +m0:=a0-r0 +--R +--R +--R (189) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1293 +d0:=D(m0,x) +--R +--R +--R (190) 0 +--R Type: Expression(Integer) +--E 190 + +--S 191 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^7 +--R +--R +--R (191) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1293 +r0:=-1/6*a^3*A/x^6-1/5*a^2*(3*A*b+a*B)/x^5-3/4*a*b*(A*b+a*B)/x^4-_ + 1/3*b^2*(A*b+3*a*B)/x^3-1/2*b^3*B/x^2 +--R +--R +--R (192) +--R 1 3 4 1 3 2 3 3 2 3 2 2 +--R - - B b x + (- - A b - B a b )x + (- - A a b - - B a b)x +--R 2 3 4 4 +--R + +--R 3 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 5 5 6 +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 192 + +--S 193 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (193) +--R 3 4 3 2 3 2 2 2 +--R - 30B b x + (- 20A b - 60B a b )x + (- 45A a b - 45B a b)x +--R + +--R 2 3 3 +--R (- 36A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1293 +m0:=a0-r0 +--R +--R +--R (194) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1293 +d0:=D(m0,x) +--R +--R +--R (195) 0 +--R Type: Expression(Integer) +--E 195 + +--S 196 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^8 +--R +--R +--R (196) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1293 +r0:=-1/7*a^3*A/x^7-1/6*a^2*(3*A*b+a*B)/x^6-3/5*a*b*(A*b+a*B)/x^5-_ + 1/4*b^2*(A*b+3*a*B)/x^4-1/3*b^3*B/x^3 +--R +--R +--R (197) +--R 1 3 4 1 3 3 2 3 3 2 3 2 2 +--R - - B b x + (- - A b - - B a b )x + (- - A a b - - B a b)x +--R 3 4 4 5 5 +--R + +--R 1 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 2 6 7 +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 197 + +--S 198 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (198) +--R 3 4 3 2 3 2 2 2 +--R - 140B b x + (- 105A b - 315B a b )x + (- 252A a b - 252B a b)x +--R + +--R 2 3 3 +--R (- 210A a b - 70B a )x - 60A a +--R / +--R 7 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1293 +m0:=a0-r0 +--R +--R +--R (199) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1293 +d0:=D(m0,x) +--R +--R +--R (200) 0 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^9 +--R +--R +--R (201) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1293 +r0:=-1/8*a^3*A/x^8-1/7*a^2*(3*A*b+a*B)/x^7-1/2*a*b*(A*b+a*B)/x^6-_ + 1/5*b^2*(A*b+3*a*B)/x^5-1/4*b^3*B/x^4 +--R +--R +--R (202) +--R 1 3 4 1 3 3 2 3 1 2 1 2 2 +--R - - B b x + (- - A b - - B a b )x + (- - A a b - - B a b)x +--R 4 5 5 2 2 +--R + +--R 3 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 7 7 8 +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 202 + +--S 203 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (203) +--R 3 4 3 2 3 2 2 2 +--R - 70B b x + (- 56A b - 168B a b )x + (- 140A a b - 140B a b)x +--R + +--R 2 3 3 +--R (- 120A a b - 40B a )x - 35A a +--R / +--R 8 +--R 280x +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1293 +m0:=a0-r0 +--R +--R +--R (204) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1293 +d0:=D(m0,x) +--R +--R +--R (205) 0 +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^10 +--R +--R +--R (206) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1293 +r0:=-1/9*a^3*A/x^9-1/8*a^2*(3*A*b+a*B)/x^8-3/7*a*b*(A*b+a*B)/x^7-_ + 1/6*b^2*(A*b+3*a*B)/x^6-1/5*b^3*B/x^5 +--R +--R +--R (207) +--R 1 3 4 1 3 1 2 3 3 2 3 2 2 +--R - - B b x + (- - A b - - B a b )x + (- - A a b - - B a b)x +--R 5 6 2 7 7 +--R + +--R 3 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 8 8 9 +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 207 + +--S 208 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (208) +--R 3 4 3 2 3 2 2 2 +--R - 504B b x + (- 420A b - 1260B a b )x + (- 1080A a b - 1080B a b)x +--R + +--R 2 3 3 +--R (- 945A a b - 315B a )x - 280A a +--R / +--R 9 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1293 +m0:=a0-r0 +--R +--R +--R (209) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1293 +d0:=D(m0,x) +--R +--R +--R (210) 0 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1293 +t0:=x^m*(a+b*x)^5*(A+B*x) +--R +--R +--R (211) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1293 +r0:=a^5*A*x^(1+m)/(1+m)+a^4*(5*A*b+a*B)*x^(2+m)/(2+m)+_ + 5*a^3*b*(2*A*b+a*B)*x^(3+m)/(3+m)+10*a^2*b^2*(A*b+a*B)*x^(4+m)/(4+m)+_ + 5*a*b^3*(A*b+2*a*B)*x^(5+m)/(5+m)+b^4*(A*b+5*a*B)*x^(6+m)/(6+m)+_ + b^5*B*x^(7+m)/(7+m) +--R +--R +--R (212) +--R 5 6 5 5 5 4 5 3 5 2 5 +--R B b m + 21B b m + 175B b m + 735B b m + 1624B b m + 1764B b m +--R + +--R 5 +--R 720B b +--R * +--R m + 7 +--R x +--R + +--R 5 4 6 5 4 5 5 4 4 +--R (A b + 5B a b )m + (22A b + 110B a b )m + (190A b + 950B a b )m +--R + +--R 5 4 3 5 4 2 +--R (820A b + 4100B a b )m + (1849A b + 9245B a b )m +--R + +--R 5 4 5 4 +--R (2038A b + 10190B a b )m + 840A b + 4200B a b +--R * +--R m + 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5A a b + 10B a b )m + (115A a b + 230B a b )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035A a b + 2070B a b )m + (4625A a b + 9250B a b )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720A a b + 21440B a b )m + (12060A a b + 24120B a b )m +--R + +--R 4 2 3 +--R 5040A a b + 10080B a b +--R * +--R m + 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10A a b + 10B a b )m + (240A a b + 240B a b )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260A a b + 2260B a b )m + (10560A a b + 10560B a b )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450A a b + 25450B a b )m + (29520A a b + 29520B a b )m +--R + +--R 2 3 3 2 +--R 12600A a b + 12600B a b +--R * +--R m + 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10A a b + 5B a b)m + (250A a b + 125B a b)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470A a b + 1235B a b)m + (12190A a b + 6095B a b)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120A a b + 15560B a b)m + (37960A a b + 18980B a b)m +--R + +--R 3 2 4 +--R 16800A a b + 8400B a b +--R * +--R m + 3 +--R x +--R + +--R 4 5 6 4 5 5 4 5 4 +--R (5A a b + B a )m + (130A a b + 26B a )m + (1350A a b + 270B a )m +--R + +--R 4 5 3 4 5 2 +--R (7100A a b + 1420B a )m + (19645A a b + 3929B a )m +--R + +--R 4 5 4 5 +--R (26370A a b + 5274B a )m + 12600A a b + 2520B a +--R * +--R m + 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R A a m + 27A a m + 295A a m + 1665A a m + 5104A a m + 8028A a m +--R + +--R 5 +--R 5040A a +--R * +--R m + 1 +--R x +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (213) +--R 5 6 5 5 5 4 5 3 5 2 5 +--R B b m + 21B b m + 175B b m + 735B b m + 1624B b m + 1764B b m +--R + +--R 5 +--R 720B b +--R * +--R 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (A b + 5B a b )m + (22A b + 110B a b )m +--R + +--R 5 4 4 5 4 3 +--R (190A b + 950B a b )m + (820A b + 4100B a b )m +--R + +--R 5 4 2 5 4 5 +--R (1849A b + 9245B a b )m + (2038A b + 10190B a b )m + 840A b +--R + +--R 4 +--R 4200B a b +--R * +--R 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5A a b + 10B a b )m + (115A a b + 230B a b )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035A a b + 2070B a b )m + (4625A a b + 9250B a b )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720A a b + 21440B a b )m + (12060A a b + 24120B a b )m +--R + +--R 4 2 3 +--R 5040A a b + 10080B a b +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10A a b + 10B a b )m + (240A a b + 240B a b )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260A a b + 2260B a b )m + (10560A a b + 10560B a b )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450A a b + 25450B a b )m + (29520A a b + 29520B a b )m +--R + +--R 2 3 3 2 +--R 12600A a b + 12600B a b +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10A a b + 5B a b)m + (250A a b + 125B a b)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470A a b + 1235B a b)m + (12190A a b + 6095B a b)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120A a b + 15560B a b)m + (37960A a b + 18980B a b)m +--R + +--R 3 2 4 +--R 16800A a b + 8400B a b +--R * +--R 3 +--R x +--R + +--R 4 5 6 4 5 5 4 5 4 +--R (5A a b + B a )m + (130A a b + 26B a )m + (1350A a b + 270B a )m +--R + +--R 4 5 3 4 5 2 +--R (7100A a b + 1420B a )m + (19645A a b + 3929B a )m +--R + +--R 4 5 4 5 +--R (26370A a b + 5274B a )m + 12600A a b + 2520B a +--R * +--R 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R A a m + 27A a m + 295A a m + 1665A a m + 5104A a m + 8028A a m +--R + +--R 5 +--R 5040A a +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1293 +m0:=a0-r0 +--R +--R +--R (214) +--R 5 6 5 5 5 4 5 3 5 2 +--R B b m + 21B b m + 175B b m + 735B b m + 1624B b m +--R + +--R 5 5 +--R 1764B b m + 720B b +--R * +--R 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (A b + 5B a b )m + (22A b + 110B a b )m +--R + +--R 5 4 4 5 4 3 +--R (190A b + 950B a b )m + (820A b + 4100B a b )m +--R + +--R 5 4 2 5 4 5 +--R (1849A b + 9245B a b )m + (2038A b + 10190B a b )m + 840A b +--R + +--R 4 +--R 4200B a b +--R * +--R 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5A a b + 10B a b )m + (115A a b + 230B a b )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035A a b + 2070B a b )m + (4625A a b + 9250B a b )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720A a b + 21440B a b )m + (12060A a b + 24120B a b )m +--R + +--R 4 2 3 +--R 5040A a b + 10080B a b +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10A a b + 10B a b )m + (240A a b + 240B a b )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260A a b + 2260B a b )m + (10560A a b + 10560B a b )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450A a b + 25450B a b )m + (29520A a b + 29520B a b )m +--R + +--R 2 3 3 2 +--R 12600A a b + 12600B a b +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10A a b + 5B a b)m + (250A a b + 125B a b)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470A a b + 1235B a b)m + (12190A a b + 6095B a b)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120A a b + 15560B a b)m + (37960A a b + 18980B a b)m +--R + +--R 3 2 4 +--R 16800A a b + 8400B a b +--R * +--R 3 +--R x +--R + +--R 4 5 6 4 5 5 +--R (5A a b + B a )m + (130A a b + 26B a )m +--R + +--R 4 5 4 4 5 3 +--R (1350A a b + 270B a )m + (7100A a b + 1420B a )m +--R + +--R 4 5 2 4 5 4 +--R (19645A a b + 3929B a )m + (26370A a b + 5274B a )m + 12600A a b +--R + +--R 5 +--R 2520B a +--R * +--R 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R A a m + 27A a m + 295A a m + 1665A a m + 5104A a m +--R + +--R 5 5 +--R 8028A a m + 5040A a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R - B b m - 21B b m - 175B b m - 735B b m - 1624B b m - 1764B b m +--R + +--R 5 +--R - 720B b +--R * +--R m + 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (- A b - 5B a b )m + (- 22A b - 110B a b )m +--R + +--R 5 4 4 5 4 3 +--R (- 190A b - 950B a b )m + (- 820A b - 4100B a b )m +--R + +--R 5 4 2 5 4 5 +--R (- 1849A b - 9245B a b )m + (- 2038A b - 10190B a b )m - 840A b +--R + +--R 4 +--R - 4200B a b +--R * +--R m + 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (- 5A a b - 10B a b )m + (- 115A a b - 230B a b )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (- 1035A a b - 2070B a b )m + (- 4625A a b - 9250B a b )m +--R + +--R 4 2 3 2 4 2 3 +--R (- 10720A a b - 21440B a b )m + (- 12060A a b - 24120B a b )m +--R + +--R 4 2 3 +--R - 5040A a b - 10080B a b +--R * +--R m + 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 10A a b - 10B a b )m + (- 240A a b - 240B a b )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (- 2260A a b - 2260B a b )m + (- 10560A a b - 10560B a b )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (- 25450A a b - 25450B a b )m + (- 29520A a b - 29520B a b )m +--R + +--R 2 3 3 2 +--R - 12600A a b - 12600B a b +--R * +--R m + 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (- 10A a b - 5B a b)m + (- 250A a b - 125B a b)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (- 2470A a b - 1235B a b)m + (- 12190A a b - 6095B a b)m +--R + +--R 3 2 4 2 3 2 4 +--R (- 31120A a b - 15560B a b)m + (- 37960A a b - 18980B a b)m +--R + +--R 3 2 4 +--R - 16800A a b - 8400B a b +--R * +--R m + 3 +--R x +--R + +--R 4 5 6 4 5 5 +--R (- 5A a b - B a )m + (- 130A a b - 26B a )m +--R + +--R 4 5 4 4 5 3 +--R (- 1350A a b - 270B a )m + (- 7100A a b - 1420B a )m +--R + +--R 4 5 2 4 5 4 +--R (- 19645A a b - 3929B a )m + (- 26370A a b - 5274B a )m - 12600A a b +--R + +--R 5 +--R - 2520B a +--R * +--R m + 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R - A a m - 27A a m - 295A a m - 1665A a m - 5104A a m - 8028A a m +--R + +--R 5 +--R - 5040A a +--R * +--R m + 1 +--R x +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1293 +d0:=D(m0,x) +--R +--R +--R (215) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R * +--R m log(x) +--R %e +--R + +--R 5 m + 6 5 4 m + 5 4 2 3 m + 4 +--R - B b x + (- A b - 5B a b )x + (- 5A a b - 10B a b )x +--R + +--R 2 3 3 2 m + 3 3 2 4 m + 2 +--R (- 10A a b - 10B a b )x + (- 10A a b - 5B a b)x +--R + +--R 4 5 m + 1 5 m +--R (- 5A a b - B a )x - A a x +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1293 +t0:=x^5*(a+b*x)^5*(A+B*x) +--R +--R +--R (216) +--R 5 11 5 4 10 4 2 3 9 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 8 3 2 4 7 4 5 6 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 1293 +r0:=1/6*a^5*A*x^6+1/7*a^4*(5*A*b+a*B)*x^7+5/8*a^3*b*(2*A*b+a*B)*x^8+_ + 10/9*a^2*b^2*(A*b+a*B)*x^9+1/2*a*b^3*(A*b+2*a*B)*x^10+_ + 1/11*b^4*(A*b+5*a*B)*x^11+1/12*b^5*B*x^12 +--R +--R +--R (217) +--R 1 5 12 1 5 5 4 11 1 4 2 3 10 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + B a b )x +--R 12 11 11 2 +--R + +--R 10 2 3 10 3 2 9 5 3 2 5 4 8 5 4 1 5 7 +--R (-- A a b + -- B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x +--R 9 9 4 8 7 7 +--R + +--R 1 5 6 +--R - A a x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 217 + +--S 218 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (218) +--R 1 5 12 1 5 5 4 11 1 4 2 3 10 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + B a b )x +--R 12 11 11 2 +--R + +--R 10 2 3 10 3 2 9 5 3 2 5 4 8 5 4 1 5 7 +--R (-- A a b + -- B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x +--R 9 9 4 8 7 7 +--R + +--R 1 5 6 +--R - A a x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 1293 +m0:=a0-r0 +--R +--R +--R (219) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 219 + +--S 220 of 1293 +d0:=D(m0,x) +--R +--R +--R (220) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 220 + +--S 221 of 1293 +t0:=x^4*(a+b*x)^5*(A+B*x) +--R +--R +--R (221) +--R 5 10 5 4 9 4 2 3 8 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 7 3 2 4 6 4 5 5 5 4 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 1293 +r0:=1/5*a^5*A*x^5+1/6*a^4*(5*A*b+a*B)*x^6+5/7*a^3*b*(2*A*b+a*B)*x^7+_ + 5/4*a^2*b^2*(A*b+a*B)*x^8+5/9*a*b^3*(A*b+2*a*B)*x^9+_ + 1/10*b^4*(A*b+5*a*B)*x^10+1/11*b^5*B*x^11 +--R +--R +--R (222) +--R 1 5 11 1 5 1 4 10 5 4 10 2 3 9 +--R -- B b x + (-- A b + - B a b )x + (- A a b + -- B a b )x +--R 11 10 2 9 9 +--R + +--R 5 2 3 5 3 2 8 10 3 2 5 4 7 5 4 1 5 6 +--R (- A a b + - B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x +--R 4 4 7 7 6 6 +--R + +--R 1 5 5 +--R - A a x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (223) +--R 1 5 11 1 5 1 4 10 5 4 10 2 3 9 +--R -- B b x + (-- A b + - B a b )x + (- A a b + -- B a b )x +--R 11 10 2 9 9 +--R + +--R 5 2 3 5 3 2 8 10 3 2 5 4 7 5 4 1 5 6 +--R (- A a b + - B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x +--R 4 4 7 7 6 6 +--R + +--R 1 5 5 +--R - A a x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 1293 +m0:=a0-r0 +--R +--R +--R (224) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 1293 +d0:=D(m0,x) +--R +--R +--R (225) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +--S 226 of 1293 +t0:=x^3*(a+b*x)^5*(A+B*x) +--R +--R +--R (226) +--R 5 9 5 4 8 4 2 3 7 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 6 3 2 4 5 4 5 4 5 3 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 1293 +r0:=1/4*a^5*A*x^4+1/5*a^4*(5*A*b+a*B)*x^5+5/6*a^3*b*(2*A*b+a*B)*x^6+_ + 10/7*a^2*b^2*(A*b+a*B)*x^7+5/8*a*b^3*(A*b+2*a*B)*x^8+_ + 1/9*b^4*(A*b+5*a*B)*x^9+1/10*b^5*B*x^10 +--R +--R +--R (227) +--R 1 5 10 1 5 5 4 9 5 4 5 2 3 8 +--R -- B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 10 9 9 8 4 +--R + +--R 10 2 3 10 3 2 7 5 3 2 5 4 6 4 1 5 5 +--R (-- A a b + -- B a b )x + (- A a b + - B a b)x + (A a b + - B a )x +--R 7 7 3 6 5 +--R + +--R 1 5 4 +--R - A a x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (228) +--R 1 5 10 1 5 5 4 9 5 4 5 2 3 8 +--R -- B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 10 9 9 8 4 +--R + +--R 10 2 3 10 3 2 7 5 3 2 5 4 6 4 1 5 5 +--R (-- A a b + -- B a b )x + (- A a b + - B a b)x + (A a b + - B a )x +--R 7 7 3 6 5 +--R + +--R 1 5 4 +--R - A a x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 1293 +m0:=a0-r0 +--R +--R +--R (229) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 1293 +d0:=D(m0,x) +--R +--R +--R (230) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +--S 231 of 1293 +t0:=x^2*(a+b*x)^5*(A+B*x) +--R +--R +--R (231) +--R 5 8 5 4 7 4 2 3 6 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 5 3 2 4 4 4 5 3 5 2 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 1293 +r0:=1/6*a^2*(A*b-a*B)*(a+b*x)^6/b^4-1/7*a*(2*A*b-3*a*B)*(a+b*x)^7/b^4+_ + 1/8*(A*b-3*a*B)*(a+b*x)^8/b^4+1/9*B*(a+b*x)^9/b^4 +--R +--R +--R (232) +--R 1 9 9 1 9 5 8 8 5 8 10 2 7 7 +--R - B b x + (- A b + - B a b )x + (- A a b + -- B a b )x +--R 9 8 8 7 7 +--R + +--R 5 2 7 5 3 6 6 3 6 4 5 5 5 4 5 1 5 4 4 +--R (- A a b + - B a b )x + (2A a b + B a b )x + (- A a b + - B a b )x +--R 3 3 4 4 +--R + +--R 1 5 4 3 1 8 1 9 +--R - A a b x + --- A a b - --- B a +--R 3 168 504 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 232 + +--S 233 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (233) +--R 1 5 9 1 5 5 4 8 5 4 10 2 3 7 +--R - B b x + (- A b + - B a b )x + (- A a b + -- B a b )x +--R 9 8 8 7 7 +--R + +--R 5 2 3 5 3 2 6 3 2 4 5 5 4 1 5 4 +--R (- A a b + - B a b )x + (2A a b + B a b)x + (- A a b + - B a )x +--R 3 3 4 4 +--R + +--R 1 5 3 +--R - A a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 1293 +m0:=a0-r0 +--R +--R +--R 1 8 1 9 +--R - --- A a b + --- B a +--R 168 504 +--R (234) ---------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 234 + +--S 235 of 1293 +d0:=D(m0,x) +--R +--R +--R (235) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 235 + +--S 236 of 1293 +t0:=x*(a+b*x)^5*(A+B*x) +--R +--R +--R (236) +--R 5 7 5 4 6 4 2 3 5 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 4 3 2 4 3 4 5 2 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 236 + +--S 237 of 1293 +r0:=-1/6*a*(A*b-a*B)*(a+b*x)^6/b^3+1/7*(A*b-2*a*B)*(a+b*x)^7/b^3+_ + 1/8*B*(a+b*x)^8/b^3 +--R +--R +--R (237) +--R 1 8 8 1 8 5 7 7 5 7 5 2 6 6 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 8 7 7 6 3 +--R + +--R 2 6 3 5 5 5 3 5 5 4 4 4 5 4 4 1 5 3 3 +--R (2A a b + 2B a b )x + (- A a b + - B a b )x + (- A a b + - B a b )x +--R 2 4 3 3 +--R + +--R 1 5 3 2 1 7 1 8 +--R - A a b x - -- A a b + --- B a +--R 2 42 168 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 237 + +--S 238 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (238) +--R 1 5 8 1 5 5 4 7 5 4 5 2 3 6 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 8 7 7 6 3 +--R + +--R 2 3 3 2 5 5 3 2 5 4 4 5 4 1 5 3 +--R (2A a b + 2B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x +--R 2 4 3 3 +--R + +--R 1 5 2 +--R - A a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 238 + +--S 239 of 1293 +m0:=a0-r0 +--R +--R +--R 1 7 1 8 +--R -- A a b - --- B a +--R 42 168 +--R (239) ------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 239 + +--S 240 of 1293 +d0:=D(m0,x) +--R +--R +--R (240) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 240 + +--S 241 of 1293 +t0:=(a+b*x)^5*(A+B*x) +--R +--R +--R (241) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 241 + +--S 242 of 1293 +r0:=1/6*(A*b-a*B)*(a+b*x)^6/b^2+1/7*B*(a+b*x)^7/b^2 +--R +--R +--R (242) +--R 1 7 7 1 7 5 6 6 6 2 5 5 +--R - B b x + (- A b + - B a b )x + (A a b + 2B a b )x +--R 7 6 6 +--R + +--R 5 2 5 5 3 4 4 10 3 4 5 4 3 3 +--R (- A a b + - B a b )x + (-- A a b + - B a b )x +--R 2 2 3 3 +--R + +--R 5 4 3 1 5 2 2 5 2 1 6 1 7 +--R (- A a b + - B a b )x + A a b x + - A a b - -- B a +--R 2 2 6 42 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 242 + +--S 243 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (243) +--R 1 5 7 1 5 5 4 6 4 2 3 5 +--R - B b x + (- A b + - B a b )x + (A a b + 2B a b )x +--R 7 6 6 +--R + +--R 5 2 3 5 3 2 4 10 3 2 5 4 3 5 4 1 5 2 +--R (- A a b + - B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x +--R 2 2 3 3 2 2 +--R + +--R 5 +--R A a x +--R Type: Polynomial(Fraction(Integer)) +--E 243 + +--S 244 of 1293 +m0:=a0-r0 +--R +--R +--R 1 6 1 7 +--R - - A a b + -- B a +--R 6 42 +--R (244) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 244 + +--S 245 of 1293 +d0:=D(m0,x) +--R +--R +--R (245) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 245 + +--S 246 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x +--R +--R +--R (246) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1293 +r0:=5*a^4*A*b*x+5*a^3*A*b^2*x^2+10/3*a^2*A*b^3*x^3+5/4*a*A*b^4*x^4+_ + 1/5*A*b^5*x^5+1/6*B*(a+b*x)^6/b+a^5*A*log(x) +--R +--R +--R (247) +--R 5 6 6 6 5 5 +--R 60A a b log(x) + 10B b x + (12A b + 60B a b )x +--R + +--R 5 2 4 4 2 4 3 3 3 +--R (75A a b + 150B a b )x + (200A a b + 200B a b )x +--R + +--R 3 3 4 2 2 4 2 5 6 +--R (300A a b + 150B a b )x + (300A a b + 60B a b)x + 10B a +--R / +--R 60b +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (248) +--R 5 5 6 5 4 5 +--R 60A a log(x) + 10B b x + (12A b + 60B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (75A a b + 150B a b )x + (200A a b + 200B a b )x +--R + +--R 3 2 4 2 4 5 +--R (300A a b + 150B a b)x + (300A a b + 60B a )x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1293 +m0:=a0-r0 +--R +--R +--R 6 +--R B a +--R (249) - ---- +--R 6b +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1293 +d0:=D(m0,x) +--R +--R +--R (250) 0 +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^2 +--R +--R +--R (251) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1293 +r0:=-a^5*A/x+5*a^3*b*(2*A*b+a*B)*x+5*a^2*b^2*(A*b+a*B)*x^2+_ + 5/3*a*b^3*(A*b+2*a*B)*x^3+1/4*b^4*(A*b+5*a*B)*x^4+_ + 1/5*b^5*B*x^5+a^4*(5*A*b+a*B)*log(x) +--R +--R +--R (252) +--R 4 5 5 6 5 4 5 +--R (300A a b + 60B a )x log(x) + 12B b x + (15A b + 75B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (100A a b + 200B a b )x + (300A a b + 300B a b )x +--R + +--R 3 2 4 2 5 +--R (600A a b + 300B a b)x - 60A a +--R / +--R 60x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (253) +--R 4 5 5 6 5 4 5 +--R (300A a b + 60B a )x log(x) + 12B b x + (15A b + 75B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (100A a b + 200B a b )x + (300A a b + 300B a b )x +--R + +--R 3 2 4 2 5 +--R (600A a b + 300B a b)x - 60A a +--R / +--R 60x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1293 +m0:=a0-r0 +--R +--R +--R (254) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1293 +d0:=D(m0,x) +--R +--R +--R (255) 0 +--R Type: Expression(Integer) +--E 255 + +--S 256 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^3 +--R +--R +--R (256) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1293 +r0:=-1/2*a^5*A/x^2-a^4*(5*A*b+a*B)/x+10*a^2*b^2*(A*b+a*B)*x+_ + 5/2*a*b^3*(A*b+2*a*B)*x^2+1/3*b^4*(A*b+5*a*B)*x^3+_ + 1/4*b^5*B*x^4+5*a^3*b*(2*A*b+a*B)*log(x) +--R +--R +--R (257) +--R 3 2 4 2 5 6 5 4 5 +--R (120A a b + 60B a b)x log(x) + 3B b x + (4A b + 20B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (30A a b + 60B a b )x + (120A a b + 120B a b )x +--R + +--R 4 5 5 +--R (- 60A a b - 12B a )x - 6A a +--R / +--R 2 +--R 12x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (258) +--R 3 2 4 2 5 6 5 4 5 +--R (120A a b + 60B a b)x log(x) + 3B b x + (4A b + 20B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (30A a b + 60B a b )x + (120A a b + 120B a b )x +--R + +--R 4 5 5 +--R (- 60A a b - 12B a )x - 6A a +--R / +--R 2 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1293 +m0:=a0-r0 +--R +--R +--R (259) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1293 +d0:=D(m0,x) +--R +--R +--R (260) 0 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^4 +--R +--R +--R (261) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1293 +r0:=-1/3*a^5*A/x^3-1/2*a^4*(5*A*b+a*B)/x^2-5*a^3*b*(2*A*b+a*B)/x+_ + 5*a*b^3*(A*b+2*a*B)*x+1/2*b^4*(A*b+5*a*B)*x^2+1/3*b^5*B*x^3+_ + 10*a^2*b^2*(A*b+a*B)*log(x) +--R +--R +--R (262) +--R 2 3 3 2 3 5 6 5 4 5 +--R (60A a b + 60B a b )x log(x) + 2B b x + (3A b + 15B a b )x +--R + +--R 4 2 3 4 3 2 4 2 4 5 +--R (30A a b + 60B a b )x + (- 60A a b - 30B a b)x + (- 15A a b - 3B a )x +--R + +--R 5 +--R - 2A a +--R / +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (263) +--R 2 3 3 2 3 5 6 5 4 5 +--R (60A a b + 60B a b )x log(x) + 2B b x + (3A b + 15B a b )x +--R + +--R 4 2 3 4 3 2 4 2 4 5 +--R (30A a b + 60B a b )x + (- 60A a b - 30B a b)x + (- 15A a b - 3B a )x +--R + +--R 5 +--R - 2A a +--R / +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1293 +m0:=a0-r0 +--R +--R +--R (264) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1293 +d0:=D(m0,x) +--R +--R +--R (265) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^5 +--R +--R +--R (266) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1293 +r0:=-1/4*a^5*A/x^4-1/3*a^4*(5*A*b+a*B)/x^3-5/2*a^3*b*(2*A*b+a*B)/x^2-_ + 10*a^2*b^2*(A*b+a*B)/x+b^4*(A*b+5*a*B)*x+1/2*b^5*B*x^2+_ + 5*a*b^3*(A*b+2*a*B)*log(x) +--R +--R +--R (267) +--R 4 2 3 4 5 6 5 4 5 +--R (60A a b + 120B a b )x log(x) + 6B b x + (12A b + 60B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 120A a b - 120B a b )x + (- 60A a b - 30B a b)x +--R + +--R 4 5 5 +--R (- 20A a b - 4B a )x - 3A a +--R / +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (268) +--R 4 2 3 4 5 6 5 4 5 +--R (60A a b + 120B a b )x log(x) + 6B b x + (12A b + 60B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 120A a b - 120B a b )x + (- 60A a b - 30B a b)x +--R + +--R 4 5 5 +--R (- 20A a b - 4B a )x - 3A a +--R / +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1293 +m0:=a0-r0 +--R +--R +--R (269) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1293 +d0:=D(m0,x) +--R +--R +--R (270) 0 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^6 +--R +--R +--R (271) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1293 +r0:=-1/5*a^5*A/x^5-1/4*a^4*(5*A*b+a*B)/x^4-5/3*a^3*b*(2*A*b+a*B)/x^3-_ + 5*a^2*b^2*(A*b+a*B)/x^2-5*a*b^3*(A*b+2*a*B)/x+b^5*B*x+_ + b^4*(A*b+5*a*B)*log(x) +--R +--R +--R (272) +--R 5 4 5 5 6 4 2 3 4 +--R (60A b + 300B a b )x log(x) + 60B b x + (- 300A a b - 600B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 300A a b - 300B a b )x + (- 200A a b - 100B a b)x +--R + +--R 4 5 5 +--R (- 75A a b - 15B a )x - 12A a +--R / +--R 5 +--R 60x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (273) +--R 5 4 5 5 6 4 2 3 4 +--R (60A b + 300B a b )x log(x) + 60B b x + (- 300A a b - 600B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 300A a b - 300B a b )x + (- 200A a b - 100B a b)x +--R + +--R 4 5 5 +--R (- 75A a b - 15B a )x - 12A a +--R / +--R 5 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1293 +m0:=a0-r0 +--R +--R +--R (274) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1293 +d0:=D(m0,x) +--R +--R +--R (275) 0 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^7 +--R +--R +--R (276) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1293 +r0:=-1/5*a^5*B/x^5-5/4*a^4*b*B/x^4-10/3*a^3*b^2*B/x^3-5*a^2*b^3*B/x^2-_ + 5*a*b^4*B/x-1/6*A*(a+b*x)^6/(a*x^6)+b^5*B*log(x) +--R +--R +--R (277) +--R 5 6 6 6 5 2 4 5 +--R 60B a b x log(x) - 10A b x + (- 60A a b - 300B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 150A a b - 300B a b )x + (- 200A a b - 200B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 150A a b - 75B a b)x + (- 60A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60a x +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (278) +--R 5 6 5 4 5 4 2 3 4 +--R 60B b x log(x) + (- 60A b - 300B a b )x + (- 150A a b - 300B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 200A a b - 200B a b )x + (- 150A a b - 75B a b)x +--R + +--R 4 5 5 +--R (- 60A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1293 +m0:=a0-r0 +--R +--R +--R 6 +--R A b +--R (279) ---- +--R 6a +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1293 +d0:=D(m0,x) +--R +--R +--R (280) 0 +--R Type: Expression(Integer) +--E 280 + +--S 281 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^8 +--R +--R +--R (281) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1293 +r0:=-1/7*A*(a+b*x)^6/(a*x^7)+1/42*(A*b-7*a*B)*(a+b*x)^6/(a^2*x^6) +--R +--R +--R (282) +--R 1 7 1 6 7 2 5 6 1 2 5 5 3 4 5 +--R (-- A b - - B a b )x - B a b x + (- - A a b - - B a b )x +--R 42 6 2 2 +--R + +--R 5 3 4 10 4 3 4 5 4 3 5 5 2 3 +--R (- - A a b - -- B a b )x + (- - A a b - - B a b )x +--R 3 3 2 2 +--R + +--R 5 2 6 2 5 6 1 7 1 7 +--R (- 2A a b - B a b)x + (- - A a b - - B a )x - - A a +--R 6 6 7 +--R / +--R 2 7 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 282 + +--S 283 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (283) +--R 5 6 5 4 5 4 2 3 4 +--R - 42B b x + (- 21A b - 105B a b )x + (- 70A a b - 140B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 105A a b - 105B a b )x + (- 84A a b - 42B a b)x +--R + +--R 4 5 5 +--R (- 35A a b - 7B a )x - 6A a +--R / +--R 7 +--R 42x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1293 +m0:=a0-r0 +--R +--R +--R 7 6 +--R - A b + 7B a b +--R (284) ---------------- +--R 2 +--R 42a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1293 +d0:=D(m0,x) +--R +--R +--R (285) 0 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^9 +--R +--R +--R (286) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1293 +r0:=-1/8*A*(a+b*x)^6/(a*x^8)+1/28*(A*b-4*a*B)*(a+b*x)^6/(a^2*x^7)-_ + 1/168*b*(A*b-4*a*B)*(a+b*x)^6/(a^3*x^6) +--R +--R +--R (287) +--R 1 8 1 7 8 1 3 5 6 1 3 5 5 4 4 5 +--R (- --- A b + -- B a b )x - - B a b x + (- - A a b - - B a b )x +--R 168 42 2 3 3 +--R + +--R 5 4 4 5 5 3 4 5 3 6 2 3 +--R (- - A a b - - B a b )x + (- 2A a b - 2B a b )x +--R 4 2 +--R + +--R 5 6 2 5 7 2 5 7 1 8 1 8 +--R (- - A a b - - B a b)x + (- - A a b - - B a )x - - A a +--R 3 6 7 7 8 +--R / +--R 3 8 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 287 + +--S 288 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (288) +--R 5 6 5 4 5 4 2 3 4 +--R - 84B b x + (- 56A b - 280B a b )x + (- 210A a b - 420B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 336A a b - 336B a b )x + (- 280A a b - 140B a b)x +--R + +--R 4 5 5 +--R (- 120A a b - 24B a )x - 21A a +--R / +--R 8 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1293 +m0:=a0-r0 +--R +--R +--R 8 7 +--R A b - 4B a b +--R (289) -------------- +--R 3 +--R 168a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1293 +d0:=D(m0,x) +--R +--R +--R (290) 0 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^10 +--R +--R +--R (291) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1293 +r0:=-1/9*a^5*A/x^9-1/8*a^4*(5*A*b+a*B)/x^8-5/7*a^3*b*(2*A*b+a*B)/x^7-_ + 5/3*a^2*b^2*(A*b+a*B)/x^6-a*b^3*(A*b+2*a*B)/x^5-_ + 1/4*b^4*(A*b+5*a*B)/x^4-1/3*b^5*B/x^3 +--R +--R +--R (292) +--R 1 5 6 1 5 5 4 5 4 2 3 4 +--R - - B b x + (- - A b - - B a b )x + (- A a b - 2B a b )x +--R 3 4 4 +--R + +--R 5 2 3 5 3 2 3 10 3 2 5 4 2 +--R (- - A a b - - B a b )x + (- -- A a b - - B a b)x +--R 3 3 7 7 +--R + +--R 5 4 1 5 1 5 +--R (- - A a b - - B a )x - - A a +--R 8 8 9 +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 292 + +--S 293 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (293) +--R 5 6 5 4 5 4 2 3 4 +--R - 168B b x + (- 126A b - 630B a b )x + (- 504A a b - 1008B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 840A a b - 840B a b )x + (- 720A a b - 360B a b)x +--R + +--R 4 5 5 +--R (- 315A a b - 63B a )x - 56A a +--R / +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1293 +m0:=a0-r0 +--R +--R +--R (294) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1293 +d0:=D(m0,x) +--R +--R +--R (295) 0 +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^11 +--R +--R +--R (296) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1293 +r0:=-1/10*a^5*A/x^10-1/9*a^4*(5*A*b+a*B)/x^9-5/8*a^3*b*(2*A*b+a*B)/x^8-_ + 10/7*a^2*b^2*(A*b+a*B)/x^7-5/6*a*b^3*(A*b+2*a*B)/x^6-_ + 1/5*b^4*(A*b+5*a*B)/x^5-1/4*b^5*B/x^4 +--R +--R +--R (297) +--R 1 5 6 1 5 4 5 5 4 5 2 3 4 +--R - - B b x + (- - A b - B a b )x + (- - A a b - - B a b )x +--R 4 5 6 3 +--R + +--R 10 2 3 10 3 2 3 5 3 2 5 4 2 +--R (- -- A a b - -- B a b )x + (- - A a b - - B a b)x +--R 7 7 4 8 +--R + +--R 5 4 1 5 1 5 +--R (- - A a b - - B a )x - -- A a +--R 9 9 10 +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 297 + +--S 298 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (298) +--R 5 6 5 4 5 4 2 3 4 +--R - 630B b x + (- 504A b - 2520B a b )x + (- 2100A a b - 4200B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 3600A a b - 3600B a b )x + (- 3150A a b - 1575B a b)x +--R + +--R 4 5 5 +--R (- 1400A a b - 280B a )x - 252A a +--R / +--R 10 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1293 +m0:=a0-r0 +--R +--R +--R (299) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1293 +d0:=D(m0,x) +--R +--R +--R (300) 0 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^12 +--R +--R +--R (301) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1293 +r0:=-1/11*a^5*A/x^11-1/10*a^4*(5*A*b+a*B)/x^10-5/9*a^3*b*(2*A*b+a*B)/x^9-_ + 5/4*a^2*b^2*(A*b+a*B)/x^8-5/7*a*b^3*(A*b+2*a*B)/x^7-_ + 1/6*b^4*(A*b+5*a*B)/x^6-1/5*b^5*B/x^5 +--R +--R +--R (302) +--R 1 5 6 1 5 5 4 5 5 4 10 2 3 4 +--R - - B b x + (- - A b - - B a b )x + (- - A a b - -- B a b )x +--R 5 6 6 7 7 +--R + +--R 5 2 3 5 3 2 3 10 3 2 5 4 2 +--R (- - A a b - - B a b )x + (- -- A a b - - B a b)x +--R 4 4 9 9 +--R + +--R 1 4 1 5 1 5 +--R (- - A a b - -- B a )x - -- A a +--R 2 10 11 +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 302 + +--S 303 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (303) +--R 5 6 5 4 5 +--R - 2772B b x + (- 2310A b - 11550B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (- 9900A a b - 19800B a b )x + (- 17325A a b - 17325B a b )x +--R + +--R 3 2 4 2 4 5 5 +--R (- 15400A a b - 7700B a b)x + (- 6930A a b - 1386B a )x - 1260A a +--R / +--R 11 +--R 13860x +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1293 +m0:=a0-r0 +--R +--R +--R (304) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1293 +d0:=D(m0,x) +--R +--R +--R (305) 0 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1293 +t0:=x^m*(a+b*x)^10*(A+B*x) +--R +--R +--R (306) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1293 +r0:=a^10*A*x^(1+m)/(1+m)+a^9*(10*A*b+a*B)*x^(2+m)/(2+m)+_ + 5*a^8*b*(9*A*b+2*a*B)*x^(3+m)/(3+m)+_ + 15*a^7*b^2*(8*A*b+3*a*B)*x^(4+m)/(4+m)+_ + 30*a^6*b^3*(7*A*b+4*a*B)*x^(5+m)/(5+m)+_ + 42*a^5*b^4*(6*A*b+5*a*B)*x^(6+m)/(6+m)+_ + 42*a^4*b^5*(5*A*b+6*a*B)*x^(7+m)/(7+m)+_ + 30*a^3*b^6*(4*A*b+7*a*B)*x^(8+m)/(8+m)+_ + 15*a^2*b^7*(3*A*b+8*a*B)*x^(9+m)/(9+m)+_ + 5*a*b^8*(2*A*b+9*a*B)*x^(10+m)/(10+m)+_ + b^9*(A*b+10*a*B)*x^(11+m)/(11+m)+b^10*B*x^(12+m)/(12+m) +--R +--R +--R (307) +--R 10 11 10 10 10 9 10 8 10 7 +--R B b m + 66B b m + 1925B b m + 32670B b m + 357423B b m +--R + +--R 10 6 10 5 10 4 10 3 +--R 2637558B b m + 13339535B b m + 45995730B b m + 105258076B b m +--R + +--R 10 2 10 10 +--R 150917976B b m + 120543840B b m + 39916800B b +--R * +--R m + 12 +--R x +--R + +--R 10 9 11 10 9 10 +--R (A b + 10B a b )m + (67A b + 670B a b )m +--R + +--R 10 9 9 10 9 8 +--R (1980A b + 19800B a b )m + (33990A b + 339900B a b )m +--R + +--R 10 9 7 10 9 6 +--R (375573A b + 3755730B a b )m + (2795331A b + 27953310B a b )m +--R + +--R 10 9 5 +--R (14241590A b + 142415900B a b )m +--R + +--R 10 9 4 +--R (49412660A b + 494126600B a b )m +--R + +--R 10 9 3 +--R (113667576A b + 1136675760B a b )m +--R + +--R 10 9 2 +--R (163671552A b + 1636715520B a b )m +--R + +--R 10 9 10 9 +--R (131172480A b + 1311724800B a b )m + 43545600A b + 435456000B a b +--R * +--R m + 11 +--R x +--R + +--R 9 2 8 11 9 2 8 10 +--R (10A a b + 45B a b )m + (680A a b + 3060B a b )m +--R + +--R 9 2 8 9 9 2 8 8 +--R (20370A a b + 91665B a b )m + (354000A a b + 1593000B a b )m +--R + +--R 9 2 8 7 +--R (3954630A a b + 17795835B a b )m +--R + +--R 9 2 8 6 +--R (29720040A a b + 133740180B a b )m +--R + +--R 9 2 8 5 +--R (152701910A a b + 687158595B a b )m +--R + +--R 9 2 8 4 +--R (533682400A a b + 2401570800B a b )m +--R + +--R 9 2 8 3 +--R (1235244360A a b + 5558599620B a b )m +--R + +--R 9 2 8 2 +--R (1787705280A a b + 8044673760B a b )m +--R + +--R 9 2 8 9 +--R (1438542720A a b + 6473442240B a b )m + 479001600A a b +--R + +--R 2 8 +--R 2155507200B a b +--R * +--R m + 10 +--R x +--R + +--R 2 8 3 7 11 2 8 3 7 10 +--R (45A a b + 120B a b )m + (3105A a b + 8280B a b )m +--R + +--R 2 8 3 7 9 2 8 3 7 8 +--R (94320A a b + 251520B a b )m + (1660770A a b + 4428720B a b )m +--R + +--R 2 8 3 7 7 +--R (18778905A a b + 50077080B a b )m +--R + +--R 2 8 3 7 6 +--R (142688385A a b + 380502360B a b )m +--R + +--R 2 8 3 7 5 +--R (740364930A a b + 1974306480B a b )m +--R + +--R 2 8 3 7 4 +--R (2609872380A a b + 6959659680B a b )m +--R + +--R 2 8 3 7 3 +--R (6085456200A a b + 16227883200B a b )m +--R + +--R 2 8 3 7 2 +--R (8861564160A a b + 23630837760B a b )m +--R + +--R 2 8 3 7 2 8 +--R (7166102400A a b + 19109606400B a b )m + 2395008000A a b +--R + +--R 3 7 +--R 6386688000B a b +--R * +--R m + 9 +--R x +--R + +--R 3 7 4 6 11 3 7 4 6 10 +--R (120A a b + 210B a b )m + (8400A a b + 14700B a b )m +--R + +--R 3 7 4 6 9 3 7 4 6 8 +--R (258840A a b + 452970B a b )m + (4621680A a b + 8087940B a b )m +--R + +--R 3 7 4 6 7 +--R (52962120A a b + 92683710B a b )m +--R + +--R 3 7 4 6 6 +--R (407499120A a b + 713123460B a b )m +--R + +--R 3 7 4 6 5 +--R (2138834760A a b + 3742960830B a b )m +--R + +--R 3 7 4 6 4 +--R (7617739920A a b + 13331044860B a b )m +--R + +--R 3 7 4 6 3 +--R (17922900960A a b + 31365076680B a b )m +--R + +--R 3 7 4 6 2 +--R (26298578880A a b + 46022513040B a b )m +--R + +--R 3 7 4 6 3 7 +--R (21398515200A a b + 37447401600B a b )m + 7185024000A a b +--R + +--R 4 6 +--R 12573792000B a b +--R * +--R m + 8 +--R x +--R + +--R 4 6 5 5 11 4 6 5 5 10 +--R (210A a b + 252B a b )m + (14910A a b + 17892B a b )m +--R + +--R 4 6 5 5 9 4 6 5 5 8 +--R (466200A a b + 559440B a b )m + (8448300A a b + 10137960B a b )m +--R + +--R 4 6 5 5 7 +--R (98249130A a b + 117898956B a b )m +--R + +--R 4 6 5 5 6 +--R (766849230A a b + 920219076B a b )m +--R + +--R 4 6 5 5 5 +--R (4080003900A a b + 4896004680B a b )m +--R + +--R 4 6 5 5 4 +--R (14714704200A a b + 17657645040B a b )m +--R + +--R 4 6 5 5 3 +--R (35010506160A a b + 42012607392B a b )m +--R + +--R 4 6 5 5 2 +--R (51869583360A a b + 62243500032B a b )m +--R + +--R 4 6 5 5 4 6 +--R (42540422400A a b + 51048506880B a b )m + 14370048000A a b +--R + +--R 5 5 +--R 17244057600B a b +--R * +--R m + 7 +--R x +--R + +--R 5 5 6 4 11 5 5 6 4 10 +--R (252A a b + 210B a b )m + (18144A a b + 15120B a b )m +--R + +--R 5 5 6 4 9 5 5 6 4 8 +--R (575820A a b + 479850B a b )m + (10599120A a b + 8832600B a b )m +--R + +--R 5 5 6 4 7 +--R (125269956A a b + 104391630B a b )m +--R + +--R 5 5 6 4 6 +--R (993892032A a b + 828243360B a b )m +--R + +--R 5 5 6 4 5 +--R (5374186020A a b + 4478488350B a b )m +--R + +--R 5 5 6 4 4 +--R (19684561680A a b + 16403801400B a b )m +--R + +--R 5 5 6 4 3 +--R (47508752592A a b + 39590627160B a b )m +--R + +--R 5 5 6 4 2 +--R (71279236224A a b + 59399363520B a b )m +--R + +--R 5 5 6 4 5 5 +--R (59077589760A a b + 49231324800B a b )m + 20118067200A a b +--R + +--R 6 4 +--R 16765056000B a b +--R * +--R m + 6 +--R x +--R + +--R 6 4 7 3 11 6 4 7 3 10 +--R (210A a b + 120B a b )m + (15330A a b + 8760B a b )m +--R + +--R 6 4 7 3 9 6 4 7 3 8 +--R (493920A a b + 282240B a b )m + (9242100A a b + 5281200B a b )m +--R + +--R 6 4 7 3 7 +--R (111176730A a b + 63529560B a b )m +--R + +--R 6 4 7 3 6 +--R (898709490A a b + 513548280B a b )m +--R + +--R 6 4 7 3 5 +--R (4954401060A a b + 2831086320B a b )m +--R + +--R 6 4 7 3 4 +--R (18502726200A a b + 10572986400B a b )m +--R + +--R 6 4 7 3 3 +--R (45499804560A a b + 25999888320B a b )m +--R + +--R 6 4 7 3 2 +--R (69444103680A a b + 39682344960B a b )m +--R + +--R 6 4 7 3 6 4 +--R (58406987520A a b + 33375421440B a b )m + 20118067200A a b +--R + +--R 7 3 +--R 11496038400B a b +--R * +--R m + 5 +--R x +--R + +--R 7 3 8 2 11 7 3 8 2 10 +--R (120A a b + 45B a b )m + (8880A a b + 3330B a b )m +--R + +--R 7 3 8 2 9 7 3 8 2 8 +--R (290520A a b + 108945B a b )m + (5530320A a b + 2073870B a b )m +--R + +--R 7 3 8 2 7 +--R (67814280A a b + 25430355B a b )m +--R + +--R 7 3 8 2 6 +--R (559938960A a b + 209977110B a b )m +--R + +--R 7 3 8 2 5 +--R (3159071880A a b + 1184651955B a b )m +--R + +--R 7 3 8 2 4 +--R (12092130480A a b + 4534548930B a b )m +--R + +--R 7 3 8 2 3 +--R (30496298400A a b + 11436111900B a b )m +--R + +--R 7 3 8 2 2 +--R (47696592960A a b + 17886222360B a b )m +--R + +--R 7 3 8 2 7 3 +--R (41000774400A a b + 15375290400B a b )m + 14370048000A a b +--R + +--R 8 2 +--R 5388768000B a b +--R * +--R m + 4 +--R x +--R + +--R 8 2 9 11 8 2 9 10 +--R (45A a b + 10B a b)m + (3375A a b + 750B a b)m +--R + +--R 8 2 9 9 8 2 9 8 +--R (112140A a b + 24920B a b)m + (2173230A a b + 482940B a b)m +--R + +--R 8 2 9 7 +--R (27206145A a b + 6045810B a b)m +--R + +--R 8 2 9 6 +--R (230080095A a b + 51128910B a b)m +--R + +--R 8 2 9 5 +--R (1334320110A a b + 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+--R 7 3 8 2 8 +--R (5530320A a b + 2073870B a b )m +--R + +--R 7 3 8 2 7 +--R (67814280A a b + 25430355B a b )m +--R + +--R 7 3 8 2 6 +--R (559938960A a b + 209977110B a b )m +--R + +--R 7 3 8 2 5 +--R (3159071880A a b + 1184651955B a b )m +--R + +--R 7 3 8 2 4 +--R (12092130480A a b + 4534548930B a b )m +--R + +--R 7 3 8 2 3 +--R (30496298400A a b + 11436111900B a b )m +--R + +--R 7 3 8 2 2 +--R (47696592960A a b + 17886222360B a b )m +--R + +--R 7 3 8 2 7 3 +--R (41000774400A a b + 15375290400B a b )m + 14370048000A a b +--R + +--R 8 2 +--R 5388768000B a b +--R * +--R 4 +--R x +--R + +--R 8 2 9 11 8 2 9 10 +--R (45A a b + 10B a b)m + (3375A a b + 750B a b)m +--R + +--R 8 2 9 9 8 2 9 8 +--R (112140A a b + 24920B a b)m + (2173230A a b + 482940B a b)m +--R + +--R 8 2 9 7 +--R (27206145A a b + 6045810B a b)m +--R + +--R 8 2 9 6 +--R (230080095A a b + 51128910B a b)m +--R + +--R 8 2 9 5 +--R (1334320110A a b + 296515580B a b)m +--R + +--R 8 2 9 4 +--R (5270196420A a b + 1171154760B a b)m +--R + +--R 8 2 9 3 +--R (13763718360A a b + 3058604080B a b)m +--R + +--R 8 2 9 2 +--R (22339514880A a b + 4964336640B a b)m +--R + +--R 8 2 9 8 2 +--R (19901635200A a b + 4422585600B a b)m + 7185024000A a b +--R + +--R 9 +--R 1596672000B a b +--R * +--R 3 +--R x +--R + +--R 9 10 11 9 10 10 +--R (10A a b + B a )m + (760A a b + 76B a )m +--R + +--R 9 10 9 9 10 8 +--R (25650A a b + 2565B a )m + (506400A a b + 50640B a )m +--R + +--R 9 10 7 9 10 6 +--R (6481830A a b + 648183B a )m + (56302680A a b + 5630268B a )m +--R + +--R 9 10 5 +--R (337296950A a b + 33729695B a )m +--R + +--R 9 10 4 +--R (1386107600A a b + 138610760B a )m +--R + +--R 9 10 3 +--R (3799853160A a b + 379985316B a )m +--R + +--R 9 10 2 +--R (6540442560A a b + 654044256B a )m +--R + +--R 9 10 9 +--R (6234710400A a b + 623471040B a )m + 2395008000A a b +--R + +--R 10 +--R 239500800B a +--R * +--R 2 +--R x +--R + +--R 10 11 10 10 10 9 10 8 +--R A a m + 77A a m + 2640A a m + 53130A a m +--R + +--R 10 7 10 6 10 5 +--R 696333A a m + 6230301A a m + 38759930A a m +--R + +--R 10 4 10 3 10 2 +--R 167310220A a m + 489896616A a m + 924118272A a m +--R + +--R 10 10 +--R 1007441280A a m + 479001600A a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 10 11 10 10 10 9 10 8 10 7 +--R - B b m - 66B b m - 1925B b m - 32670B b m - 357423B b m +--R + +--R 10 6 10 5 10 4 +--R - 2637558B b m - 13339535B b m - 45995730B b m +--R + +--R 10 3 10 2 10 10 +--R - 105258076B b m - 150917976B b m - 120543840B b m - 39916800B b +--R * +--R m + 12 +--R x +--R + +--R 10 9 11 10 9 10 +--R (- A b - 10B a b )m + (- 67A b - 670B a b )m +--R + +--R 10 9 9 10 9 8 +--R (- 1980A b - 19800B a b )m + (- 33990A b - 339900B a b )m +--R + +--R 10 9 7 +--R (- 375573A b - 3755730B a b )m +--R + +--R 10 9 6 +--R (- 2795331A b - 27953310B a b )m +--R + +--R 10 9 5 +--R (- 14241590A b - 142415900B a b )m +--R + +--R 10 9 4 +--R (- 49412660A b - 494126600B a b )m +--R + +--R 10 9 3 +--R (- 113667576A b - 1136675760B a b )m +--R + +--R 10 9 2 +--R (- 163671552A b - 1636715520B a b )m +--R + +--R 10 9 10 +--R (- 131172480A b - 1311724800B a b )m - 43545600A b +--R + +--R 9 +--R - 435456000B a b +--R * +--R m + 11 +--R x +--R + +--R 9 2 8 11 9 2 8 10 +--R (- 10A a b - 45B a b )m + (- 680A a b - 3060B a b )m +--R + +--R 9 2 8 9 9 2 8 8 +--R (- 20370A a b - 91665B a b )m + (- 354000A a b - 1593000B a b )m +--R + +--R 9 2 8 7 +--R (- 3954630A a b - 17795835B a b )m +--R + +--R 9 2 8 6 +--R (- 29720040A a b - 133740180B a b )m +--R + +--R 9 2 8 5 +--R (- 152701910A a b - 687158595B a b )m +--R + +--R 9 2 8 4 +--R (- 533682400A a b - 2401570800B a b )m +--R + +--R 9 2 8 3 +--R (- 1235244360A a b - 5558599620B a b )m +--R + +--R 9 2 8 2 +--R (- 1787705280A a b - 8044673760B a b )m +--R + +--R 9 2 8 9 +--R (- 1438542720A a b - 6473442240B a b )m - 479001600A a b +--R + +--R 2 8 +--R - 2155507200B a b +--R * +--R m + 10 +--R x +--R + +--R 2 8 3 7 11 2 8 3 7 10 +--R (- 45A a b - 120B a b )m + (- 3105A a b - 8280B a b )m +--R + +--R 2 8 3 7 9 +--R (- 94320A a b - 251520B a b )m +--R + +--R 2 8 3 7 8 +--R (- 1660770A a b - 4428720B a b )m +--R + +--R 2 8 3 7 7 +--R (- 18778905A a b - 50077080B a b )m +--R + +--R 2 8 3 7 6 +--R (- 142688385A a b - 380502360B a b )m +--R + +--R 2 8 3 7 5 +--R (- 740364930A a b - 1974306480B a b )m +--R + +--R 2 8 3 7 4 +--R (- 2609872380A a b - 6959659680B a b )m +--R + +--R 2 8 3 7 3 +--R (- 6085456200A a b - 16227883200B a b )m +--R + +--R 2 8 3 7 2 +--R (- 8861564160A a b - 23630837760B a b )m +--R + +--R 2 8 3 7 2 8 +--R (- 7166102400A a b - 19109606400B a b )m - 2395008000A a b +--R + +--R 3 7 +--R - 6386688000B a b +--R * +--R m + 9 +--R x +--R + +--R 3 7 4 6 11 3 7 4 6 10 +--R (- 120A a b - 210B a b )m + (- 8400A a b - 14700B a b )m +--R + +--R 3 7 4 6 9 +--R (- 258840A a b - 452970B a b )m +--R + +--R 3 7 4 6 8 +--R (- 4621680A a b - 8087940B a b )m +--R + +--R 3 7 4 6 7 +--R (- 52962120A a b - 92683710B a b )m +--R + +--R 3 7 4 6 6 +--R (- 407499120A a b - 713123460B a b )m +--R + +--R 3 7 4 6 5 +--R (- 2138834760A a b - 3742960830B a b )m +--R + +--R 3 7 4 6 4 +--R (- 7617739920A a b - 13331044860B a b )m +--R + +--R 3 7 4 6 3 +--R (- 17922900960A a b - 31365076680B a b )m +--R + +--R 3 7 4 6 2 +--R (- 26298578880A a b - 46022513040B a b )m +--R + +--R 3 7 4 6 3 7 +--R (- 21398515200A a b - 37447401600B a b )m - 7185024000A a b +--R + +--R 4 6 +--R - 12573792000B a b +--R * +--R m + 8 +--R x +--R + +--R 4 6 5 5 11 4 6 5 5 10 +--R (- 210A a b - 252B a b )m + (- 14910A a b - 17892B a b )m +--R + +--R 4 6 5 5 9 +--R (- 466200A a b - 559440B a b )m +--R + +--R 4 6 5 5 8 +--R (- 8448300A a b - 10137960B a b )m +--R + +--R 4 6 5 5 7 +--R (- 98249130A a b - 117898956B a b )m +--R + +--R 4 6 5 5 6 +--R (- 766849230A a b - 920219076B a b )m +--R + +--R 4 6 5 5 5 +--R (- 4080003900A a b - 4896004680B a b )m +--R + +--R 4 6 5 5 4 +--R (- 14714704200A a b - 17657645040B a b )m +--R + +--R 4 6 5 5 3 +--R (- 35010506160A a b - 42012607392B a b )m +--R + +--R 4 6 5 5 2 +--R (- 51869583360A a b - 62243500032B a b )m +--R + +--R 4 6 5 5 4 6 +--R (- 42540422400A a b - 51048506880B a b )m - 14370048000A a b +--R + +--R 5 5 +--R - 17244057600B a b +--R * +--R m + 7 +--R x +--R + +--R 5 5 6 4 11 5 5 6 4 10 +--R (- 252A a b - 210B a b )m + (- 18144A a b - 15120B a b )m +--R + +--R 5 5 6 4 9 +--R (- 575820A a b - 479850B a b )m +--R + +--R 5 5 6 4 8 +--R (- 10599120A a b - 8832600B a b )m +--R + +--R 5 5 6 4 7 +--R (- 125269956A a b - 104391630B a b )m +--R + +--R 5 5 6 4 6 +--R (- 993892032A a b - 828243360B a b )m +--R + +--R 5 5 6 4 5 +--R (- 5374186020A a b - 4478488350B a b )m +--R + +--R 5 5 6 4 4 +--R (- 19684561680A a b - 16403801400B a b )m +--R + +--R 5 5 6 4 3 +--R (- 47508752592A a b - 39590627160B a b )m +--R + +--R 5 5 6 4 2 +--R (- 71279236224A a b - 59399363520B a b )m +--R + +--R 5 5 6 4 5 5 +--R (- 59077589760A a b - 49231324800B a b )m - 20118067200A a b +--R + +--R 6 4 +--R - 16765056000B a b +--R * +--R m + 6 +--R x +--R + +--R 6 4 7 3 11 6 4 7 3 10 +--R (- 210A a b - 120B a b )m + (- 15330A a b - 8760B a b )m +--R + +--R 6 4 7 3 9 +--R (- 493920A a b - 282240B a b )m +--R + +--R 6 4 7 3 8 +--R (- 9242100A a b - 5281200B a b )m +--R + +--R 6 4 7 3 7 +--R (- 111176730A a b - 63529560B a b )m +--R + +--R 6 4 7 3 6 +--R (- 898709490A a b - 513548280B a b )m +--R + +--R 6 4 7 3 5 +--R (- 4954401060A a b - 2831086320B a b )m +--R + +--R 6 4 7 3 4 +--R (- 18502726200A a b - 10572986400B a b )m +--R + +--R 6 4 7 3 3 +--R (- 45499804560A a b - 25999888320B a b )m +--R + +--R 6 4 7 3 2 +--R (- 69444103680A a b - 39682344960B a b )m +--R + +--R 6 4 7 3 6 4 +--R (- 58406987520A a b - 33375421440B a b )m - 20118067200A a b +--R + +--R 7 3 +--R - 11496038400B a b +--R * +--R m + 5 +--R x +--R + +--R 7 3 8 2 11 7 3 8 2 10 +--R (- 120A a b - 45B a b )m + (- 8880A a b - 3330B a b )m +--R + +--R 7 3 8 2 9 +--R (- 290520A a b - 108945B a b )m +--R + +--R 7 3 8 2 8 +--R (- 5530320A a b - 2073870B a b )m +--R + +--R 7 3 8 2 7 +--R (- 67814280A a b - 25430355B a b )m +--R + +--R 7 3 8 2 6 +--R (- 559938960A a b - 209977110B a b )m +--R + +--R 7 3 8 2 5 +--R (- 3159071880A a b - 1184651955B a b )m +--R + +--R 7 3 8 2 4 +--R (- 12092130480A a b - 4534548930B a b )m +--R + +--R 7 3 8 2 3 +--R (- 30496298400A a b - 11436111900B a b )m +--R + +--R 7 3 8 2 2 +--R (- 47696592960A a b - 17886222360B a b )m +--R + +--R 7 3 8 2 7 3 +--R (- 41000774400A a b - 15375290400B a b )m - 14370048000A a b +--R + +--R 8 2 +--R - 5388768000B a b +--R * +--R m + 4 +--R x +--R + +--R 8 2 9 11 8 2 9 10 +--R (- 45A a b - 10B a b)m + (- 3375A a b - 750B a b)m +--R + +--R 8 2 9 9 8 2 9 8 +--R (- 112140A a b - 24920B a b)m + (- 2173230A a b - 482940B a b)m +--R + +--R 8 2 9 7 +--R (- 27206145A a b - 6045810B a b)m +--R + +--R 8 2 9 6 +--R (- 230080095A a b - 51128910B a b)m +--R + +--R 8 2 9 5 +--R (- 1334320110A a b - 296515580B a b)m +--R + +--R 8 2 9 4 +--R (- 5270196420A a b - 1171154760B a b)m +--R + +--R 8 2 9 3 +--R (- 13763718360A a b - 3058604080B a b)m +--R + +--R 8 2 9 2 +--R (- 22339514880A a b - 4964336640B a b)m +--R + +--R 8 2 9 8 2 +--R (- 19901635200A a b - 4422585600B a b)m - 7185024000A a b +--R + +--R 9 +--R - 1596672000B a b +--R * +--R m + 3 +--R x +--R + +--R 9 10 11 9 10 10 +--R (- 10A a b - B a )m + (- 760A a b - 76B a )m +--R + +--R 9 10 9 9 10 8 +--R (- 25650A a b - 2565B a )m + (- 506400A a b - 50640B a )m +--R + +--R 9 10 7 9 10 6 +--R (- 6481830A a b - 648183B a )m + (- 56302680A a b - 5630268B a )m +--R + +--R 9 10 5 +--R (- 337296950A a b - 33729695B a )m +--R + +--R 9 10 4 +--R (- 1386107600A a b - 138610760B a )m +--R + +--R 9 10 3 +--R (- 3799853160A a b - 379985316B a )m +--R + +--R 9 10 2 +--R (- 6540442560A a b - 654044256B a )m +--R + +--R 9 10 9 +--R (- 6234710400A a b - 623471040B a )m - 2395008000A a b +--R + +--R 10 +--R - 239500800B a +--R * +--R m + 2 +--R x +--R + +--R 10 11 10 10 10 9 10 8 10 7 +--R - A a m - 77A a m - 2640A a m - 53130A a m - 696333A a m +--R + +--R 10 6 10 5 10 4 +--R - 6230301A a m - 38759930A a m - 167310220A a m +--R + +--R 10 3 10 2 10 +--R - 489896616A a m - 924118272A a m - 1007441280A a m +--R + +--R 10 +--R - 479001600A a +--R * +--R m + 1 +--R x +--R / +--R 12 11 10 9 8 7 6 +--R m + 78m + 2717m + 55770m + 749463m + 6926634m + 44990231m +--R + +--R 5 4 3 2 +--R 206070150m + 657206836m + 1414014888m + 1931559552m + 1486442880m +--R + +--R 479001600 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1293 +d0:=D(m0,x) +--R +--R +--R (310) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R * +--R m log(x) +--R %e +--R + +--R 10 m + 11 10 9 m + 10 +--R - B b x + (- A b - 10B a b )x +--R + +--R 9 2 8 m + 9 2 8 3 7 m + 8 +--R (- 10A a b - 45B a b )x + (- 45A a b - 120B a b )x +--R + +--R 3 7 4 6 m + 7 4 6 5 5 m + 6 +--R (- 120A a b - 210B a b )x + (- 210A a b - 252B a b )x +--R + +--R 5 5 6 4 m + 5 6 4 7 3 m + 4 +--R (- 252A a b - 210B a b )x + (- 210A a b - 120B a b )x +--R + +--R 7 3 8 2 m + 3 8 2 9 m + 2 +--R (- 120A a b - 45B a b )x + (- 45A a b - 10B a b)x +--R + +--R 9 10 m + 1 10 m +--R (- 10A a b - B a )x - A a x +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1293 +t0:=x^10*(a+b*x)^10*(A+B*x) +--R +--R +--R (311) +--R 10 21 10 9 20 9 2 8 19 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 18 3 7 4 6 17 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 16 5 5 6 4 15 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 14 7 3 8 2 13 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 12 9 10 11 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 311 + +--S 312 of 1293 +r0:=1/11*a^10*A*x^11+1/12*a^9*(10*A*b+a*B)*x^12+_ + 5/13*a^8*b*(9*A*b+2*a*B)*x^13+15/14*a^7*b^2*(8*A*b+3*a*B)*x^14+_ + 2*a^6*b^3*(7*A*b+4*a*B)*x^15+21/8*a^5*b^4*(6*A*b+5*a*B)*x^16+_ + 42/17*a^4*b^5*(5*A*b+6*a*B)*x^17+5/3*a^3*b^6*(4*A*b+7*a*B)*x^18+_ + 15/19*a^2*b^7*(3*A*b+8*a*B)*x^19+1/4*a*b^8*(2*A*b+9*a*B)*x^20+_ + 1/21*b^9*(A*b+10*a*B)*x^21+1/22*b^10*B*x^22 +--R +--R +--R (312) +--R 1 10 22 1 10 10 9 21 1 9 9 2 8 20 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x +--R 22 21 21 2 4 +--R + +--R 45 2 8 120 3 7 19 20 3 7 35 4 6 18 +--R (-- A a b + --- B a b )x + (-- A a b + -- B a b )x +--R 19 19 3 3 +--R + +--R 210 4 6 252 5 5 17 63 5 5 105 6 4 16 +--R (--- A a b + --- B a b )x + (-- A a b + --- B a b )x +--R 17 17 4 8 +--R + +--R 6 4 7 3 15 60 7 3 45 8 2 14 +--R (14A a b + 8B a b )x + (-- A a b + -- B a b )x +--R 7 14 +--R + +--R 45 8 2 10 9 13 5 9 1 10 12 1 10 11 +--R (-- A a b + -- B a b)x + (- A a b + -- B a )x + -- A a x +--R 13 13 6 12 11 +--R Type: Polynomial(Fraction(Integer)) +--E 312 + +--S 313 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (313) +--R 1 10 22 1 10 10 9 21 1 9 9 2 8 20 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x +--R 22 21 21 2 4 +--R + +--R 45 2 8 120 3 7 19 20 3 7 35 4 6 18 +--R (-- A a b + --- B a b )x + (-- A a b + -- B a b )x +--R 19 19 3 3 +--R + +--R 210 4 6 252 5 5 17 63 5 5 105 6 4 16 +--R (--- A a b + --- B a b )x + (-- A a b + --- B a b )x +--R 17 17 4 8 +--R + +--R 6 4 7 3 15 60 7 3 45 8 2 14 +--R (14A a b + 8B a b )x + (-- A a b + -- B a b )x +--R 7 14 +--R + +--R 45 8 2 10 9 13 5 9 1 10 12 1 10 11 +--R (-- A a b + -- B a b)x + (- A a b + -- B a )x + -- A a x +--R 13 13 6 12 11 +--R Type: Polynomial(Fraction(Integer)) +--E 313 + +--S 314 of 1293 +m0:=a0-r0 +--R +--R +--R (314) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 314 + +--S 315 of 1293 +d0:=D(m0,x) +--R +--R +--R (315) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 315 + +--S 316 of 1293 +t0:=x^9*(a+b*x)^10*(A+B*x) +--R +--R +--R (316) +--R 10 20 10 9 19 9 2 8 18 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 17 3 7 4 6 16 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 15 5 5 6 4 14 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 13 7 3 8 2 12 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 11 9 10 10 10 9 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 316 + +--S 317 of 1293 +r0:=1/10*a^10*A*x^10+1/11*a^9*(10*A*b+a*B)*x^11+_ + 5/12*a^8*b*(9*A*b+2*a*B)*x^12+15/13*a^7*b^2*(8*A*b+3*a*B)*x^13+_ + 15/7*a^6*b^3*(7*A*b+4*a*B)*x^14+14/5*a^5*b^4*(6*A*b+5*a*B)*x^15+_ + 21/8*a^4*b^5*(5*A*b+6*a*B)*x^16+30/17*a^3*b^6*(4*A*b+7*a*B)*x^17+_ + 5/6*a^2*b^7*(3*A*b+8*a*B)*x^18+5/19*a*b^8*(2*A*b+9*a*B)*x^19+_ + 1/20*b^9*(A*b+10*a*B)*x^20+1/21*b^10*B*x^21 +--R +--R +--R (317) +--R 1 10 21 1 10 1 9 20 10 9 45 2 8 19 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 21 20 2 19 19 +--R + +--R 5 2 8 20 3 7 18 120 3 7 210 4 6 17 +--R (- A a b + -- B a b )x + (--- A a b + --- B a b )x +--R 2 3 17 17 +--R + +--R 105 4 6 63 5 5 16 84 5 5 6 4 15 +--R (--- A a b + -- B a b )x + (-- A a b + 14B a b )x +--R 8 4 5 +--R + +--R 6 4 60 7 3 14 120 7 3 45 8 2 13 +--R (15A a b + -- B a b )x + (--- A a b + -- B a b )x +--R 7 13 13 +--R + +--R 15 8 2 5 9 12 10 9 1 10 11 1 10 10 +--R (-- A a b + - B a b)x + (-- A a b + -- B a )x + -- A a x +--R 4 6 11 11 10 +--R Type: Polynomial(Fraction(Integer)) +--E 317 + +--S 318 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (318) +--R 1 10 21 1 10 1 9 20 10 9 45 2 8 19 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 21 20 2 19 19 +--R + +--R 5 2 8 20 3 7 18 120 3 7 210 4 6 17 +--R (- A a b + -- B a b )x + (--- A a b + --- B a b )x +--R 2 3 17 17 +--R + +--R 105 4 6 63 5 5 16 84 5 5 6 4 15 +--R (--- A a b + -- B a b )x + (-- A a b + 14B a b )x +--R 8 4 5 +--R + +--R 6 4 60 7 3 14 120 7 3 45 8 2 13 +--R (15A a b + -- B a b )x + (--- A a b + -- B a b )x +--R 7 13 13 +--R + +--R 15 8 2 5 9 12 10 9 1 10 11 1 10 10 +--R (-- A a b + - B a b)x + (-- A a b + -- B a )x + -- A a x +--R 4 6 11 11 10 +--R Type: Polynomial(Fraction(Integer)) +--E 318 + +--S 319 of 1293 +m0:=a0-r0 +--R +--R +--R (319) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 319 + +--S 320 of 1293 +d0:=D(m0,x) +--R +--R +--R (320) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 320 + +--S 321 of 1293 +t0:=x^8*(a+b*x)^10*(A+B*x) +--R +--R +--R (321) +--R 10 19 10 9 18 9 2 8 17 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 16 3 7 4 6 15 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 14 5 5 6 4 13 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 12 7 3 8 2 11 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 10 9 10 9 10 8 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 321 + +--S 322 of 1293 +r0:=1/9*a^10*A*x^9+1/10*a^9*(10*A*b+a*B)*x^10+_ + 5/11*a^8*b*(9*A*b+2*a*B)*x^11+5/4*a^7*b^2*(8*A*b+3*a*B)*x^12+_ + 30/13*a^6*b^3*(7*A*b+4*a*B)*x^13+3*a^5*b^4*(6*A*b+5*a*B)*x^14+_ + 14/5*a^4*b^5*(5*A*b+6*a*B)*x^15+15/8*a^3*b^6*(4*A*b+7*a*B)*x^16+_ + 15/17*a^2*b^7*(3*A*b+8*a*B)*x^17+5/18*a*b^8*(2*A*b+9*a*B)*x^18+_ + 1/19*b^9*(A*b+10*a*B)*x^19+1/20*b^10*B*x^20 +--R +--R +--R (322) +--R 1 10 20 1 10 10 9 19 5 9 5 2 8 18 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x +--R 20 19 19 9 2 +--R + +--R 45 2 8 120 3 7 17 15 3 7 105 4 6 16 +--R (-- A a b + --- B a b )x + (-- A a b + --- B a b )x +--R 17 17 2 8 +--R + +--R 4 6 84 5 5 15 5 5 6 4 14 +--R (14A a b + -- B a b )x + (18A a b + 15B a b )x +--R 5 +--R + +--R 210 6 4 120 7 3 13 7 3 15 8 2 12 +--R (--- A a b + --- B a b )x + (10A a b + -- B a b )x +--R 13 13 4 +--R + +--R 45 8 2 10 9 11 9 1 10 10 1 10 9 +--R (-- A a b + -- B a b)x + (A a b + -- B a )x + - A a x +--R 11 11 10 9 +--R Type: Polynomial(Fraction(Integer)) +--E 322 + +--S 323 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (323) +--R 1 10 20 1 10 10 9 19 5 9 5 2 8 18 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x +--R 20 19 19 9 2 +--R + +--R 45 2 8 120 3 7 17 15 3 7 105 4 6 16 +--R (-- A a b + --- B a b )x + (-- A a b + --- B a b )x +--R 17 17 2 8 +--R + +--R 4 6 84 5 5 15 5 5 6 4 14 +--R (14A a b + -- B a b )x + (18A a b + 15B a b )x +--R 5 +--R + +--R 210 6 4 120 7 3 13 7 3 15 8 2 12 +--R (--- A a b + --- B a b )x + (10A a b + -- B a b )x +--R 13 13 4 +--R + +--R 45 8 2 10 9 11 9 1 10 10 1 10 9 +--R (-- A a b + -- B a b)x + (A a b + -- B a )x + - A a x +--R 11 11 10 9 +--R Type: Polynomial(Fraction(Integer)) +--E 323 + +--S 324 of 1293 +m0:=a0-r0 +--R +--R +--R (324) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 324 + +--S 325 of 1293 +d0:=D(m0,x) +--R +--R +--R (325) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 325 + +--S 326 of 1293 +t0:=x^7*(a+b*x)^10*(A+B*x) +--R +--R +--R (326) +--R 10 18 10 9 17 9 2 8 16 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 15 3 7 4 6 14 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 13 5 5 6 4 12 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 11 7 3 8 2 10 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 9 9 10 8 10 7 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 326 + +--S 327 of 1293 +r0:=-1/11*a^7*(A*b-a*B)*(a+b*x)^11/b^9+_ + 1/12*a^6*(7*A*b-8*a*B)*(a+b*x)^12/b^9-_ + 7/13*a^5*(3*A*b-4*a*B)*(a+b*x)^13/b^9+_ + 1/2*a^4*(5*A*b-8*a*B)*(a+b*x)^14/b^9-_ + 7/3*a^3*(A*b-2*a*B)*(a+b*x)^15/b^9+_ + 7/16*a^2*(3*A*b-8*a*B)*(a+b*x)^16/b^9-_ + 7/17*a*(A*b-4*a*B)*(a+b*x)^17/b^9+_ + 1/18*(A*b-8*a*B)*(a+b*x)^18/b^9+1/19*B*(a+b*x)^19/b^9 +--R +--R +--R (327) +--R 1 19 19 1 19 5 18 18 10 18 45 2 17 17 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 19 18 9 17 17 +--R + +--R 45 2 17 15 3 16 16 3 16 4 15 15 +--R (-- A a b + -- B a b )x + (8A a b + 14B a b )x +--R 16 2 +--R + +--R 4 15 5 14 14 252 5 14 210 6 13 13 +--R (15A a b + 18B a b )x + (--- A a b + --- B a b )x +--R 13 13 +--R + +--R 35 6 13 7 12 12 120 7 12 45 8 11 11 +--R (-- A a b + 10B a b )x + (--- A a b + -- B a b )x +--R 2 11 11 +--R + +--R 9 8 11 9 10 10 10 9 10 1 10 9 9 1 10 9 8 +--R (- A a b + B a b )x + (-- A a b + - B a b )x + - A a b x +--R 2 9 9 8 +--R + +--R 1 18 1 19 +--R - ------ A a b + ------ B a +--R 350064 831402 +--R / +--R 9 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 327 + +--S 328 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (328) +--R 1 10 19 1 10 5 9 18 10 9 45 2 8 17 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 19 18 9 17 17 +--R + +--R 45 2 8 15 3 7 16 3 7 4 6 15 +--R (-- A a b + -- B a b )x + (8A a b + 14B a b )x +--R 16 2 +--R + +--R 4 6 5 5 14 252 5 5 210 6 4 13 +--R (15A a b + 18B a b )x + (--- A a b + --- B a b )x +--R 13 13 +--R + +--R 35 6 4 7 3 12 120 7 3 45 8 2 11 +--R (-- A a b + 10B a b )x + (--- A a b + -- B a b )x +--R 2 11 11 +--R + +--R 9 8 2 9 10 10 9 1 10 9 1 10 8 +--R (- A a b + B a b)x + (-- A a b + - B a )x + - A a x +--R 2 9 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 328 + +--S 329 of 1293 +m0:=a0-r0 +--R +--R +--R 1 18 1 19 +--R ------ A a b - ------ B a +--R 350064 831402 +--R (329) ---------------------------- +--R 9 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 329 + +--S 330 of 1293 +d0:=D(m0,x) +--R +--R +--R (330) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 330 + +--S 331 of 1293 +t0:=x^6*(a+b*x)^10*(A+B*x) +--R +--R +--R (331) +--R 10 17 10 9 16 9 2 8 15 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 14 3 7 4 6 13 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 12 5 5 6 4 11 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 10 7 3 8 2 9 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 8 9 10 7 10 6 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 331 + +--S 332 of 1293 +r0:=1/11*a^6*(A*b-a*B)*(a+b*x)^11/b^8-1/12*a^5*(6*A*b-7*a*B)*(a+b*x)^12/b^8+_ + 3/13*a^4*(5*A*b-7*a*B)*(a+b*x)^13/b^8-_ + 5/14*a^3*(4*A*b-7*a*B)*(a+b*x)^14/b^8+_ + 1/3*a^2*(3*A*b-7*a*B)*(a+b*x)^15/b^8-_ + 3/16*a*(2*A*b-7*a*B)*(a+b*x)^16/b^8+_ + 1/17*(A*b-7*a*B)*(a+b*x)^17/b^8+1/18*B*(a+b*x)^18/b^8 +--R +--R +--R (332) +--R 1 18 18 1 18 10 17 17 5 17 45 2 16 16 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x +--R 18 17 17 8 16 +--R + +--R 2 16 3 15 15 60 3 15 4 14 14 +--R (3A a b + 8B a b )x + (-- A a b + 15B a b )x +--R 7 +--R + +--R 210 4 14 252 5 13 13 5 13 35 6 12 12 +--R (--- A a b + --- B a b )x + (21A a b + -- B a b )x +--R 13 13 2 +--R + +--R 210 6 12 120 7 11 11 7 11 9 8 10 10 +--R (--- A a b + --- B a b )x + (12A a b + - B a b )x +--R 11 11 2 +--R + +--R 8 10 10 9 9 9 5 9 9 1 10 8 8 1 10 8 7 +--R (5A a b + -- B a b )x + (- A a b + - B a b )x + - A a b x +--R 9 4 8 7 +--R + +--R 1 17 1 18 +--R ------ A a b - ------ B a +--R 136136 350064 +--R / +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 332 + +--S 333 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (333) +--R 1 10 18 1 10 10 9 17 5 9 45 2 8 16 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x +--R 18 17 17 8 16 +--R + +--R 2 8 3 7 15 60 3 7 4 6 14 +--R (3A a b + 8B a b )x + (-- A a b + 15B a b )x +--R 7 +--R + +--R 210 4 6 252 5 5 13 5 5 35 6 4 12 +--R (--- A a b + --- B a b )x + (21A a b + -- B a b )x +--R 13 13 2 +--R + +--R 210 6 4 120 7 3 11 7 3 9 8 2 10 +--R (--- A a b + --- B a b )x + (12A a b + - B a b )x +--R 11 11 2 +--R + +--R 8 2 10 9 9 5 9 1 10 8 1 10 7 +--R (5A a b + -- B a b)x + (- A a b + - B a )x + - A a x +--R 9 4 8 7 +--R Type: Polynomial(Fraction(Integer)) +--E 333 + +--S 334 of 1293 +m0:=a0-r0 +--R +--R +--R 1 17 1 18 +--R - ------ A a b + ------ B a +--R 136136 350064 +--R (334) ------------------------------ +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 334 + +--S 335 of 1293 +d0:=D(m0,x) +--R +--R +--R (335) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 335 + +--S 336 of 1293 +t0:=x^5*(a+b*x)^10*(A+B*x) +--R +--R +--R (336) +--R 10 16 10 9 15 9 2 8 14 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 13 3 7 4 6 12 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 11 5 5 6 4 10 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 9 7 3 8 2 8 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 7 9 10 6 10 5 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 336 + +--S 337 of 1293 +r0:=-1/11*a^5*(A*b-a*B)*(a+b*x)^11/b^7+_ + 1/12*a^4*(5*A*b-6*a*B)*(a+b*x)^12/b^7-_ + 5/13*a^3*(2*A*b-3*a*B)*(a+b*x)^13/b^7+_ + 5/7*a^2*(A*b-2*a*B)*(a+b*x)^14/b^7-_ + 1/3*a*(A*b-3*a*B)*(a+b*x)^15/b^7+_ + 1/16*(A*b-6*a*B)*(a+b*x)^16/b^7+1/17*B*(a+b*x)^17/b^7 +--R +--R +--R (337) +--R 1 17 17 1 17 5 16 16 2 16 2 15 15 +--R -- B b x + (-- A b + - B a b )x + (- A a b + 3B a b )x +--R 17 16 8 3 +--R + +--R 45 2 15 60 3 14 14 120 3 14 210 4 13 13 +--R (-- A a b + -- B a b )x + (--- A a b + --- B a b )x +--R 14 7 13 13 +--R + +--R 35 4 13 5 12 12 252 5 12 210 6 11 11 +--R (-- A a b + 21B a b )x + (--- A a b + --- B a b )x +--R 2 11 11 +--R + +--R 6 11 7 10 10 40 7 10 8 9 9 +--R (21A a b + 12B a b )x + (-- A a b + 5B a b )x +--R 3 +--R + +--R 45 8 9 5 9 8 8 10 9 8 1 10 7 7 1 10 7 6 +--R (-- A a b + - B a b )x + (-- A a b + - B a b )x + - A a b x +--R 8 4 7 7 6 +--R + +--R 1 16 1 17 +--R - ----- A a b + ------ B a +--R 48048 136136 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 337 + +--S 338 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (338) +--R 1 10 17 1 10 5 9 16 2 9 2 8 15 +--R -- B b x + (-- A b + - B a b )x + (- A a b + 3B a b )x +--R 17 16 8 3 +--R + +--R 45 2 8 60 3 7 14 120 3 7 210 4 6 13 +--R (-- A a b + -- B a b )x + (--- A a b + --- B a b )x +--R 14 7 13 13 +--R + +--R 35 4 6 5 5 12 252 5 5 210 6 4 11 +--R (-- A a b + 21B a b )x + (--- A a b + --- B a b )x +--R 2 11 11 +--R + +--R 6 4 7 3 10 40 7 3 8 2 9 +--R (21A a b + 12B a b )x + (-- A a b + 5B a b )x +--R 3 +--R + +--R 45 8 2 5 9 8 10 9 1 10 7 1 10 6 +--R (-- A a b + - B a b)x + (-- A a b + - B a )x + - A a x +--R 8 4 7 7 6 +--R Type: Polynomial(Fraction(Integer)) +--E 338 + +--S 339 of 1293 +m0:=a0-r0 +--R +--R +--R 1 16 1 17 +--R ----- A a b - ------ B a +--R 48048 136136 +--R (339) --------------------------- +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 339 + +--S 340 of 1293 +d0:=D(m0,x) +--R +--R +--R (340) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 340 + +--S 341 of 1293 +t0:=x^4*(a+b*x)^10*(A+B*x) +--R +--R +--R (341) +--R 10 15 10 9 14 9 2 8 13 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 12 3 7 4 6 11 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 10 5 5 6 4 9 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 8 7 3 8 2 7 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 6 9 10 5 10 4 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 341 + +--S 342 of 1293 +r0:=1/11*a^4*(A*b-a*B)*(a+b*x)^11/b^6-_ + 1/12*a^3*(4*A*b-5*a*B)*(a+b*x)^12/b^6+_ + 2/13*a^2*(3*A*b-5*a*B)*(a+b*x)^13/b^6-_ + 1/7*a*(2*A*b-5*a*B)*(a+b*x)^14/b^6+_ + 1/15*(A*b-5*a*B)*(a+b*x)^15/b^6+1/16*B*(a+b*x)^16/b^6 +--R +--R +--R (342) +--R 1 16 16 1 16 2 15 15 5 15 45 2 14 14 +--R -- B b x + (-- A b + - B a b )x + (- A a b + -- B a b )x +--R 16 15 3 7 14 +--R + +--R 45 2 14 120 3 13 13 3 13 35 4 12 12 +--R (-- A a b + --- B a b )x + (10A a b + -- B a b )x +--R 13 13 2 +--R + +--R 210 4 12 252 5 11 11 126 5 11 6 10 10 +--R (--- A a b + --- B a b )x + (--- A a b + 21B a b )x +--R 11 11 5 +--R + +--R 70 6 10 40 7 9 9 7 9 45 8 8 8 +--R (-- A a b + -- B a b )x + (15A a b + -- B a b )x +--R 3 3 8 +--R + +--R 45 8 8 10 9 7 7 5 9 7 1 10 6 6 1 10 6 5 +--R (-- A a b + -- B a b )x + (- A a b + - B a b )x + - A a b x +--R 7 7 3 6 5 +--R + +--R 1 15 1 16 +--R ----- A a b - ----- B a +--R 15015 48048 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 342 + +--S 343 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (343) +--R 1 10 16 1 10 2 9 15 5 9 45 2 8 14 +--R -- B b x + (-- A b + - B a b )x + (- A a b + -- B a b )x +--R 16 15 3 7 14 +--R + +--R 45 2 8 120 3 7 13 3 7 35 4 6 12 +--R (-- A a b + --- B a b )x + (10A a b + -- B a b )x +--R 13 13 2 +--R + +--R 210 4 6 252 5 5 11 126 5 5 6 4 10 +--R (--- A a b + --- B a b )x + (--- A a b + 21B a b )x +--R 11 11 5 +--R + +--R 70 6 4 40 7 3 9 7 3 45 8 2 8 +--R (-- A a b + -- B a b )x + (15A a b + -- B a b )x +--R 3 3 8 +--R + +--R 45 8 2 10 9 7 5 9 1 10 6 1 10 5 +--R (-- A a b + -- B a b)x + (- A a b + - B a )x + - A a x +--R 7 7 3 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 343 + +--S 344 of 1293 +m0:=a0-r0 +--R +--R +--R 1 15 1 16 +--R - ----- A a b + ----- B a +--R 15015 48048 +--R (344) ---------------------------- +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 344 + +--S 345 of 1293 +d0:=D(m0,x) +--R +--R +--R (345) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 345 + +--S 346 of 1293 +t0:=x^3*(a+b*x)^10*(A+B*x) +--R +--R +--R (346) +--R 10 14 10 9 13 9 2 8 12 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 11 3 7 4 6 10 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 9 5 5 6 4 8 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 7 7 3 8 2 6 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 5 9 10 4 10 3 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 346 + +--S 347 of 1293 +r0:=-1/11*a^3*(A*b-a*B)*(a+b*x)^11/b^5+_ + 1/12*a^2*(3*A*b-4*a*B)*(a+b*x)^12/b^5-_ + 3/13*a*(A*b-2*a*B)*(a+b*x)^13/b^5+_ + 1/14*(A*b-4*a*B)*(a+b*x)^14/b^5+1/15*B*(a+b*x)^15/b^5 +--R +--R +--R (347) +--R 1 15 15 1 15 5 14 14 10 14 45 2 13 13 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 15 14 7 13 13 +--R + +--R 15 2 13 3 12 12 120 3 12 210 4 11 11 +--R (-- A a b + 10B a b )x + (--- A a b + --- B a b )x +--R 4 11 11 +--R + +--R 4 11 126 5 10 10 5 10 70 6 9 9 +--R (21A a b + --- B a b )x + (28A a b + -- B a b )x +--R 5 3 +--R + +--R 105 6 9 7 8 8 120 7 8 45 8 7 7 +--R (--- A a b + 15B a b )x + (--- A a b + -- B a b )x +--R 4 7 7 +--R + +--R 15 8 7 5 9 6 6 9 6 1 10 5 5 1 10 5 4 +--R (-- A a b + - B a b )x + (2A a b + - B a b )x + - A a b x +--R 2 3 5 4 +--R + +--R 1 14 1 15 +--R - ---- A a b + ----- B a +--R 4004 15015 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 347 + +--S 348 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (348) +--R 1 10 15 1 10 5 9 14 10 9 45 2 8 13 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 15 14 7 13 13 +--R + +--R 15 2 8 3 7 12 120 3 7 210 4 6 11 +--R (-- A a b + 10B a b )x + (--- A a b + --- B a b )x +--R 4 11 11 +--R + +--R 4 6 126 5 5 10 5 5 70 6 4 9 +--R (21A a b + --- B a b )x + (28A a b + -- B a b )x +--R 5 3 +--R + +--R 105 6 4 7 3 8 120 7 3 45 8 2 7 +--R (--- A a b + 15B a b )x + (--- A a b + -- B a b )x +--R 4 7 7 +--R + +--R 15 8 2 5 9 6 9 1 10 5 1 10 4 +--R (-- A a b + - B a b)x + (2A a b + - B a )x + - A a x +--R 2 3 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 348 + +--S 349 of 1293 +m0:=a0-r0 +--R +--R +--R 1 14 1 15 +--R ---- A a b - ----- B a +--R 4004 15015 +--R (349) ------------------------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 349 + +--S 350 of 1293 +d0:=D(m0,x) +--R +--R +--R (350) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 350 + +--S 351 of 1293 +t0:=x^2*(a+b*x)^10*(A+B*x) +--R +--R +--R (351) +--R 10 13 10 9 12 9 2 8 11 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 10 3 7 4 6 9 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 8 5 5 6 4 7 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 6 7 3 8 2 5 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 4 9 10 3 10 2 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 351 + +--S 352 of 1293 +r0:=1/11*a^2*(A*b-a*B)*(a+b*x)^11/b^4-_ + 1/12*a*(2*A*b-3*a*B)*(a+b*x)^12/b^4+_ + 1/13*(A*b-3*a*B)*(a+b*x)^13/b^4+1/14*B*(a+b*x)^14/b^4 +--R +--R +--R (352) +--R 1 14 14 1 14 10 13 13 5 13 15 2 12 12 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x +--R 14 13 13 6 4 +--R + +--R 45 2 12 120 3 11 11 3 11 4 10 10 +--R (-- A a b + --- B a b )x + (12A a b + 21B a b )x +--R 11 11 +--R + +--R 70 4 10 5 9 9 63 5 9 105 6 8 8 +--R (-- A a b + 28B a b )x + (-- A a b + --- B a b )x +--R 3 2 4 +--R + +--R 6 8 120 7 7 7 7 7 15 8 6 6 +--R (30A a b + --- B a b )x + (20A a b + -- B a b )x +--R 7 2 +--R + +--R 8 6 9 5 5 5 9 5 1 10 4 4 1 10 4 3 +--R (9A a b + 2B a b )x + (- A a b + - B a b )x + - A a b x +--R 2 4 3 +--R + +--R 1 13 1 14 +--R --- A a b - ---- B a +--R 858 4004 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 352 + +--S 353 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (353) +--R 1 10 14 1 10 10 9 13 5 9 15 2 8 12 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x +--R 14 13 13 6 4 +--R + +--R 45 2 8 120 3 7 11 3 7 4 6 10 +--R (-- A a b + --- B a b )x + (12A a b + 21B a b )x +--R 11 11 +--R + +--R 70 4 6 5 5 9 63 5 5 105 6 4 8 +--R (-- A a b + 28B a b )x + (-- A a b + --- B a b )x +--R 3 2 4 +--R + +--R 6 4 120 7 3 7 7 3 15 8 2 6 8 2 9 5 +--R (30A a b + --- B a b )x + (20A a b + -- B a b )x + (9A a b + 2B a b)x +--R 7 2 +--R + +--R 5 9 1 10 4 1 10 3 +--R (- A a b + - B a )x + - A a x +--R 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 353 + +--S 354 of 1293 +m0:=a0-r0 +--R +--R +--R 1 13 1 14 +--R - --- A a b + ---- B a +--R 858 4004 +--R (354) ------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 354 + +--S 355 of 1293 +d0:=D(m0,x) +--R +--R +--R (355) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 355 + +--S 356 of 1293 +t0:=x*(a+b*x)^10*(A+B*x) +--R +--R +--R (356) +--R 10 12 10 9 11 9 2 8 10 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 9 3 7 4 6 8 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 7 5 5 6 4 6 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 5 7 3 8 2 4 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 3 9 10 2 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 356 + +--S 357 of 1293 +r0:=-1/11*a*(A*b-a*B)*(a+b*x)^11/b^3+1/12*(A*b-2*a*B)*(a+b*x)^12/b^3+_ + 1/13*B*(a+b*x)^13/b^3 +--R +--R +--R (357) +--R 1 13 13 1 13 5 12 12 10 12 45 2 11 11 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 13 12 6 11 11 +--R + +--R 9 2 11 3 10 10 40 3 10 70 4 9 9 +--R (- A a b + 12B a b )x + (-- A a b + -- B a b )x +--R 2 3 3 +--R + +--R 105 4 9 63 5 8 8 5 8 6 7 7 +--R (--- A a b + -- B a b )x + (36A a b + 30B a b )x +--R 4 2 +--R + +--R 6 7 7 6 6 7 6 8 5 5 +--R (35A a b + 20B a b )x + (24A a b + 9B a b )x +--R + +--R 45 8 5 5 9 4 4 10 9 4 1 10 3 3 1 10 3 2 +--R (-- A a b + - B a b )x + (-- A a b + - B a b )x + - A a b x +--R 4 2 3 3 2 +--R + +--R 1 12 1 13 +--R - --- A a b + --- B a +--R 132 858 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 357 + +--S 358 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (358) +--R 1 10 13 1 10 5 9 12 10 9 45 2 8 11 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 13 12 6 11 11 +--R + +--R 9 2 8 3 7 10 40 3 7 70 4 6 9 +--R (- A a b + 12B a b )x + (-- A a b + -- B a b )x +--R 2 3 3 +--R + +--R 105 4 6 63 5 5 8 5 5 6 4 7 +--R (--- A a b + -- B a b )x + (36A a b + 30B a b )x +--R 4 2 +--R + +--R 6 4 7 3 6 7 3 8 2 5 45 8 2 5 9 4 +--R (35A a b + 20B a b )x + (24A a b + 9B a b )x + (-- A a b + - B a b)x +--R 4 2 +--R + +--R 10 9 1 10 3 1 10 2 +--R (-- A a b + - B a )x + - A a x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 358 + +--S 359 of 1293 +m0:=a0-r0 +--R +--R +--R 1 12 1 13 +--R --- A a b - --- B a +--R 132 858 +--R (359) ---------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 359 + +--S 360 of 1293 +d0:=D(m0,x) +--R +--R +--R (360) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 360 + +--S 361 of 1293 +t0:=(a+b*x)^10*(A+B*x) +--R +--R +--R (361) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 361 + +--S 362 of 1293 +r0:=1/11*(A*b-a*B)*(a+b*x)^11/b^2+1/12*B*(a+b*x)^12/b^2 +--R +--R +--R (362) +--R 1 12 12 1 12 10 11 11 11 9 2 10 10 +--R -- B b x + (-- A b + -- B a b )x + (A a b + - B a b )x +--R 12 11 11 2 +--R + +--R 2 10 40 3 9 9 3 9 105 4 8 8 +--R (5A a b + -- B a b )x + (15A a b + --- B a b )x +--R 3 4 +--R + +--R 4 8 5 7 7 5 7 6 6 6 +--R (30A a b + 36B a b )x + (42A a b + 35B a b )x +--R + +--R 6 6 7 5 5 7 5 45 8 4 4 +--R (42A a b + 24B a b )x + (30A a b + -- B a b )x +--R 4 +--R + +--R 8 4 10 9 3 3 9 3 1 10 2 2 10 2 1 11 +--R (15A a b + -- B a b )x + (5A a b + - B a b )x + A a b x + -- A a b +--R 3 2 11 +--R + +--R 1 12 +--R - --- B a +--R 132 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 362 + +--S 363 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (363) +--R 1 10 12 1 10 10 9 11 9 9 2 8 10 +--R -- B b x + (-- A b + -- B a b )x + (A a b + - B a b )x +--R 12 11 11 2 +--R + +--R 2 8 40 3 7 9 3 7 105 4 6 8 +--R (5A a b + -- B a b )x + (15A a b + --- B a b )x +--R 3 4 +--R + +--R 4 6 5 5 7 5 5 6 4 6 6 4 7 3 5 +--R (30A a b + 36B a b )x + (42A a b + 35B a b )x + (42A a b + 24B a b )x +--R + +--R 7 3 45 8 2 4 8 2 10 9 3 9 1 10 2 +--R (30A a b + -- B a b )x + (15A a b + -- B a b)x + (5A a b + - B a )x +--R 4 3 2 +--R + +--R 10 +--R A a x +--R Type: Polynomial(Fraction(Integer)) +--E 363 + +--S 364 of 1293 +m0:=a0-r0 +--R +--R +--R 1 11 1 12 +--R - -- A a b + --- B a +--R 11 132 +--R (364) ----------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 364 + +--S 365 of 1293 +d0:=D(m0,x) +--R +--R +--R (365) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 365 + +--S 366 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x +--R +--R +--R (366) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 1293 +r0:=10*a^9*A*b*x+45/2*a^8*A*b^2*x^2+40*a^7*A*b^3*x^3+_ + 105/2*a^6*A*b^4*x^4+252/5*a^5*A*b^5*x^5+35*a^4*A*b^6*x^6+_ + 120/7*a^3*A*b^7*x^7+45/8*a^2*A*b^8*x^8+10/9*a*A*b^9*x^9+_ + 1/10*A*b^10*x^10+1/11*B*(a+b*x)^11/b+a^10*A*log(x) +--R +--R +--R (367) +--R 10 11 11 11 10 10 +--R 27720A a b log(x) + 2520B b x + (2772A b + 27720B a b )x +--R + +--R 10 2 9 9 2 9 3 8 8 +--R (30800A a b + 138600B a b )x + (155925A a b + 415800B a b )x +--R + +--R 3 8 4 7 7 4 7 5 6 6 +--R (475200A a b + 831600B a b )x + (970200A a b + 1164240B a b )x +--R + +--R 5 6 6 5 5 6 5 7 4 4 +--R (1397088A a b + 1164240B a b )x + (1455300A a b + 831600B a b )x +--R + +--R 7 4 8 3 3 8 3 9 2 2 +--R (1108800A a b + 415800B a b )x + (623700A a b + 138600B a b )x +--R + +--R 9 2 10 11 +--R (277200A a b + 27720B a b)x + 2520B a +--R / +--R 27720b +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (368) +--R 10 10 11 10 9 10 +--R 27720A a log(x) + 2520B b x + (2772A b + 27720B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (30800A a b + 138600B a b )x + (155925A a b + 415800B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (475200A a b + 831600B a b )x + (970200A a b + 1164240B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (1397088A a b + 1164240B a b )x + (1455300A a b + 831600B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (1108800A a b + 415800B a b )x + (623700A a b + 138600B a b)x +--R + +--R 9 10 +--R (277200A a b + 27720B a )x +--R / +--R 27720 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1293 +m0:=a0-r0 +--R +--R +--R 11 +--R B a +--R (369) - ----- +--R 11b +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1293 +d0:=D(m0,x) +--R +--R +--R (370) 0 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^2 +--R +--R +--R (371) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 1293 +r0:=-a^10*A/x+5*a^8*b*(9*A*b+2*a*B)*x+15/2*a^7*b^2*(8*A*b+3*a*B)*x^2+_ + 10*a^6*b^3*(7*A*b+4*a*B)*x^3+21/2*a^5*b^4*(6*A*b+5*a*B)*x^4+_ + 42/5*a^4*b^5*(5*A*b+6*a*B)*x^5+5*a^3*b^6*(4*A*b+7*a*B)*x^6+_ + 15/7*a^2*b^7*(3*A*b+8*a*B)*x^7+5/8*a*b^8*(2*A*b+9*a*B)*x^8+_ + 1/9*b^9*(A*b+10*a*B)*x^9+1/10*b^10*B*x^10+a^9*(10*A*b+a*B)*log(x) +--R +--R +--R (372) +--R 9 10 10 11 +--R (25200A a b + 2520B a )x log(x) + 252B b x +--R + +--R 10 9 10 9 2 8 9 +--R (280A b + 2800B a b )x + (3150A a b + 14175B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (16200A a b + 43200B a b )x + (50400A a b + 88200B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (105840A a b + 127008B a b )x + (158760A a b + 132300B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (176400A a b + 100800B a b )x + (151200A a b + 56700B a b )x +--R + +--R 8 2 9 2 10 +--R (113400A a b + 25200B a b)x - 2520A a +--R / +--R 2520x +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (373) +--R 9 10 10 11 +--R (25200A a b + 2520B a )x log(x) + 252B b x +--R + +--R 10 9 10 9 2 8 9 +--R (280A b + 2800B a b )x + (3150A a b + 14175B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (16200A a b + 43200B a b )x + (50400A a b + 88200B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (105840A a b + 127008B a b )x + (158760A a b + 132300B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (176400A a b + 100800B a b )x + (151200A a b + 56700B a b )x +--R + +--R 8 2 9 2 10 +--R (113400A a b + 25200B a b)x - 2520A a +--R / +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1293 +m0:=a0-r0 +--R +--R +--R (374) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1293 +d0:=D(m0,x) +--R +--R +--R (375) 0 +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^3 +--R +--R +--R (376) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 1293 +r0:=-1/2*a^10*A/x^2-a^9*(10*A*b+a*B)/x+15*a^7*b^2*(8*A*b+3*a*B)*x+_ + 15*a^6*b^3*(7*A*b+4*a*B)*x^2+14*a^5*b^4*(6*A*b+5*a*B)*x^3+_ + 21/2*a^4*b^5*(5*A*b+6*a*B)*x^4+6*a^3*b^6*(4*A*b+7*a*B)*x^5+_ + 5/2*a^2*b^7*(3*A*b+8*a*B)*x^6+5/7*a*b^8*(2*A*b+9*a*B)*x^7+_ + 1/8*b^9*(A*b+10*a*B)*x^8+1/9*b^10*B*x^9+5*a^8*b*(9*A*b+2*a*B)*log(x) +--R +--R +--R (377) +--R 8 2 9 2 10 11 10 9 10 +--R (22680A a b + 5040B a b)x log(x) + 56B b x + (63A b + 630B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (720A a b + 3240B a b )x + (3780A a b + 10080B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (12096A a b + 21168B a b )x + (26460A a b + 31752B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (42336A a b + 35280B a b )x + (52920A a b + 30240B a b )x +--R + +--R 7 3 8 2 3 9 10 10 +--R (60480A a b + 22680B a b )x + (- 5040A a b - 504B a )x - 252A a +--R / +--R 2 +--R 504x +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (378) +--R 8 2 9 2 10 11 10 9 10 +--R (22680A a b + 5040B a b)x log(x) + 56B b x + (63A b + 630B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (720A a b + 3240B a b )x + (3780A a b + 10080B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (12096A a b + 21168B a b )x + (26460A a b + 31752B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (42336A a b + 35280B a b )x + (52920A a b + 30240B a b )x +--R + +--R 7 3 8 2 3 9 10 10 +--R (60480A a b + 22680B a b )x + (- 5040A a b - 504B a )x - 252A a +--R / +--R 2 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 1293 +m0:=a0-r0 +--R +--R +--R (379) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1293 +d0:=D(m0,x) +--R +--R +--R (380) 0 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^4 +--R +--R +--R (381) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 1293 +r0:=-1/3*a^10*A/x^3-1/2*a^9*(10*A*b+a*B)/x^2-5*a^8*b*(9*A*b+2*a*B)/x+_ + 30*a^6*b^3*(7*A*b+4*a*B)*x+21*a^5*b^4*(6*A*b+5*a*B)*x^2+_ + 14*a^4*b^5*(5*A*b+6*a*B)*x^3+15/2*a^3*b^6*(4*A*b+7*a*B)*x^4+_ + 3*a^2*b^7*(3*A*b+8*a*B)*x^5+5/6*a*b^8*(2*A*b+9*a*B)*x^6+_ + 1/7*b^9*(A*b+10*a*B)*x^7+1/8*b^10*B*x^8+15*a^7*b^2*(8*A*b+3*a*B)*log(x) +--R +--R +--R (382) +--R 7 3 8 2 3 10 11 +--R (20160A a b + 7560B a b )x log(x) + 21B b x +--R + +--R 10 9 10 9 2 8 9 +--R (24A b + 240B a b )x + (280A a b + 1260B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (1512A a b + 4032B a b )x + (5040A a b + 8820B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (11760A a b + 14112B a b )x + (21168A a b + 17640B a b )x +--R + +--R 6 4 7 3 4 8 2 9 2 +--R (35280A a b + 20160B a b )x + (- 7560A a b - 1680B a b)x +--R + +--R 9 10 10 +--R (- 840A a b - 84B a )x - 56A a +--R / +--R 3 +--R 168x +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (383) +--R 7 3 8 2 3 10 11 +--R (20160A a b + 7560B a b )x log(x) + 21B b x +--R + +--R 10 9 10 9 2 8 9 +--R (24A b + 240B a b )x + (280A a b + 1260B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (1512A a b + 4032B a b )x + (5040A a b + 8820B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (11760A a b + 14112B a b )x + (21168A a b + 17640B a b )x +--R + +--R 6 4 7 3 4 8 2 9 2 +--R (35280A a b + 20160B a b )x + (- 7560A a b - 1680B a b)x +--R + +--R 9 10 10 +--R (- 840A a b - 84B a )x - 56A a +--R / +--R 3 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 1293 +m0:=a0-r0 +--R +--R +--R (384) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1293 +d0:=D(m0,x) +--R +--R +--R (385) 0 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^5 +--R +--R +--R (386) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 1293 +r0:=-1/4*a^10*A/x^4-1/3*a^9*(10*A*b+a*B)/x^3-5/2*a^8*b*(9*A*b+2*a*B)/x^2-_ + 15*a^7*b^2*(8*A*b+3*a*B)/x+42*a^5*b^4*(6*A*b+5*a*B)*x+_ + 21*a^4*b^5*(5*A*b+6*a*B)*x^2+10*a^3*b^6*(4*A*b+7*a*B)*x^3+_ + 15/4*a^2*b^7*(3*A*b+8*a*B)*x^4+a*b^8*(2*A*b+9*a*B)*x^5+_ + 1/6*b^9*(A*b+10*a*B)*x^6+1/7*b^10*B*x^7+30*a^6*b^3*(7*A*b+4*a*B)*log(x) +--R +--R +--R (387) +--R 6 4 7 3 4 10 11 +--R (17640A a b + 10080B a b )x log(x) + 12B b x +--R + +--R 10 9 10 9 2 8 9 +--R (14A b + 140B a b )x + (168A a b + 756B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (945A a b + 2520B a b )x + (3360A a b + 5880B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (8820A a b + 10584B a b )x + (21168A a b + 17640B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 10080A a b - 3780B a b )x + (- 1890A a b - 420B a b)x +--R + +--R 9 10 10 +--R (- 280A a b - 28B a )x - 21A a +--R / +--R 4 +--R 84x +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (388) +--R 6 4 7 3 4 10 11 +--R (17640A a b + 10080B a b )x log(x) + 12B b x +--R + +--R 10 9 10 9 2 8 9 +--R (14A b + 140B a b )x + (168A a b + 756B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (945A a b + 2520B a b )x + (3360A a b + 5880B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (8820A a b + 10584B a b )x + (21168A a b + 17640B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 10080A a b - 3780B a b )x + (- 1890A a b - 420B a b)x +--R + +--R 9 10 10 +--R (- 280A a b - 28B a )x - 21A a +--R / +--R 4 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1293 +m0:=a0-r0 +--R +--R +--R (389) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1293 +d0:=D(m0,x) +--R +--R +--R (390) 0 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^6 +--R +--R +--R (391) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 1293 +r0:=-1/5*a^10*A/x^5-1/4*a^9*(10*A*b+a*B)/x^4-5/3*a^8*b*(9*A*b+2*a*B)/x^3-_ + 15/2*a^7*b^2*(8*A*b+3*a*B)/x^2-30*a^6*b^3*(7*A*b+4*a*B)/x+_ + 42*a^4*b^5*(5*A*b+6*a*B)*x+15*a^3*b^6*(4*A*b+7*a*B)*x^2+_ + 5*a^2*b^7*(3*A*b+8*a*B)*x^3+5/4*a*b^8*(2*A*b+9*a*B)*x^4+_ + 1/5*b^9*(A*b+10*a*B)*x^5+1/6*b^10*B*x^6+42*a^5*b^4*(6*A*b+5*a*B)*log(x) +--R +--R +--R (392) +--R 5 5 6 4 5 10 11 +--R (15120A a b + 12600B a b )x log(x) + 10B b x +--R + +--R 10 9 10 9 2 8 9 +--R (12A b + 120B a b )x + (150A a b + 675B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (900A a b + 2400B a b )x + (3600A a b + 6300B a b )x +--R + +--R 4 6 5 5 6 6 4 7 3 4 +--R (12600A a b + 15120B a b )x + (- 12600A a b - 7200B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 3600A a b - 1350B a b )x + (- 900A a b - 200B a b)x +--R + +--R 9 10 10 +--R (- 150A a b - 15B a )x - 12A a +--R / +--R 5 +--R 60x +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (393) +--R 5 5 6 4 5 10 11 +--R (15120A a b + 12600B a b )x log(x) + 10B b x +--R + +--R 10 9 10 9 2 8 9 +--R (12A b + 120B a b )x + (150A a b + 675B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (900A a b + 2400B a b )x + (3600A a b + 6300B a b )x +--R + +--R 4 6 5 5 6 6 4 7 3 4 +--R (12600A a b + 15120B a b )x + (- 12600A a b - 7200B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 3600A a b - 1350B a b )x + (- 900A a b - 200B a b)x +--R + +--R 9 10 10 +--R (- 150A a b - 15B a )x - 12A a +--R / +--R 5 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1293 +m0:=a0-r0 +--R +--R +--R (394) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1293 +d0:=D(m0,x) +--R +--R +--R (395) 0 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^7 +--R +--R +--R (396) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 1293 +r0:=-1/6*a^10*A/x^6-1/5*a^9*(10*A*b+a*B)/x^5-5/4*a^8*b*(9*A*b+2*a*B)/x^4-_ + 5*a^7*b^2*(8*A*b+3*a*B)/x^3-15*a^6*b^3*(7*A*b+4*a*B)/x^2-_ + 42*a^5*b^4*(6*A*b+5*a*B)/x+30*a^3*b^6*(4*A*b+7*a*B)*x+_ + 15/2*a^2*b^7*(3*A*b+8*a*B)*x^2+5/3*a*b^8*(2*A*b+9*a*B)*x^3+_ + 1/4*b^9*(A*b+10*a*B)*x^4+1/5*b^10*B*x^5+42*a^4*b^5*(5*A*b+6*a*B)*log(x) +--R +--R +--R (397) +--R 4 6 5 5 6 10 11 +--R (12600A a b + 15120B a b )x log(x) + 12B b x +--R + +--R 10 9 10 9 2 8 9 +--R (15A b + 150B a b )x + (200A a b + 900B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (1350A a b + 3600B a b )x + (7200A a b + 12600B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 15120A a b - 12600B a b )x + (- 6300A a b - 3600B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2400A a b - 900B a b )x + (- 675A a b - 150B a b)x +--R + +--R 9 10 10 +--R (- 120A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60x +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (398) +--R 4 6 5 5 6 10 11 +--R (12600A a b + 15120B a b )x log(x) + 12B b x +--R + +--R 10 9 10 9 2 8 9 +--R (15A b + 150B a b )x + (200A a b + 900B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (1350A a b + 3600B a b )x + (7200A a b + 12600B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 15120A a b - 12600B a b )x + (- 6300A a b - 3600B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2400A a b - 900B a b )x + (- 675A a b - 150B a b)x +--R + +--R 9 10 10 +--R (- 120A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1293 +m0:=a0-r0 +--R +--R +--R (399) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1293 +d0:=D(m0,x) +--R +--R +--R (400) 0 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^8 +--R +--R +--R (401) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 1293 +r0:=-1/7*a^10*A/x^7-1/6*a^9*(10*A*b+a*B)/x^6-a^8*b*(9*A*b+2*a*B)/x^5-_ + 15/4*a^7*b^2*(8*A*b+3*a*B)/x^4-10*a^6*b^3*(7*A*b+4*a*B)/x^3-_ + 21*a^5*b^4*(6*A*b+5*a*B)/x^2-42*a^4*b^5*(5*A*b+6*a*B)/x+_ + 15*a^2*b^7*(3*A*b+8*a*B)*x+5/2*a*b^8*(2*A*b+9*a*B)*x^2+_ + 1/3*b^9*(A*b+10*a*B)*x^3+1/4*b^10*B*x^4+30*a^3*b^6*(4*A*b+7*a*B)*log(x) +--R +--R +--R (402) +--R 3 7 4 6 7 10 11 +--R (10080A a b + 17640B a b )x log(x) + 21B b x +--R + +--R 10 9 10 9 2 8 9 +--R (28A b + 280B a b )x + (420A a b + 1890B a b )x +--R + +--R 2 8 3 7 8 4 6 5 5 6 +--R (3780A a b + 10080B a b )x + (- 17640A a b - 21168B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 10584A a b - 8820B a b )x + (- 5880A a b - 3360B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2520A a b - 945B a b )x + (- 756A a b - 168B a b)x +--R + +--R 9 10 10 +--R (- 140A a b - 14B a )x - 12A a +--R / +--R 7 +--R 84x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (403) +--R 3 7 4 6 7 10 11 +--R (10080A a b + 17640B a b )x log(x) + 21B b x +--R + +--R 10 9 10 9 2 8 9 +--R (28A b + 280B a b )x + (420A a b + 1890B a b )x +--R + +--R 2 8 3 7 8 4 6 5 5 6 +--R (3780A a b + 10080B a b )x + (- 17640A a b - 21168B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 10584A a b - 8820B a b )x + (- 5880A a b - 3360B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2520A a b - 945B a b )x + (- 756A a b - 168B a b)x +--R + +--R 9 10 10 +--R (- 140A a b - 14B a )x - 12A a +--R / +--R 7 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1293 +m0:=a0-r0 +--R +--R +--R (404) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1293 +d0:=D(m0,x) +--R +--R +--R (405) 0 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^9 +--R +--R +--R (406) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 1293 +r0:=-1/8*a^10*A/x^8-1/7*a^9*(10*A*b+a*B)/x^7-5/6*a^8*b*(9*A*b+2*a*B)/x^6-_ + 3*a^7*b^2*(8*A*b+3*a*B)/x^5-15/2*a^6*b^3*(7*A*b+4*a*B)/x^4-_ + 14*a^5*b^4*(6*A*b+5*a*B)/x^3-21*a^4*b^5*(5*A*b+6*a*B)/x^2-_ + 30*a^3*b^6*(4*A*b+7*a*B)/x+5*a*b^8*(2*A*b+9*a*B)*x+_ + 1/2*b^9*(A*b+10*a*B)*x^2+1/3*b^10*B*x^3+15*a^2*b^7*(3*A*b+8*a*B)*log(x) +--R +--R +--R (407) +--R 2 8 3 7 8 10 11 +--R (7560A a b + 20160B a b )x log(x) + 56B b x +--R + +--R 10 9 10 9 2 8 9 +--R (84A b + 840B a b )x + (1680A a b + 7560B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 20160A a b - 35280B a b )x + (- 17640A a b - 21168B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 14112A a b - 11760B a b )x + (- 8820A a b - 5040B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 4032A a b - 1512B a b )x + (- 1260A a b - 280B a b)x +--R + +--R 9 10 10 +--R (- 240A a b - 24B a )x - 21A a +--R / +--R 8 +--R 168x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (408) +--R 2 8 3 7 8 10 11 +--R (7560A a b + 20160B a b )x log(x) + 56B b x +--R + +--R 10 9 10 9 2 8 9 +--R (84A b + 840B a b )x + (1680A a b + 7560B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 20160A a b - 35280B a b )x + (- 17640A a b - 21168B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 14112A a b - 11760B a b )x + (- 8820A a b - 5040B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 4032A a b - 1512B a b )x + (- 1260A a b - 280B a b)x +--R + +--R 9 10 10 +--R (- 240A a b - 24B a )x - 21A a +--R / +--R 8 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1293 +m0:=a0-r0 +--R +--R +--R (409) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1293 +d0:=D(m0,x) +--R +--R +--R (410) 0 +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^10 +--R +--R +--R (411) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 1293 +r0:=-1/9*a^10*A/x^9-1/8*a^9*(10*A*b+a*B)/x^8-5/7*a^8*b*(9*A*b+2*a*B)/x^7-_ + 5/2*a^7*b^2*(8*A*b+3*a*B)/x^6-6*a^6*b^3*(7*A*b+4*a*B)/x^5-_ + 21/2*a^5*b^4*(6*A*b+5*a*B)/x^4-14*a^4*b^5*(5*A*b+6*a*B)/x^3-_ + 15*a^3*b^6*(4*A*b+7*a*B)/x^2-15*a^2*b^7*(3*A*b+8*a*B)/x+_ + b^9*(A*b+10*a*B)*x+1/2*b^10*B*x^2+5*a*b^8*(2*A*b+9*a*B)*log(x) +--R +--R +--R (412) +--R 9 2 8 9 10 11 +--R (5040A a b + 22680B a b )x log(x) + 252B b x +--R + +--R 10 9 10 2 8 3 7 8 +--R (504A b + 5040B a b )x + (- 22680A a b - 60480B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 30240A a b - 52920B a b )x + (- 35280A a b - 42336B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 31752A a b - 26460B a b )x + (- 21168A a b - 12096B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 10080A a b - 3780B a b )x + (- 3240A a b - 720B a b)x +--R + +--R 9 10 10 +--R (- 630A a b - 63B a )x - 56A a +--R / +--R 9 +--R 504x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (413) +--R 9 2 8 9 10 11 +--R (5040A a b + 22680B a b )x log(x) + 252B b x +--R + +--R 10 9 10 2 8 3 7 8 +--R (504A b + 5040B a b )x + (- 22680A a b - 60480B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 30240A a b - 52920B a b )x + (- 35280A a b - 42336B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 31752A a b - 26460B a b )x + (- 21168A a b - 12096B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 10080A a b - 3780B a b )x + (- 3240A a b - 720B a b)x +--R + +--R 9 10 10 +--R (- 630A a b - 63B a )x - 56A a +--R / +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1293 +m0:=a0-r0 +--R +--R +--R (414) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1293 +d0:=D(m0,x) +--R +--R +--R (415) 0 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^11 +--R +--R +--R (416) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 1293 +r0:=-1/10*a^10*A/x^10-1/9*a^9*(10*A*b+a*B)/x^9-5/8*a^8*b*(9*A*b+2*a*B)/x^8-_ + 15/7*a^7*b^2*(8*A*b+3*a*B)/x^7-5*a^6*b^3*(7*A*b+4*a*B)/x^6-_ + 42/5*a^5*b^4*(6*A*b+5*a*B)/x^5-21/2*a^4*b^5*(5*A*b+6*a*B)/x^4-_ + 10*a^3*b^6*(4*A*b+7*a*B)/x^3-15/2*a^2*b^7*(3*A*b+8*a*B)/x^2-_ + 5*a*b^8*(2*A*b+9*a*B)/x+b^10*B*x+b^9*(A*b+10*a*B)*log(x) +--R +--R +--R (417) +--R 10 9 10 10 11 +--R (2520A b + 25200B a b )x log(x) + 2520B b x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 25200A a b - 113400B a b )x + (- 56700A a b - 151200B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 100800A a b - 176400B a b )x + (- 132300A a b - 158760B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 127008A a b - 105840B a b )x + (- 88200A a b - 50400B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 43200A a b - 16200B a b )x + (- 14175A a b - 3150B a b)x +--R + +--R 9 10 10 +--R (- 2800A a b - 280B a )x - 252A a +--R / +--R 10 +--R 2520x +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (418) +--R 10 9 10 10 11 +--R (2520A b + 25200B a b )x log(x) + 2520B b x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 25200A a b - 113400B a b )x + (- 56700A a b - 151200B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 100800A a b - 176400B a b )x + (- 132300A a b - 158760B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 127008A a b - 105840B a b )x + (- 88200A a b - 50400B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 43200A a b - 16200B a b )x + (- 14175A a b - 3150B a b)x +--R + +--R 9 10 10 +--R (- 2800A a b - 280B a )x - 252A a +--R / +--R 10 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1293 +m0:=a0-r0 +--R +--R +--R (419) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1293 +d0:=D(m0,x) +--R +--R +--R (420) 0 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^12 +--R +--R +--R (421) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 1293 +r0:=-1/10*a^10*B/x^10-10/9*a^9*b*B/x^9-45/8*a^8*b^2*B/x^8-_ + 120/7*a^7*b^3*B/x^7-35*a^6*b^4*B/x^6-252/5*a^5*b^5*B/x^5-_ + 105/2*a^4*b^6*B/x^4-40*a^3*b^7*B/x^3-45/2*a^2*b^8*B/x^2-_ + 10*a*b^9*B/x-1/11*A*(a+b*x)^11/(a*x^11)+b^10*B*log(x) +--R +--R +--R (422) +--R 10 11 11 11 10 2 9 10 +--R 27720B a b x log(x) - 2520A b x + (- 27720A a b - 277200B a b )x +--R + +--R 2 9 3 8 9 3 8 4 7 8 +--R (- 138600A a b - 623700B a b )x + (- 415800A a b - 1108800B a b )x +--R + +--R 4 7 5 6 7 5 6 6 5 6 +--R (- 831600A a b - 1455300B a b )x + (- 1164240A a b - 1397088B a b )x +--R + +--R 6 5 7 4 5 7 4 8 3 4 +--R (- 1164240A a b - 970200B a b )x + (- 831600A a b - 475200B a b )x +--R + +--R 8 3 9 2 3 9 2 10 2 +--R (- 415800A a b - 155925B a b )x + (- 138600A a b - 30800B a b)x +--R + +--R 10 11 11 +--R (- 27720A a b - 2772B a )x - 2520A a +--R / +--R 11 +--R 27720a x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (423) +--R 10 11 10 9 10 +--R 27720B b x log(x) + (- 27720A b - 277200B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 138600A a b - 623700B a b )x + (- 415800A a b - 1108800B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 831600A a b - 1455300B a b )x + (- 1164240A a b - 1397088B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 1164240A a b - 970200B a b )x + (- 831600A a b - 475200B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 415800A a b - 155925B a b )x + (- 138600A a b - 30800B a b)x +--R + +--R 9 10 10 +--R (- 27720A a b - 2772B a )x - 2520A a +--R / +--R 11 +--R 27720x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1293 +m0:=a0-r0 +--R +--R +--R 11 +--R A b +--R (424) ----- +--R 11a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1293 +d0:=D(m0,x) +--R +--R +--R (425) 0 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^13 +--R +--R +--R (426) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 1293 +r0:=-1/12*A*(a+b*x)^11/(a*x^12)+1/132*(A*b-12*a*B)*(a+b*x)^11/(a^2*x^11) +--R +--R +--R (427) +--R 1 12 1 11 12 2 10 11 1 2 10 3 9 10 +--R (--- A b - -- B a b )x - B a b x + (- - A a b - 5B a b )x +--R 132 11 2 +--R + +--R 10 3 9 4 8 9 45 4 8 5 7 8 +--R (- -- A a b - 15B a b )x + (- -- A a b - 30B a b )x +--R 3 4 +--R + +--R 5 7 6 6 7 6 6 7 5 6 +--R (- 24A a b - 42B a b )x + (- 35A a b - 42B a b )x +--R + +--R 7 5 8 4 5 105 8 4 9 3 4 +--R (- 36A a b - 30B a b )x + (- --- A a b - 15B a b )x +--R 4 +--R + +--R 40 9 3 10 2 3 9 10 2 11 2 +--R (- -- A a b - 5B a b )x + (- - A a b - B a b)x +--R 3 2 +--R + +--R 10 11 1 12 1 12 +--R (- -- A a b - -- B a )x - -- A a +--R 11 11 12 +--R / +--R 2 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 427 + +--S 428 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (428) +--R 10 11 10 9 10 9 2 8 9 +--R - 132B b x + (- 66A b - 660B a b )x + (- 440A a b - 1980B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (- 1485A a b - 3960B a b )x + (- 3168A a b - 5544B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (- 4620A a b - 5544B a b )x + (- 4752A a b - 3960B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (- 3465A a b - 1980B a b )x + (- 1760A a b - 660B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (- 594A a b - 132B a b)x + (- 120A a b - 12B a )x - 11A a +--R / +--R 12 +--R 132x +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1293 +m0:=a0-r0 +--R +--R +--R 12 11 +--R - A b + 12B a b +--R (429) ------------------- +--R 2 +--R 132a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1293 +d0:=D(m0,x) +--R +--R +--R (430) 0 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^14 +--R +--R +--R (431) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 1293 +r0:=-1/13*A*(a+b*x)^11/(a*x^13)+1/156*(2*A*b-13*a*B)*(a+b*x)^11/(a^2*x^12)-_ + 1/1716*b*(2*A*b-13*a*B)*(a+b*x)^11/(a^3*x^11) +--R +--R +--R (432) +--R 1 13 1 12 13 1 3 10 11 +--R (- --- A b + --- B a b )x - - B a b x +--R 858 132 2 +--R + +--R 1 3 10 10 4 9 10 5 4 9 45 5 8 9 +--R (- - A a b - -- B a b )x + (- - A a b - -- B a b )x +--R 3 3 2 4 +--R + +--R 5 8 6 7 8 6 7 7 6 7 +--R (- 9A a b - 24B a b )x + (- 20A a b - 35B a b )x +--R + +--R 7 6 8 5 6 63 8 5 105 9 4 5 +--R (- 30A a b - 36B a b )x + (- -- A a b - --- B a b )x +--R 2 4 +--R + +--R 70 9 4 40 10 3 4 10 3 9 11 2 3 +--R (- -- A a b - -- B a b )x + (- 12A a b - - B a b )x +--R 3 3 2 +--R + +--R 45 11 2 10 12 2 5 12 1 13 1 13 +--R (- -- A a b - -- B a b)x + (- - A a b - -- B a )x - -- A a +--R 11 11 6 12 13 +--R / +--R 3 13 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 432 + +--S 433 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (433) +--R 10 11 10 9 10 +--R - 858B b x + (- 572A b - 5720B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 4290A a b - 19305B a b )x + (- 15444A a b - 41184B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 34320A a b - 60060B a b )x + (- 51480A a b - 61776B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 54054A a b - 45045B a b )x + (- 40040A a b - 22880B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 20592A a b - 7722B a b )x + (- 7020A a b - 1560B a b)x +--R + +--R 9 10 10 +--R (- 1430A a b - 143B a )x - 132A a +--R / +--R 13 +--R 1716x +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 1293 +m0:=a0-r0 +--R +--R +--R 13 12 +--R 2A b - 13B a b +--R (434) ------------------ +--R 3 +--R 1716a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1293 +d0:=D(m0,x) +--R +--R +--R (435) 0 +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^15 +--R +--R +--R (436) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 1293 +r0:=-1/14*A*(a+b*x)^11/(a*x^14)+1/182*(3*A*b-14*a*B)*(a+b*x)^11/(a^2*x^13)-_ + 1/1092*b*(3*A*b-14*a*B)*(a+b*x)^11/(a^3*x^12)+_ + 1/12012*b^2*(3*A*b-14*a*B)*(a+b*x)^11/(a^4*x^11) +--R +--R +--R (437) +--R 1 14 1 13 14 1 4 10 11 +--R (---- A b - --- B a b )x - - B a b x +--R 4004 858 3 +--R + +--R 1 4 10 5 5 9 10 5 9 6 8 9 +--R (- - A a b - - B a b )x + (- 2A a b - 9B a b )x +--R 4 2 +--R + +--R 15 6 8 7 7 8 120 7 7 8 6 7 +--R (- -- A a b - 20B a b )x + (- --- A a b - 30B a b )x +--R 2 7 +--R + +--R 105 8 6 63 9 5 6 9 5 70 10 4 5 +--R (- --- A a b - -- B a b )x + (- 28A a b - -- B a b )x +--R 4 2 3 +--R + +--R 10 4 11 3 4 120 11 3 45 12 2 3 +--R (- 21A a b - 12B a b )x + (- --- A a b - -- B a b )x +--R 11 11 +--R + +--R 15 12 2 5 13 2 10 13 1 14 1 14 +--R (- -- A a b - - B a b)x + (- -- A a b - -- B a )x - -- A a +--R 4 6 13 13 14 +--R / +--R 4 14 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 437 + +--S 438 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (438) +--R 10 11 10 9 10 +--R - 4004B b x + (- 3003A b - 30030B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 24024A a b - 108108B a b )x + (- 90090A a b - 240240B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 205920A a b - 360360B a b )x + (- 315315A a b - 378378B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 336336A a b - 280280B a b )x + (- 252252A a b - 144144B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 131040A a b - 49140B a b )x + (- 45045A a b - 10010B a b)x +--R + +--R 9 10 10 +--R (- 9240A a b - 924B a )x - 858A a +--R / +--R 14 +--R 12012x +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1293 +m0:=a0-r0 +--R +--R +--R 14 13 +--R - 3A b + 14B a b +--R (439) -------------------- +--R 4 +--R 12012a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1293 +d0:=D(m0,x) +--R +--R +--R (440) 0 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^16 +--R +--R +--R (441) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 1293 +r0:=-1/15*A*(a+b*x)^11/(a*x^15)+1/210*(4*A*b-15*a*B)*(a+b*x)^11/(a^2*x^14)-_ + 1/910*b*(4*A*b-15*a*B)*(a+b*x)^11/(a^3*x^13)+_ + 1/5460*b^2*(4*A*b-15*a*B)*(a+b*x)^11/(a^4*x^12)-_ + 1/60060*b^3*(4*A*b-15*a*B)*(a+b*x)^11/(a^5*x^11) +--R +--R +--R (442) +--R 1 15 1 14 15 1 5 10 11 +--R (- ----- A b + ---- B a b )x - - B a b x +--R 15015 4004 4 +--R + +--R 1 5 10 6 9 10 5 6 9 15 7 8 9 +--R (- - A a b - 2B a b )x + (- - A a b - -- B a b )x +--R 5 3 2 +--R + +--R 45 7 8 120 8 7 8 8 7 105 9 6 7 +--R (- -- A a b - --- B a b )x + (- 15A a b - --- B a b )x +--R 7 7 4 +--R + +--R 70 9 6 10 5 6 126 10 5 11 4 5 +--R (- -- A a b - 28B a b )x + (- --- A a b - 21B a b )x +--R 3 5 +--R + +--R 210 11 4 120 12 3 4 12 3 15 13 2 3 +--R (- --- A a b - --- B a b )x + (- 10A a b - -- B a b )x +--R 11 11 4 +--R + +--R 45 13 2 10 14 2 5 14 1 15 1 15 +--R (- -- A a b - -- B a b)x + (- - A a b - -- B a )x - -- A a +--R 13 13 7 14 15 +--R / +--R 5 15 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 442 + +--S 443 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (443) +--R 10 11 10 9 10 +--R - 15015B b x + (- 12012A b - 120120B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 100100A a b - 450450B a b )x + (- 386100A a b - 1029600B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 900900A a b - 1576575B a b )x + (- 1401400A a b - 1681680B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 1513512A a b - 1261260B a b )x + (- 1146600A a b - 655200B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 600600A a b - 225225B a b )x + (- 207900A a b - 46200B a b)x +--R + +--R 9 10 10 +--R (- 42900A a b - 4290B a )x - 4004A a +--R / +--R 15 +--R 60060x +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 1293 +m0:=a0-r0 +--R +--R +--R 15 14 +--R 4A b - 15B a b +--R (444) ------------------ +--R 5 +--R 60060a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1293 +d0:=D(m0,x) +--R +--R +--R (445) 0 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^17 +--R +--R +--R (446) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 1293 +r0:=-1/16*A*(a+b*x)^11/(a*x^16)+1/240*(5*A*b-16*a*B)*(a+b*x)^11/(a^2*x^15)-_ + 1/840*b*(5*A*b-16*a*B)*(a+b*x)^11/(a^3*x^14)+_ + 1/3640*b^2*(5*A*b-16*a*B)*(a+b*x)^11/(a^4*x^13)-_ + 1/21840*b^3*(5*A*b-16*a*B)*(a+b*x)^11/(a^5*x^12)+_ + 1/240240*b^4*(5*A*b-16*a*B)*(a+b*x)^11/(a^6*x^11) +--R +--R +--R (447) +--R 1 16 1 15 16 1 6 10 11 +--R (----- A b - ----- B a b )x - - B a b x +--R 48048 15015 5 +--R + +--R 1 6 10 5 7 9 10 10 7 9 45 8 8 9 +--R (- - A a b - - B a b )x + (- -- A a b - -- B a b )x +--R 6 3 7 7 +--R + +--R 45 8 8 9 7 8 40 9 7 70 10 6 7 +--R (- -- A a b - 15B a b )x + (- -- A a b - -- B a b )x +--R 8 3 3 +--R + +--R 10 6 126 11 5 6 252 11 5 210 12 4 5 +--R (- 21A a b - --- B a b )x + (- --- A a b - --- B a b )x +--R 5 11 11 +--R + +--R 35 12 4 13 3 4 120 13 3 45 14 2 3 +--R (- -- A a b - 10B a b )x + (- --- A a b - -- B a b )x +--R 2 13 13 +--R + +--R 45 14 2 5 15 2 2 15 1 16 1 16 +--R (- -- A a b - - B a b)x + (- - A a b - -- B a )x - -- A a +--R 14 7 3 15 16 +--R / +--R 6 16 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 447 + +--S 448 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (448) +--R 10 11 10 9 10 +--R - 48048B b x + (- 40040A b - 400400B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 343200A a b - 1544400B a b )x + (- 1351350A a b - 3603600B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 3203200A a b - 5605600B a b )x + (- 5045040A a b - 6054048B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 5503680A a b - 4586400B a b )x + (- 4204200A a b - 2402400B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2217600A a b - 831600B a b )x + (- 772200A a b - 171600B a b)x +--R + +--R 9 10 10 +--R (- 160160A a b - 16016B a )x - 15015A a +--R / +--R 16 +--R 240240x +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1293 +m0:=a0-r0 +--R +--R +--R 16 15 +--R - 5A b + 16B a b +--R (449) -------------------- +--R 6 +--R 240240a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1293 +d0:=D(m0,x) +--R +--R +--R (450) 0 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^18 +--R +--R +--R (451) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 1293 +r0:=-1/17*A*(a+b*x)^11/(a*x^17)+1/272*(6*A*b-17*a*B)*(a+b*x)^11/(a^2*x^16)-_ + 1/816*b*(6*A*b-17*a*B)*(a+b*x)^11/(a^3*x^15)+_ + 1/2856*b^2*(6*A*b-17*a*B)*(a+b*x)^11/(a^4*x^14)-_ + 1/12376*b^3*(6*A*b-17*a*B)*(a+b*x)^11/(a^5*x^13)+_ + 1/74256*b^4*(6*A*b-17*a*B)*(a+b*x)^11/(a^6*x^12)-_ + 1/816816*b^5*(6*A*b-17*a*B)*(a+b*x)^11/(a^7*x^11) +--R +--R +--R (452) +--R 1 17 1 16 17 1 7 10 11 +--R (- ------ A b + ----- B a b )x - - B a b x +--R 136136 48048 6 +--R + +--R 1 7 10 10 8 9 10 5 8 9 45 9 8 9 +--R (- - A a b - -- B a b )x + (- - A a b - -- B a b )x +--R 7 7 4 8 +--R + +--R 9 8 40 10 7 8 10 7 11 6 7 +--R (- 5A a b - -- B a b )x + (- 12A a b - 21B a b )x +--R 3 +--R + +--R 210 11 6 252 12 5 6 12 5 35 13 4 5 +--R (- --- A a b - --- B a b )x + (- 21A a b - -- B a b )x +--R 11 11 2 +--R + +--R 210 13 4 120 14 3 4 60 14 3 45 15 2 3 +--R (- --- A a b - --- B a b )x + (- -- A a b - -- B a b )x +--R 13 13 7 14 +--R + +--R 15 2 2 16 2 5 16 1 17 1 17 +--R (- 3A a b - - B a b)x + (- - A a b - -- B a )x - -- A a +--R 3 8 16 17 +--R / +--R 7 17 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 452 + +--S 453 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (453) +--R 10 11 10 9 10 +--R - 136136B b x + (- 116688A b - 1166880B a b )x +--R + +--R 9 2 8 9 +--R (- 1021020A a b - 4594590B a b )x +--R + +--R 2 8 3 7 8 +--R (- 4084080A a b - 10890880B a b )x +--R + +--R 3 7 4 6 7 +--R (- 9801792A a b - 17153136B a b )x +--R + +--R 4 6 5 5 6 +--R (- 15593760A a b - 18712512B a b )x +--R + +--R 5 5 6 4 5 +--R (- 17153136A a b - 14294280B a b )x +--R + +--R 6 4 7 3 4 +--R (- 13194720A a b - 7539840B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 7001280A a b - 2625480B a b )x + (- 2450448A a b - 544544B a b)x +--R + +--R 9 10 10 +--R (- 510510A a b - 51051B a )x - 48048A a +--R / +--R 17 +--R 816816x +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1293 +m0:=a0-r0 +--R +--R +--R 17 16 +--R 6A b - 17B a b +--R (454) ------------------ +--R 7 +--R 816816a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1293 +d0:=D(m0,x) +--R +--R +--R (455) 0 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^19 +--R +--R +--R (456) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 1293 +r0:=-1/18*a^10*A/x^18-1/17*a^9*(10*A*b+a*B)/x^17-_ + 5/16*a^8*b*(9*A*b+2*a*B)/x^16-a^7*b^2*(8*A*b+3*a*B)/x^15-_ + 15/7*a^6*b^3*(7*A*b+4*a*B)/x^14-42/13*a^5*b^4*(6*A*b+5*a*B)/x^13-_ + 7/2*a^4*b^5*(5*A*b+6*a*B)/x^12-30/11*a^3*b^6*(4*A*b+7*a*B)/x^11-_ + 3/2*a^2*b^7*(3*A*b+8*a*B)/x^10-5/9*a*b^8*(2*A*b+9*a*B)/x^9-_ + 1/8*b^9*(A*b+10*a*B)/x^8-1/7*b^10*B/x^7 +--R +--R +--R (457) +--R 1 10 11 1 10 5 9 10 10 9 2 8 9 +--R - - B b x + (- - A b - - B a b )x + (- -- A a b - 5B a b )x +--R 7 8 4 9 +--R + +--R 9 2 8 3 7 8 120 3 7 210 4 6 7 +--R (- - A a b - 12B a b )x + (- --- A a b - --- B a b )x +--R 2 11 11 +--R + +--R 35 4 6 5 5 6 252 5 5 210 6 4 5 +--R (- -- A a b - 21B a b )x + (- --- A a b - --- B a b )x +--R 2 13 13 +--R + +--R 6 4 60 7 3 4 7 3 8 2 3 +--R (- 15A a b - -- B a b )x + (- 8A a b - 3B a b )x +--R 7 +--R + +--R 45 8 2 5 9 2 10 9 1 10 1 10 +--R (- -- A a b - - B a b)x + (- -- A a b - -- B a )x - -- A a +--R 16 8 17 17 18 +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 457 + +--S 458 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (458) +--R 10 11 10 9 10 +--R - 350064B b x + (- 306306A b - 3063060B a b )x +--R + +--R 9 2 8 9 +--R (- 2722720A a b - 12252240B a b )x +--R + +--R 2 8 3 7 8 +--R (- 11027016A a b - 29405376B a b )x +--R + +--R 3 7 4 6 7 +--R (- 26732160A a b - 46781280B a b )x +--R + +--R 4 6 5 5 6 +--R (- 42882840A a b - 51459408B a b )x +--R + +--R 5 5 6 4 5 +--R (- 47500992A a b - 39584160B a b )x +--R + +--R 6 4 7 3 4 +--R (- 36756720A a b - 21003840B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 19603584A a b - 7351344B a b )x + (- 6891885A a b - 1531530B a b)x +--R + +--R 9 10 10 +--R (- 1441440A a b - 144144B a )x - 136136A a +--R / +--R 18 +--R 2450448x +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 1293 +m0:=a0-r0 +--R +--R +--R (459) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1293 +d0:=D(m0,x) +--R +--R +--R (460) 0 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^20 +--R +--R +--R (461) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 20 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 1293 +r0:=-1/19*a^10*A/x^19-1/18*a^9*(10*A*b+a*B)/x^18-_ + 5/17*a^8*b*(9*A*b+2*a*B)/x^17-15/16*a^7*b^2*(8*A*b+3*a*B)/x^16-_ + 2*a^6*b^3*(7*A*b+4*a*B)/x^15-3*a^5*b^4*(6*A*b+5*a*B)/x^14-_ + 42/13*a^4*b^5*(5*A*b+6*a*B)/x^13-5/2*a^3*b^6*(4*A*b+7*a*B)/x^12-_ + 15/11*a^2*b^7*(3*A*b+8*a*B)/x^11-1/2*a*b^8*(2*A*b+9*a*B)/x^10-_ + 1/9*b^9*(A*b+10*a*B)/x^9-1/8*b^10*B/x^8 +--R +--R +--R (462) +--R 1 10 11 1 10 10 9 10 9 9 2 8 9 +--R - - B b x + (- - A b - -- B a b )x + (- A a b - - B a b )x +--R 8 9 9 2 +--R + +--R 45 2 8 120 3 7 8 3 7 35 4 6 7 +--R (- -- A a b - --- B a b )x + (- 10A a b - -- B a b )x +--R 11 11 2 +--R + +--R 210 4 6 252 5 5 6 5 5 6 4 5 +--R (- --- A a b - --- B a b )x + (- 18A a b - 15B a b )x +--R 13 13 +--R + +--R 6 4 7 3 4 15 7 3 45 8 2 3 +--R (- 14A a b - 8B a b )x + (- -- A a b - -- B a b )x +--R 2 16 +--R + +--R 45 8 2 10 9 2 5 9 1 10 1 10 +--R (- -- A a b - -- B a b)x + (- - A a b - -- B a )x - -- A a +--R 17 17 9 18 19 +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 462 + +--S 463 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (463) +--R 10 11 10 9 10 +--R - 831402B b x + (- 739024A b - 7390240B a b )x +--R + +--R 9 2 8 9 +--R (- 6651216A a b - 29930472B a b )x +--R + +--R 2 8 3 7 8 +--R (- 27209520A a b - 72558720B a b )x +--R + +--R 3 7 4 6 7 +--R (- 66512160A a b - 116396280B a b )x +--R + +--R 4 6 5 5 6 +--R (- 107442720A a b - 128931264B a b )x +--R + +--R 5 5 6 4 5 +--R (- 119721888A a b - 99768240B a b )x +--R + +--R 6 4 7 3 4 +--R (- 93117024A a b - 53209728B a b )x +--R + +--R 7 3 8 2 3 +--R (- 49884120A a b - 18706545B a b )x +--R + +--R 8 2 9 2 9 10 +--R (- 17606160A a b - 3912480B a b)x + (- 3695120A a b - 369512B a )x +--R + +--R 10 +--R - 350064A a +--R / +--R 19 +--R 6651216x +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 1293 +m0:=a0-r0 +--R +--R +--R (464) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1293 +d0:=D(m0,x) +--R +--R +--R (465) 0 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^21 +--R +--R +--R (466) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 21 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 1293 +r0:=-1/20*a^10*A/x^20-1/19*a^9*(10*A*b+a*B)/x^19-_ + 5/18*a^8*b*(9*A*b+2*a*B)/x^18-15/17*a^7*b^2*(8*A*b+3*a*B)/x^17-_ + 15/8*a^6*b^3*(7*A*b+4*a*B)/x^16-14/5*a^5*b^4*(6*A*b+5*a*B)/x^15-_ + 3*a^4*b^5*(5*A*b+6*a*B)/x^14-30/13*a^3*b^6*(4*A*b+7*a*B)/x^13-_ + 5/4*a^2*b^7*(3*A*b+8*a*B)/x^12-5/11*a*b^8*(2*A*b+9*a*B)/x^11-_ + 1/10*b^9*(A*b+10*a*B)/x^10-1/9*b^10*B/x^9 +--R +--R +--R (467) +--R 1 10 11 1 10 9 10 10 9 45 2 8 9 +--R - - B b x + (- -- A b - B a b )x + (- -- A a b - -- B a b )x +--R 9 10 11 11 +--R + +--R 15 2 8 3 7 8 120 3 7 210 4 6 7 +--R (- -- A a b - 10B a b )x + (- --- A a b - --- B a b )x +--R 4 13 13 +--R + +--R 4 6 5 5 6 84 5 5 6 4 5 +--R (- 15A a b - 18B a b )x + (- -- A a b - 14B a b )x +--R 5 +--R + +--R 105 6 4 15 7 3 4 120 7 3 45 8 2 3 +--R (- --- A a b - -- B a b )x + (- --- A a b - -- B a b )x +--R 8 2 17 17 +--R + +--R 5 8 2 5 9 2 10 9 1 10 1 10 +--R (- - A a b - - B a b)x + (- -- A a b - -- B a )x - -- A a +--R 2 9 19 19 20 +--R / +--R 20 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 467 + +--S 468 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (468) +--R 10 11 10 9 10 +--R - 1847560B b x + (- 1662804A b - 16628040B a b )x +--R + +--R 9 2 8 9 +--R (- 15116400A a b - 68023800B a b )x +--R + +--R 2 8 3 7 8 +--R (- 62355150A a b - 166280400B a b )x +--R + +--R 3 7 4 6 7 +--R (- 153489600A a b - 268606800B a b )x +--R + +--R 4 6 5 5 6 +--R (- 249420600A a b - 299304720B a b )x +--R + +--R 5 5 6 4 5 +--R (- 279351072A a b - 232792560B a b )x +--R + +--R 6 4 7 3 4 +--R (- 218243025A a b - 124710300B a b )x +--R + +--R 7 3 8 2 3 +--R (- 117374400A a b - 44015400B a b )x +--R + +--R 8 2 9 2 9 10 +--R (- 41570100A a b - 9237800B a b)x + (- 8751600A a b - 875160B a )x +--R + +--R 10 +--R - 831402A a +--R / +--R 20 +--R 16628040x +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 1293 +m0:=a0-r0 +--R +--R +--R (469) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1293 +d0:=D(m0,x) +--R +--R +--R (470) 0 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1293 +t0:=(a+b*x)^10*(A+B*x)/(d+e*x)^22 +--R +--R +--R (471) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 22 22 21 21 2 20 20 3 19 19 4 18 18 +--R e x + 22d e x + 231d e x + 1540d e x + 7315d e x +--R + +--R 5 17 17 6 16 16 7 15 15 8 14 14 +--R 26334d e x + 74613d e x + 170544d e x + 319770d e x +--R + +--R 9 13 13 10 12 12 11 11 11 12 10 10 +--R 497420d e x + 646646d e x + 705432d e x + 646646d e x +--R + +--R 13 9 9 14 8 8 15 7 7 16 6 6 +--R 497420d e x + 319770d e x + 170544d e x + 74613d e x +--R + +--R 17 5 5 18 4 4 19 3 3 20 2 2 21 22 +--R 26334d e x + 7315d e x + 1540d e x + 231d e x + 22d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 1293 +r0:=1/21*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^21)-_ + 1/20*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^20)+_ + 5/19*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^19)-_ + 5/6*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^18)+_ + 30/17*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^17)-_ + 21/8*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^16)+_ + 14/5*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x)^15)-_ + 15/7*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)/(e^12*(d+e*x)^14)+_ + 15/13*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)/(e^12*(d+e*x)^13)-_ + 5/12*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)/(e^12*(d+e*x)^12)+_ + 1/11*b^9*(11*b*B*d-A*b*e-10*a*B*e)/(e^12*(d+e*x)^11)-_ + 1/10*b^10*B/(e^12*(d+e*x)^10) +--R +--R +--R (472) +--R 1 10 11 11 1 10 10 9 11 1 10 10 10 +--R - -- B b e x + ((- -- A b - -- B a b )e - -- B b d e )x +--R 10 11 11 10 +--R + +--R 5 9 15 2 8 11 5 10 25 9 10 +--R (- - A a b - -- B a b )e + (- -- A b - -- B a b )d e +--R 6 4 66 33 +--R + +--R 1 10 2 9 +--R - -- B b d e +--R 12 +--R * +--R 9 +--R x +--R + +--R 45 2 8 120 3 7 11 15 9 135 2 8 10 +--R (- -- A a b - --- B a b )e + (- -- A a b - --- B a b )d e +--R 13 13 26 52 +--R + +--R 15 10 75 9 2 9 3 10 3 8 +--R (- --- A b - --- B a b )d e - -- B b d e +--R 286 143 52 +--R * +--R 8 +--R x +--R + +--R 60 3 7 4 6 11 180 2 8 480 3 7 10 +--R (- -- A a b - 15B a b )e + (- --- A a b - --- B a b )d e +--R 7 91 91 +--R + +--R 30 9 135 2 8 2 9 30 10 300 9 3 8 +--R (- -- A a b - --- B a b )d e + (- ---- A b - ---- B a b )d e +--R 91 91 1001 1001 +--R + +--R 3 10 4 7 +--R - -- B b d e +--R 91 +--R * +--R 7 +--R x +--R + +--R 4 6 84 5 5 11 3 7 4 6 10 +--R (- 14A a b - -- B a b )e + (- 4A a b - 7B a b )d e +--R 5 +--R + +--R 12 2 8 32 3 7 2 9 2 9 9 2 8 3 8 +--R (- -- A a b - -- B a b )d e + (- -- A a b - -- B a b )d e +--R 13 13 13 13 +--R + +--R 2 10 20 9 4 7 1 10 5 6 +--R (- --- A b - --- B a b )d e - -- B b d e +--R 143 143 65 +--R * +--R 6 +--R x +--R + +--R 63 5 5 105 6 4 11 21 4 6 63 5 5 10 +--R (- -- A a b - --- B a b )e + (- -- A a b - -- B a b )d e +--R 4 8 4 10 +--R + +--R 3 3 7 21 4 6 2 9 9 2 8 12 3 7 3 8 +--R (- - A a b - -- B a b )d e + (- -- A a b - -- B a b )d e +--R 2 8 26 13 +--R + +--R 3 9 27 2 8 4 7 3 10 15 9 5 6 +--R (- -- A a b - --- B a b )d e + (- --- A b - --- B a b )d e +--R 52 104 572 286 +--R + +--R 3 10 6 5 +--R - --- B b d e +--R 520 +--R * +--R 5 +--R x +--R + +--R 210 6 4 120 7 3 11 315 5 5 525 6 4 10 +--R (- --- A a b - --- B a b )e + (- --- A a b - --- B a b )d e +--R 17 17 68 136 +--R + +--R 105 4 6 63 5 5 2 9 15 3 7 105 4 6 3 8 +--R (- --- A a b - -- B a b )d e + (- -- A a b - --- B a b )d e +--R 68 34 34 136 +--R + +--R 45 2 8 60 3 7 4 7 15 9 135 2 8 5 6 +--R (- --- A a b - --- B a b )d e + (- --- A a b - ---- B a b )d e +--R 442 221 884 1768 +--R + +--R 15 10 75 9 6 5 3 10 7 4 +--R (- ---- A b - ---- B a b )d e - ---- B b d e +--R 9724 4862 1768 +--R * +--R 4 +--R x +--R + +--R 20 7 3 5 8 2 11 140 6 4 80 7 3 10 +--R (- -- A a b - - B a b )e + (- --- A a b - -- B a b )d e +--R 3 2 51 51 +--R + +--R 35 5 5 175 6 4 2 9 35 4 6 7 5 5 3 8 +--R (- -- A a b - --- B a b )d e + (- --- A a b - -- B a b )d e +--R 34 204 102 17 +--R + +--R 5 3 7 35 4 6 4 7 5 2 8 40 3 7 5 6 +--R (- -- A a b - --- B a b )d e + (- --- A a b - --- B a b )d e +--R 51 204 221 663 +--R + +--R 5 9 15 2 8 6 5 5 10 25 9 7 4 +--R (- ---- A a b - --- B a b )d e + (- ----- A b - ---- B a b )d e +--R 1326 884 14586 7293 +--R + +--R 1 10 8 3 +--R - ---- B b d e +--R 2652 +--R * +--R 3 +--R x +--R + +--R 45 8 2 10 9 11 20 7 3 15 8 2 10 +--R (- -- A a b - -- B a b)e + (- -- A a b - -- B a b )d e +--R 19 19 19 38 +--R + +--R 140 6 4 80 7 3 2 9 105 5 5 175 6 4 3 8 +--R (- --- A a b - --- B a b )d e + (- --- A a b - ---- B a b )d e +--R 323 323 646 1292 +--R + +--R 35 4 6 21 5 5 4 7 5 3 7 35 4 6 5 6 +--R (- --- A a b - --- B a b )d e + (- --- A a b - ---- B a b )d e +--R 646 323 323 1292 +--R + +--R 15 2 8 40 3 7 6 5 +--R (- ---- A a b - ---- B a b )d e +--R 4199 4199 +--R + +--R 5 9 45 2 8 7 4 +--R (- ---- A a b - ----- B a b )d e +--R 8398 16796 +--R + +--R 5 10 25 9 8 3 1 10 9 2 +--R (- ----- A b - ----- B a b )d e - ----- B b d e +--R 92378 46189 16796 +--R * +--R 2 +--R x +--R + +--R 1 9 1 10 11 9 8 2 1 9 10 +--R (- - A a b - -- B a )e + (- -- A a b - -- B a b)d e +--R 2 20 38 19 +--R + +--R 2 7 3 3 8 2 2 9 14 6 4 8 7 3 3 8 +--R (- -- A a b - -- B a b )d e + (- --- A a b - --- B a b )d e +--R 19 76 323 323 +--R + +--R 21 5 5 35 6 4 4 7 7 4 6 21 5 5 5 6 +--R (- ---- A a b - ---- B a b )d e + (- ---- A a b - ---- B a b )d e +--R 1292 2584 1292 3230 +--R + +--R 1 3 7 7 4 6 6 5 3 2 8 4 3 7 7 4 +--R (- --- A a b - ---- B a b )d e + (- ---- A a b - ---- B a b )d e +--R 646 2584 8398 4199 +--R + +--R 1 9 9 2 8 8 3 +--R (- ----- A a b - ----- B a b )d e +--R 16796 33592 +--R + +--R 1 10 5 9 9 2 1 10 10 +--R (- ------ A b - ----- B a b )d e - ------ B b d e +--R 184756 92378 167960 +--R * +--R x +--R + +--R 1 10 11 1 9 1 10 10 +--R - -- A a e + (- -- A a b - --- B a )d e +--R 21 42 420 +--R + +--R 3 8 2 1 9 2 9 2 7 3 1 8 2 3 8 +--R (- --- A a b - --- B a b)d e + (- --- A a b - --- B a b )d e +--R 266 399 399 532 +--R + +--R 2 6 4 8 7 3 4 7 1 5 5 5 6 4 5 6 +--R (- --- A a b - ---- B a b )d e + (- ---- A a b - ---- B a b )d e +--R 969 6783 1292 7752 +--R + +--R 1 4 6 1 5 5 6 5 1 3 7 1 4 6 7 4 +--R (- ---- A a b - ---- B a b )d e + (- ----- A a b - ---- B a b )d e +--R 3876 3230 13566 7752 +--R + +--R 1 2 8 4 3 7 8 3 +--R (- ----- A a b - ----- B a b )d e +--R 58786 88179 +--R + +--R 1 9 3 2 8 9 2 +--R (- ------ A a b - ------ B a b )d e +--R 352716 235144 +--R + +--R 1 10 5 9 10 1 10 11 +--R (- ------- A b - ------- B a b )d e - ------- B b d +--R 3879876 1939938 3527160 +--R / +--R 33 21 32 20 2 31 19 3 30 18 4 29 17 +--R e x + 21d e x + 210d e x + 1330d e x + 5985d e x +--R + +--R 5 28 16 6 27 15 7 26 14 8 25 13 +--R 20349d e x + 54264d e x + 116280d e x + 203490d e x +--R + +--R 9 24 12 10 23 11 11 22 10 12 21 9 +--R 293930d e x + 352716d e x + 352716d e x + 293930d e x +--R + +--R 13 20 8 14 19 7 15 18 6 16 17 5 +--R 203490d e x + 116280d e x + 54264d e x + 20349d e x +--R + +--R 17 16 4 18 15 3 19 14 2 20 13 21 12 +--R 5985d e x + 1330d e x + 210d e x + 21d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (473) +--R 10 11 11 +--R - 3879876B b e x +--R + +--R 10 9 11 10 10 10 +--R ((- 3527160A b - 35271600B a b )e - 3879876B b d e )x +--R + +--R 9 2 8 11 +--R (- 32332300A a b - 145495350B a b )e +--R + +--R 10 9 10 10 2 9 +--R (- 2939300A b - 29393000B a b )d e - 3233230B b d e +--R * +--R 9 +--R x +--R + +--R 2 8 3 7 11 +--R (- 134303400A a b - 358142400B a b )e +--R + +--R 9 2 8 10 +--R (- 22383900A a b - 100727550B a b )d e +--R + +--R 10 9 2 9 10 3 8 +--R (- 2034900A b - 20349000B a b )d e - 2238390B b d e +--R * +--R 8 +--R x +--R + +--R 3 7 4 6 11 +--R (- 332560800A a b - 581981400B a b )e +--R + +--R 2 8 3 7 10 +--R (- 76744800A a b - 204652800B a b )d e +--R + +--R 9 2 8 2 9 +--R (- 12790800A a b - 57558600B a b )d e +--R + +--R 10 9 3 8 10 4 7 +--R (- 1162800A b - 11628000B a b )d e - 1279080B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 5 5 11 +--R (- 543182640A a b - 651819168B a b )e +--R + +--R 3 7 4 6 10 +--R (- 155195040A a b - 271591320B a b )d e +--R + +--R 2 8 3 7 2 9 +--R (- 35814240A a b - 95504640B a b )d e +--R + +--R 9 2 8 3 8 +--R (- 5969040A a b - 26860680B a b )d e +--R + +--R 10 9 4 7 10 5 6 +--R (- 542640A b - 5426400B a b )d e - 596904B b d e +--R * +--R 6 +--R x +--R + +--R 5 5 6 4 11 +--R (- 611080470A a b - 509233725B a b )e +--R + +--R 4 6 5 5 10 +--R (- 203693490A a b - 244432188B a b )d e +--R + +--R 3 7 4 6 2 9 +--R (- 58198140A a b - 101846745B a b )d e +--R + +--R 2 8 3 7 3 8 +--R (- 13430340A a b - 35814240B a b )d e +--R + +--R 9 2 8 4 7 +--R (- 2238390A a b - 10072755B a b )d e +--R + +--R 10 9 5 6 10 6 5 +--R (- 203490A b - 2034900B a b )d e - 223839B b d e +--R * +--R 5 +--R x +--R + +--R 6 4 7 3 11 +--R (- 479278800A a b - 273873600B a b )e +--R + +--R 5 5 6 4 10 +--R (- 179729550A a b - 149774625B a b )d e +--R + +--R 4 6 5 5 2 9 +--R (- 59909850A a b - 71891820B a b )d e +--R + +--R 3 7 4 6 3 8 +--R (- 17117100A a b - 29954925B a b )d e +--R + +--R 2 8 3 7 4 7 +--R (- 3950100A a b - 10533600B a b )d e +--R + +--R 9 2 8 5 6 +--R (- 658350A a b - 2962575B a b )d e +--R + +--R 10 9 6 5 10 7 4 +--R (- 59850A b - 598500B a b )d e - 65835B b d e +--R * +--R 4 +--R x +--R + +--R 7 3 8 2 11 +--R (- 258658400A a b - 96996900B a b )e +--R + +--R 6 4 7 3 10 +--R (- 106506400A a b - 60860800B a b )d e +--R + +--R 5 5 6 4 2 9 +--R (- 39939900A a b - 33283250B a b )d e +--R + +--R 4 6 5 5 3 8 +--R (- 13313300A a b - 15975960B a b )d e +--R + +--R 3 7 4 6 4 7 +--R (- 3803800A a b - 6656650B a b )d e +--R + +--R 2 8 3 7 5 6 +--R (- 877800A a b - 2340800B a b )d e +--R + +--R 9 2 8 6 5 +--R (- 146300A a b - 658350B a b )d e +--R + +--R 10 9 7 4 10 8 3 +--R (- 13300A b - 133000B a b )d e - 14630B b d e +--R * +--R 3 +--R x +--R + +--R 8 2 9 11 +--R (- 91891800A a b - 20420400B a b)e +--R + +--R 7 3 8 2 10 +--R (- 40840800A a b - 15315300B a b )d e +--R + +--R 6 4 7 3 2 9 +--R (- 16816800A a b - 9609600B a b )d e +--R + +--R 5 5 6 4 3 8 +--R (- 6306300A a b - 5255250B a b )d e +--R + +--R 4 6 5 5 4 7 +--R (- 2102100A a b - 2522520B a b )d e +--R + +--R 3 7 4 6 5 6 +--R (- 600600A a b - 1051050B a b )d e +--R + +--R 2 8 3 7 6 5 +--R (- 138600A a b - 369600B a b )d e +--R + +--R 9 2 8 7 4 10 9 8 3 +--R (- 23100A a b - 103950B a b )d e + (- 2100A b - 21000B a b )d e +--R + +--R 10 9 2 +--R - 2310B b d e +--R * +--R 2 +--R x +--R + +--R 9 10 11 +--R (- 19399380A a b - 1939938B a )e +--R + +--R 8 2 9 10 +--R (- 9189180A a b - 2042040B a b)d e +--R + +--R 7 3 8 2 2 9 +--R (- 4084080A a b - 1531530B a b )d e +--R + +--R 6 4 7 3 3 8 +--R (- 1681680A a b - 960960B a b )d e +--R + +--R 5 5 6 4 4 7 +--R (- 630630A a b - 525525B a b )d e +--R + +--R 4 6 5 5 5 6 +--R (- 210210A a b - 252252B a b )d e +--R + +--R 3 7 4 6 6 5 +--R (- 60060A a b - 105105B a b )d e +--R + +--R 2 8 3 7 7 4 9 2 8 8 3 +--R (- 13860A a b - 36960B a b )d e + (- 2310A a b - 10395B a b )d e +--R + +--R 10 9 9 2 10 10 +--R (- 210A b - 2100B a b )d e - 231B b d e +--R * +--R x +--R + +--R 10 11 9 10 10 +--R - 1847560A a e + (- 923780A a b - 92378B a )d e +--R + +--R 8 2 9 2 9 7 3 8 2 3 8 +--R (- 437580A a b - 97240B a b)d e + (- 194480A a b - 72930B a b )d e +--R + +--R 6 4 7 3 4 7 5 5 6 4 5 6 +--R (- 80080A a b - 45760B a b )d e + (- 30030A a b - 25025B a b )d e +--R + +--R 4 6 5 5 6 5 3 7 4 6 7 4 +--R (- 10010A a b - 12012B a b )d e + (- 2860A a b - 5005B a b )d e +--R + +--R 2 8 3 7 8 3 9 2 8 9 2 +--R (- 660A a b - 1760B a b )d e + (- 110A a b - 495B a b )d e +--R + +--R 10 9 10 10 11 +--R (- 10A b - 100B a b )d e - 11B b d +--R / +--R 33 21 32 20 2 31 19 +--R 38798760e x + 814773960d e x + 8147739600d e x +--R + +--R 3 30 18 4 29 17 5 28 16 +--R 51602350800d e x + 232210578600d e x + 789515967240d e x +--R + +--R 6 27 15 7 26 14 8 25 13 +--R 2105375912640d e x + 4511519812800d e x + 7895159672400d e x +--R + +--R 9 24 12 10 23 11 +--R 11404119526800d e x + 13684943432160d e x +--R + +--R 11 22 10 12 21 9 13 20 8 +--R 13684943432160d e x + 11404119526800d e x + 7895159672400d e x +--R + +--R 14 19 7 15 18 6 16 17 5 +--R 4511519812800d e x + 2105375912640d e x + 789515967240d e x +--R + +--R 17 16 4 18 15 3 19 14 2 +--R 232210578600d e x + 51602350800d e x + 8147739600d e x +--R + +--R 20 13 21 12 +--R 814773960d e x + 38798760d e +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 1293 +m0:=a0-r0 +--R +--R +--R (474) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1293 +d0:=D(m0,x) +--R +--R +--R (475) 0 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1293 +t0:=(A+B*x)*(d+e*x)^5/(a+b*x) +--R +--R +--R (476) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 1293 +r0:=(A*b-a*B)*e*(b*d-a*e)^4*x/b^6+1/2*(A*b-a*B)*(b*d-a*e)^3*(d+e*x)^2/b^5+_ + 1/3*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^3/b^4+_ + 1/4*(A*b-a*B)*(b*d-a*e)*(d+e*x)^4/b^3+1/5*(A*b-a*B)*(d+e*x)^5/b^2+_ + 1/6*B*(d+e*x)^6/(b*e)+(A*b-a*B)*(b*d-a*e)^5*log(a+b*x)/b^7 +--R +--R +--R (477) +--R 5 6 6 4 2 5 5 +--R (- 60A a b + 60B a )e + (300A a b - 300B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 600A a b + 600B a b )d e + (600A a b - 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (- 300A a b + 300B a b )d e + (60A b - 60B a b )d e +--R * +--R log(b x + a) +--R + +--R 6 6 6 6 5 6 6 5 5 +--R 10B b e x + ((12A b - 12B a b )e + 60B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 4 +--R ((- 15A a b + 15B a b )e + (75A b - 75B a b )d e + 150B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (20A a b - 20B a b )e + (- 100A a b + 100B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (200A b - 200B a b )d e + 200B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 30A a b + 30B a b )e + (150A a b - 150B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 300A a b + 300B a b )d e + (300A b - 300B a b )d e + 150B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (60A a b - 60B a b)e + (- 300A a b + 300B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (600A a b - 600B a b )d e + (- 600A a b + 600B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (300A b - 300B a b )d e + 60B b d e +--R * +--R x +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 30A a b + 30B a b )d e + (110A a b - 110B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 145A a b + 145B a b )d e + (77A b - 77B a b )d e + 10B b d +--R / +--R 7 +--R 60b e +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (478) +--R 5 6 5 4 2 5 4 +--R (- 60A a b + 60B a )e + (300A a b - 300B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 600A a b + 600B a b )d e + (600A a b - 600B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 300A a b + 300B a b )d e + (60A b - 60B a b )d +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 10B b e x + ((12A b - 12B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 15A a b + 15B a b )e + (75A b - 75B a b )d e + 150B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (20A a b - 20B a b )e + (- 100A a b + 100B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (200A b - 200B a b )d e + 200B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 30A a b + 30B a b )e + (150A a b - 150B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 300A a b + 300B a b )d e + (300A b - 300B a b )d e + 150B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (60A a b - 60B a b)e + (- 300A a b + 300B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (600A a b - 600B a b )d e + (- 600A a b + 600B a b )d e +--R + +--R 6 5 4 6 5 +--R (300A b - 300B a b )d e + 60B b d +--R * +--R x +--R / +--R 7 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1293 +m0:=a0-r0 +--R +--R +--R (479) +--R 3 4 2 4 2 2 3 3 3 +--R (30A a b - 30B a )d e + (- 110A a b + 110B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (145A a b - 145B a b )d e + (- 77A b + 77B a b )d e - 10B b d +--R / +--R 5 +--R 60b e +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1293 +d0:=D(m0,x) +--R +--R +--R (480) 0 +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1293 +t0:=(A+B*x)*(d+e*x)^4/(a+b*x) +--R +--R +--R (481) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 1293 +r0:=(A*b-a*B)*e*(b*d-a*e)^3*x/b^5+1/2*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^2/b^4+_ + 1/3*(A*b-a*B)*(b*d-a*e)*(d+e*x)^3/b^3+1/4*(A*b-a*B)*(d+e*x)^4/b^2+_ + 1/5*B*(d+e*x)^5/(b*e)+(A*b-a*B)*(b*d-a*e)^4*log(a+b*x)/b^6 +--R +--R +--R (482) +--R 4 5 5 3 2 4 4 +--R (60A a b - 60B a )e + (- 240A a b + 240B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (360A a b - 360B a b )d e + (- 240A a b + 240B a b )d e +--R + +--R 5 4 4 +--R (60A b - 60B a b )d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 12B b e x + ((15A b - 15B a b )e + 60B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 3 +--R ((- 20A a b + 20B a b )e + (80A b - 80B a b )d e + 120B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (30A a b - 30B a b )e + (- 120A a b + 120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (180A b - 180B a b )d e + 120B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 60A a b + 60B a b)e + (240A a b - 240B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (- 360A a b + 360B a b )d e + (240A b - 240B a b )d e + 60B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (30A a b - 30B a b )d e + (- 80A a b + 80B a b )d e +--R + +--R 5 4 4 5 5 +--R (65A b - 65B a b )d e + 12B b d +--R / +--R 6 +--R 60b e +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (483) +--R 4 5 4 3 2 4 3 +--R (60A a b - 60B a )e + (- 240A a b + 240B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (360A a b - 360B a b )d e + (- 240A a b + 240B a b )d e +--R + +--R 5 4 4 +--R (60A b - 60B a b )d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 12B b e x + ((15A b - 15B a b )e + 60B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 20A a b + 20B a b )e + (80A b - 80B a b )d e + 120B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (30A a b - 30B a b )e + (- 120A a b + 120B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (180A b - 180B a b )d e + 120B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 60A a b + 60B a b)e + (240A a b - 240B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 360A a b + 360B a b )d e + (240A b - 240B a b )d e + 60B b d +--R * +--R x +--R / +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1293 +m0:=a0-r0 +--R +--R +--R (484) +--R 2 3 2 3 2 2 3 2 +--R (- 30A a b + 30B a )d e + (80A a b - 80B a b)d e +--R + +--R 3 2 4 3 5 +--R (- 65A b + 65B a b )d e - 12B b d +--R / +--R 4 +--R 60b e +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1293 +d0:=D(m0,x) +--R +--R +--R (485) 0 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1293 +t0:=(A+B*x)*(d+e*x)^3/(a+b*x) +--R +--R +--R (486) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 1293 +r0:=(A*b-a*B)*e*(b*d-a*e)^2*x/b^4+1/2*(A*b-a*B)*(b*d-a*e)*(d+e*x)^2/b^3+_ + 1/3*(A*b-a*B)*(d+e*x)^3/b^2+1/4*B*(d+e*x)^4/(b*e)+_ + (A*b-a*B)*(b*d-a*e)^3*log(a+b*x)/b^5 +--R +--R +--R (487) +--R 3 4 4 2 2 3 3 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 3B b e x + ((4A b - 4B a b )e + 12B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((- 6A a b + 6B a b )e + (18A b - 18B a b )d e + 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (36A b - 36B a b )d e + 12B b d e +--R * +--R x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 6A a b + 6B a b )d e + (10A b - 10B a b )d e + 3B b d +--R / +--R 5 +--R 12b e +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (488) +--R 3 4 3 2 2 3 2 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 3B b e x + ((4A b - 4B a b )e + 12B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 6B a b )e + (18A b - 18B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 3 2 4 3 +--R (36A b - 36B a b )d e + 12B b d +--R * +--R x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1293 +m0:=a0-r0 +--R +--R +--R 2 2 2 2 3 2 4 +--R (6A a b - 6B a )d e + (- 10A b + 10B a b)d e - 3B b d +--R (489) -------------------------------------------------------- +--R 3 +--R 12b e +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1293 +d0:=D(m0,x) +--R +--R +--R (490) 0 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1293 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (491) ---------------------------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1293 +r0:=(A*b-a*B)*e*(b*d-a*e)*x/b^3+1/2*(A*b-a*B)*(d+e*x)^2/b^2+_ + 1/3*B*(d+e*x)^3/(b*e)+(A*b-a*B)*(b*d-a*e)^2*log(a+b*x)/b^4 +--R +--R +--R (492) +--R 2 3 3 2 2 2 +--R (6A a b - 6B a )e + (- 12A a b + 12B a b)d e +--R + +--R 3 2 2 +--R (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 2B b e x + ((3A b - 3B a b )e + 6B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 6A a b + 6B a b)e + (12A b - 12B a b )d e + 6B b d e)x +--R + +--R 3 2 2 3 3 +--R (3A b - 3B a b )d e + 2B b d +--R / +--R 4 +--R 6b e +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (493) +--R 2 3 2 2 2 3 2 2 +--R ((6A a b - 6B a )e + (- 12A a b + 12B a b)d e + (6A b - 6B a b )d ) +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R 2B b e x + ((3A b - 3B a b )e + 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (12A b - 12B a b )d e + 6B b d )x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1293 +m0:=a0-r0 +--R +--R +--R 2 3 +--R (- 3A b + 3B a)d e - 2B b d +--R (494) ---------------------------- +--R 2 +--R 6b e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1293 +d0:=D(m0,x) +--R +--R +--R (495) 0 +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1293 +t0:=(A+B*x)*(d+e*x)/(a+b*x) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (496) --------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 1293 +r0:=B*(b*d-a*e)*x/b^2+1/2*e*(A+B*x)^2/(b*B)+(A*b-a*B)*(b*d-a*e)*log(a+b*x)/b^3 +--R +--R +--R (497) +--R 2 2 2 2 2 2 2 +--R ((- 2A B a b + 2B a )e + (2A B b - 2B a b)d)log(b x + a) + B b e x +--R + +--R 2 2 2 2 2 2 +--R ((2A B b - 2B a b)e + 2B b d)x + A b e +--R / +--R 3 +--R 2B b +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (498) +--R 2 2 2 2 +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)log(b x + a) + B b e x +--R + +--R 2 2 +--R ((2A b - 2B a b)e + 2B b d)x +--R / +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1293 +m0:=a0-r0 +--R +--R +--R 2 +--R A e +--R (499) - ---- +--R 2B b +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1293 +d0:=D(m0,x) +--R +--R +--R (500) 0 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1293 +t0:=(A+B*x)/(a+b*x) +--R +--R +--R B x + A +--R (501) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 1293 +r0:=B*x/b+(A*b-a*B)*log(a+b*x)/b^2 +--R +--R +--R (A b - B a)log(b x + a) + B b x +--R (502) ------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (A b - B a)log(b x + a) + B b x +--R (503) ------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1293 +m0:=a0-r0 +--R +--R +--R (504) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1293 +d0:=D(m0,x) +--R +--R +--R (505) 0 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)) +--R +--R +--R B x + A +--R (506) --------------------------- +--R 2 +--R b e x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 1293 +r0:=(A*b-a*B)*log(a+b*x)/(b*(b*d-a*e))+(B*d-A*e)*log(d+e*x)/(e*(b*d-a*e)) +--R +--R +--R (A b e - B b d)log(e x + d) + (- A b + B a)e log(b x + a) +--R (507) --------------------------------------------------------- +--R 2 2 +--R a b e - b d e +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (A b e - B b d)log(e x + d) + (- A b + B a)e log(b x + a) +--R (508) --------------------------------------------------------- +--R 2 2 +--R a b e - b d e +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1293 +m0:=a0-r0 +--R +--R +--R (509) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1293 +d0:=D(m0,x) +--R +--R +--R (510) 0 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^2) +--R +--R +--R B x + A +--R (511) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1293 +r0:=(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x))+(A*b-a*B)*log(a+b*x)/(b*d-a*e)^2-_ + (A*b-a*B)*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (512) +--R 2 +--R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a)e x + (A b - B a)d e)log(b x + a) - A a e + (A b + B a)d e +--R + +--R 2 +--R - B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (513) +--R 2 +--R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a)e x + (A b - B a)d e)log(b x + a) - A a e + (A b + B a)d e +--R + +--R 2 +--R - B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1293 +m0:=a0-r0 +--R +--R +--R (514) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1293 +d0:=D(m0,x) +--R +--R +--R (515) 0 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^3) +--R +--R +--R (516) +--R B x + A +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 516 + +--S 517 of 1293 +r0:=1/2*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^2)+(A*b-a*B)/((b*d-a*e)^2*(d+e*x))+_ + b*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^3-b*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (517) +--R 2 3 2 2 2 2 2 +--R ((2A b - 2B a b)e x + (4A b - 4B a b)d e x + (2A b - 2B a b)d e) +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 2A b + 2B a b)e x + (- 4A b + 4B a b)d e x +--R + +--R 2 2 +--R (- 2A b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 2 3 +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d e )x - A a e +--R + +--R 2 2 2 2 2 3 +--R (4A a b - B a )d e - 3A b d e + B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (518) +--R 2 3 2 2 2 2 2 +--R ((2A b - 2B a b)e x + (4A b - 4B a b)d e x + (2A b - 2B a b)d e) +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 2A b + 2B a b)e x + (- 4A b + 4B a b)d e x +--R + +--R 2 2 +--R (- 2A b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 2 3 +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d e )x - A a e +--R + +--R 2 2 2 2 2 3 +--R (4A a b - B a )d e - 3A b d e + B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1293 +m0:=a0-r0 +--R +--R +--R (519) 0 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1293 +d0:=D(m0,x) +--R +--R +--R (520) 0 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^4) +--R +--R +--R (521) +--R B x + A +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 521 + +--S 522 of 1293 +r0:=1/3*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^3)+_ + 1/2*(A*b-a*B)/((b*d-a*e)^2*(d+e*x)^2)+_ + b*(A*b-a*B)/((b*d-a*e)^3*(d+e*x))+_ + b^2*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^4-b^2*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (522) +--R 3 2 4 3 3 2 3 2 +--R (- 6A b + 6B a b )e x + (- 18A b + 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (- 18A b + 18B a b )d e x + (- 6A b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 2 3 2 +--R (6A b - 6B a b )e x + (18A b - 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (18A b - 18B a b )d e x + (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 2 2 4 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (6A b - 6B a b )d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b - 3B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 +--R (15A b - 15B a b )d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b - 3B a b )d e - 2B b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 4 3 5 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x + 6a d e +--R + +--R 3 4 4 2 2 5 3 3 6 2 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (523) +--R 3 2 4 3 3 2 3 2 +--R (- 6A b + 6B a b )e x + (- 18A b + 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (- 18A b + 18B a b )d e x + (- 6A b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 2 3 2 +--R (6A b - 6B a b )e x + (18A b - 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (18A b - 18B a b )d e x + (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 2 2 4 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (6A b - 6B a b )d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b - 3B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 +--R (15A b - 15B a b )d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b - 3B a b )d e - 2B b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 4 3 5 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x + 6a d e +--R + +--R 3 4 4 2 2 5 3 3 6 2 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1293 +m0:=a0-r0 +--R +--R +--R (524) 0 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1293 +d0:=D(m0,x) +--R +--R +--R (525) 0 +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^5) +--R +--R +--R (526) +--R B x + A +--R / +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1293 +r0:=1/4*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^4)+_ + 1/3*(A*b-a*B)/((b*d-a*e)^2*(d+e*x)^3)+_ + 1/2*b*(A*b-a*B)/((b*d-a*e)^3*(d+e*x)^2)+_ + b^2*(A*b-a*B)/((b*d-a*e)^4*(d+e*x))+_ + b^3*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^5-b^3*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (527) +--R 4 3 5 4 4 3 4 3 +--R (12A b - 12B a b )e x + (48A b - 48B a b )d e x +--R + +--R 4 3 2 3 2 4 3 3 2 +--R (72A b - 72B a b )d e x + (48A b - 48B a b )d e x +--R + +--R 4 3 4 +--R (12A b - 12B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 3 4 3 +--R (- 12A b + 12B a b )e x + (- 48A b + 48B a b )d e x +--R + +--R 4 3 2 3 2 4 3 3 2 +--R (- 72A b + 72B a b )d e x + (- 48A b + 48B a b )d e x +--R + +--R 4 3 4 +--R (- 12A b + 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 5 4 3 4 3 +--R ((12A a b - 12B a b )e + (- 12A b + 12B a b )d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 6A a b + 6B a b)e + (48A a b - 48B a b )d e +--R + +--R 4 3 2 3 +--R (- 42A b + 42B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b - 4B a )e + (- 24A a b + 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b - 72B a b )d e + (- 52A b + 52B a b )d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (16A a b - B a )d e + (- 36A a b + 6B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (48A a b - 18B a b )d e + (- 25A b + 10B a b )d e + 3B b d +--R / +--R 5 10 4 9 3 2 2 8 2 3 3 7 4 4 6 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 5 5 5 +--R - 12b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 2 8 3 2 3 7 2 3 4 6 4 5 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 5 6 4 +--R - 48b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5 4 6 4 +--R 72a d e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 5 7 3 +--R - 72b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 4 6 3 2 5 5 2 3 6 4 4 7 3 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 5 8 2 +--R - 48b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3 4 8 2 5 9 +--R 12a d e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12b d e +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (528) +--R 4 3 5 4 4 3 4 3 +--R (12A b - 12B a b )e x + (48A b - 48B a b )d e x +--R + +--R 4 3 2 3 2 4 3 3 2 +--R (72A b - 72B a b )d e x + (48A b - 48B a b )d e x +--R + +--R 4 3 4 +--R (12A b - 12B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 3 4 3 +--R (- 12A b + 12B a b )e x + (- 48A b + 48B a b )d e x +--R + +--R 4 3 2 3 2 4 3 3 2 +--R (- 72A b + 72B a b )d e x + (- 48A b + 48B a b )d e x +--R + +--R 4 3 4 +--R (- 12A b + 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 5 4 3 4 3 +--R ((12A a b - 12B a b )e + (- 12A b + 12B a b )d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 6A a b + 6B a b)e + (48A a b - 48B a b )d e +--R + +--R 4 3 2 3 +--R (- 42A b + 42B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b - 4B a )e + (- 24A a b + 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b - 72B a b )d e + (- 52A b + 52B a b )d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (16A a b - B a )d e + (- 36A a b + 6B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (48A a b - 18B a b )d e + (- 25A b + 10B a b )d e + 3B b d +--R / +--R 5 10 4 9 3 2 2 8 2 3 3 7 4 4 6 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 5 5 5 +--R - 12b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 2 8 3 2 3 7 2 3 4 6 4 5 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 5 6 4 +--R - 48b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5 4 6 4 +--R 72a d e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 5 7 3 +--R - 72b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 4 6 3 2 5 5 2 3 6 4 4 7 3 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 5 8 2 +--R - 48b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3 4 8 2 5 9 +--R 12a d e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12b d e +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1293 +m0:=a0-r0 +--R +--R +--R (529) 0 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1293 +d0:=D(m0,x) +--R +--R +--R (530) 0 +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1293 +t0:=(A+B*x)*(d+e*x)^5/(a+b*x)^2 +--R +--R +--R (531) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1293 +r0:=5*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*x/b^6-_ + (A*b-a*B)*(b*d-a*e)^5/(b^7*(a+b*x))+_ + 5*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^2/b^7+_ + 5/3*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^3/b^7+_ + 1/4*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^4/b^7+_ + 1/5*B*e^5*(a+b*x)^5/b^7+(b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)*log(a+b*x)/b^7 +--R +--R +--R (532) +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 360B a b)e + (- 1200A a b + 1500B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (1800A a b - 2400B a b )d e + (- 1200A a b + 1800B a b )d e +--R + +--R 6 5 4 6 5 +--R (300A b - 600B a b )d e + 60B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (300A a b - 360B a )e + (- 1200A a b + 1500B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (1800A a b - 2400B a b )d e + (- 1200A a b + 1800B a b )d e +--R + +--R 5 2 4 4 5 5 +--R (300A a b - 600B a b )d e + 60B a b d +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 12B b e x + ((15A b - 18B a b )e + 75B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 25A a b + 30B a b )e + (100A b - 125B a b )d e + 200B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (50A a b - 60B a b )e + (- 200A a b + 250B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (300A b - 400B a b )d e + 300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 150A a b + 180B a b )e + (600A a b - 750B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 900A a b + 1200B a b )d e + (600A b - 900B a b )d e + 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 25A a b - 78B a b)e + (400A a b - 125B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 900A a b + 800B a b )d e + (600A a b - 900B a b )d e +--R + +--R 5 4 +--R 300B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (275A a b - 438B a )e + (- 800A a b + 1375B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (900A a b - 1600B a b )d e + (- 600A a b + 900B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (300A a b - 300B a b )d e + (- 60A b + 60B a b )d +--R / +--R 8 7 +--R 60b x + 60a b +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (533) +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 360B a b)e + (- 1200A a b + 1500B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (1800A a b - 2400B a b )d e + (- 1200A a b + 1800B a b )d e +--R + +--R 6 5 4 6 5 +--R (300A b - 600B a b )d e + 60B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (300A a b - 360B a )e + (- 1200A a b + 1500B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (1800A a b - 2400B a b )d e + (- 1200A a b + 1800B a b )d e +--R + +--R 5 2 4 4 5 5 +--R (300A a b - 600B a b )d e + 60B a b d +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 12B b e x + ((15A b - 18B a b )e + 75B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 25A a b + 30B a b )e + (100A b - 125B a b )d e + 200B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (50A a b - 60B a b )e + (- 200A a b + 250B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (300A b - 400B a b )d e + 300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 150A a b + 180B a b )e + (600A a b - 750B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 900A a b + 1200B a b )d e + (600A b - 900B a b )d e + 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 300B a b)e + (900A a b - 1200B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 1200A a b + 1800B a b )d e + (600A a b - 1200B a b )d e +--R + +--R 5 4 +--R 300B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (60A a b - 60B a )e + (- 300A a b + 300B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (600A a b - 600B a b )d e + (- 600A a b + 600B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (300A a b - 300B a b )d e + (- 60A b + 60B a b )d +--R / +--R 8 7 +--R 60b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1293 +m0:=a0-r0 +--R +--R +--R (534) +--R 4 5 5 3 2 4 4 +--R (- 215A a b + 378B a )e + (500A a b - 1075B a b)d e +--R + +--R 2 3 3 2 2 3 2 3 3 2 +--R (- 300A a b + 1000B a b )d e - 300B a b d e +--R / +--R 7 +--R 60b +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1293 +d0:=D(m0,x) +--R +--R +--R (535) 0 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1293 +t0:=(A+B*x)*(d+e*x)^4/(a+b*x)^2 +--R +--R +--R (536) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 1293 +r0:=2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-_ + (A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x))+_ + e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^2/b^6+_ + 1/3*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^3/b^6+_ + 1/4*B*e^4*(a+b*x)^4/b^6+(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (537) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (16A a b - 5B a b)e + (- 72A a b + 64B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 108B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 32A a b + 55B a )e + (72A a b - 128B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 108B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (538) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (36A a b - 48B a b)e + (- 96A a b + 144B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 144B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (48A a b - 48B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 72B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1293 +m0:=a0-r0 +--R +--R +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (20A a b - 43B a )e + (- 24A a b + 80B a b)d e - 36B a b d e +--R (539) ---------------------------------------------------------------- +--R 6 +--R 12b +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1293 +d0:=D(m0,x) +--R +--R +--R (540) 0 +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1293 +t0:=(A+B*x)*(d+e*x)^3/(a+b*x)^2 +--R +--R +--R (541) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 1293 +r0:=3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-_ + (A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x))+_ + 1/2*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^2/b^5+_ + 1/3*B*e^3*(a+b*x)^3/b^5+(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (542) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 9A a b + 8B a b)e + (18A a b - 27B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (9A a b - 16B a )e + (- 18A a b + 27B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (543) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 18B a b)e + (18A a b - 36B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (6A a b - 6B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1293 +m0:=a0-r0 +--R +--R +--R 2 3 3 2 2 +--R (- 3A a b + 10B a )e - 9B a b d e +--R (544) ----------------------------------- +--R 5 +--R 6b +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1293 +d0:=D(m0,x) +--R +--R +--R (545) 0 +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1293 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (546) ---------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 1293 +r0:=e*(2*b*B*d+A*b*e-2*a*B*e)*x/b^3+1/2*B*e^2*x^2/b^2-_ + (A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x))+(b*d-a*e)*_ + (b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4 +--R +--R +--R (547) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (548) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1293 +m0:=a0-r0 +--R +--R +--R (549) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1293 +d0:=D(m0,x) +--R +--R +--R (550) 0 +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1293 +t0:=(A+B*x)*(d+e*x)/(a+b*x)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (551) --------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1293 +r0:=B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+_ + (b*B*d+A*b*e-2*a*B*e)*log(a+b*x)/b^3 +--R +--R +--R (552) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (553) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1293 +m0:=a0-r0 +--R +--R +--R (554) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1293 +d0:=D(m0,x) +--R +--R +--R (555) 0 +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1293 +t0:=(A+B*x)/(a+b*x)^2 +--R +--R +--R B x + A +--R (556) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1293 +r0:=(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2 +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (557) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (558) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1293 +m0:=a0-r0 +--R +--R +--R (559) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1293 +d0:=D(m0,x) +--R +--R +--R (560) 0 +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)) +--R +--R +--R B x + A +--R (561) ------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (2a b e + b d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 1293 +r0:=(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x))+(B*d-A*e)*log(a+b*x)/(b*d-a*e)^2-_ + (B*d-A*e)*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (562) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (563) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 1293 +m0:=a0-r0 +--R +--R +--R (564) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1293 +d0:=D(m0,x) +--R +--R +--R (565) 0 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^2) +--R +--R +--R (566) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 1293 +r0:=(-A*b+a*B)/((b*d-a*e)^2*(a+b*x))+(B*d-A*e)/((b*d-a*e)^2*(d+e*x))+_ + (b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^3-_ + (b*B*d-2*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (567) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (568) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 1293 +m0:=a0-r0 +--R +--R +--R (569) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1293 +d0:=D(m0,x) +--R +--R +--R (570) 0 +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^3) +--R +--R +--R (571) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 1293 +r0:=-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/_ + ((b*d-a*e)^2*(d+e*x)^2)+(b*B*d-2*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x))+b*(b*B*d-3*A*b*e+2*a*B*e)*_ + log(a+b*x)/(b*d-a*e)^4-b*(b*B*d-3*A*b*e+2*a*B*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (572) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (573) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1293 +m0:=a0-r0 +--R +--R +--R (574) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1293 +d0:=D(m0,x) +--R +--R +--R (575) 0 +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^4) +--R +--R +--R (576) +--R B x + A +--R / +--R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 +--R b e x + (2a b e + 4b d e )x + (a e + 8a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 3 2 2 2 3 2 4 2 +--R (4a d e + 12a b d e + 4b d e)x + (6a d e + 8a b d e + b d )x +--R + +--R 2 3 4 2 4 +--R (4a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 1293 +r0:=-b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x))+_ + 1/3*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^3)+_ + 1/2*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x)^2)+_ + b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(d+e*x))+_ + b^2*(b*B*d-4*A*b*e+3*a*B*e)*log(a+b*x)/(b*d-a*e)^5-_ + b^2*(b*B*d-4*A*b*e+3*a*B*e)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (577) +--R 4 3 4 4 3 4 +--R ((- 24A b + 18B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 18B a b )e + (- 72A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 4 3 2 2 +--R (- 72A a b + 54B a b )d e + (- 72A b + 72B a b )d e +--R + +--R 4 3 +--R 18B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((- 72A a b + 54B a b )d e + (- 24A b + 36B a b )d e + 6B b d )x +--R + +--R 3 2 2 3 3 4 +--R (- 24A a b + 18B a b )d e + 6B a b d +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 18B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 18B a b )e + (72A b - 60B a b )d e - 18B b d e )x +--R + +--R 3 2 2 3 4 3 2 2 4 3 2 +--R ((72A a b - 54B a b )d e + (72A b - 72B a b )d e - 18B b d e)x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((72A a b - 54B a b )d e + (24A b - 36B a b )d e - 6B b d )x +--R + +--R 3 2 2 3 3 4 +--R (24A a b - 18B a b )d e - 6B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 18B a b )e + (24A b - 12B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 9B a b)e + (- 48A a b + 39B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (60A b - 33B a b )d e - 15B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b - 3B a )e + (- 36A a b + 26B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 12A a b + 18B a b )d e + (44A b - 30B a b )d e - 11B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (12A a b - B a )d e + (- 36A a b + 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (20A a b + 9B a b )d e + (6A b - 17B a b )d +--R / +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e )x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 2 4 4 4 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 5 5 3 6 6 2 +--R 84a b d e - 18b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 2 4 5 3 5 6 2 +--R 18a d e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 6 7 +--R - 18b d e +--R * +--R 2 +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2 +--R 18a d e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 5 7 6 8 +--R 12a b d e - 6b d +--R * +--R x +--R + +--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7 5 8 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (578) +--R 4 3 4 4 3 4 +--R ((- 24A b + 18B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 18B a b )e + (- 72A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 4 3 2 2 +--R (- 72A a b + 54B a b )d e + (- 72A b + 72B a b )d e +--R + +--R 4 3 +--R 18B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((- 72A a b + 54B a b )d e + (- 24A b + 36B a b )d e + 6B b d )x +--R + +--R 3 2 2 3 3 4 +--R (- 24A a b + 18B a b )d e + 6B a b d +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 18B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 18B a b )e + (72A b - 60B a b )d e - 18B b d e )x +--R + +--R 3 2 2 3 4 3 2 2 4 3 2 +--R ((72A a b - 54B a b )d e + (72A b - 72B a b )d e - 18B b d e)x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((72A a b - 54B a b )d e + (24A b - 36B a b )d e - 6B b d )x +--R + +--R 3 2 2 3 3 4 +--R (24A a b - 18B a b )d e - 6B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 18B a b )e + (24A b - 12B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 9B a b)e + (- 48A a b + 39B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (60A b - 33B a b )d e - 15B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b - 3B a )e + (- 36A a b + 26B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 12A a b + 18B a b )d e + (44A b - 30B a b )d e - 11B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (12A a b - B a )d e + (- 36A a b + 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (20A a b + 9B a b )d e + (6A b - 17B a b )d +--R / +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e )x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 2 4 4 4 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 5 5 3 6 6 2 +--R 84a b d e - 18b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 2 4 5 3 5 6 2 +--R 18a d e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 6 7 +--R - 18b d e +--R * +--R 2 +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2 +--R 18a d e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 5 7 6 8 +--R 12a b d e - 6b d +--R * +--R x +--R + +--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7 5 8 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1293 +m0:=a0-r0 +--R +--R +--R (579) 0 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1293 +d0:=D(m0,x) +--R +--R +--R (580) 0 +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^5) +--R +--R +--R (581) +--R B x + A +--R / +--R 2 5 7 5 2 4 6 2 5 4 2 2 3 5 +--R b e x + (2a b e + 5b d e )x + (a e + 10a b d e + 10b d e )x +--R + +--R 2 4 2 3 2 3 2 4 2 2 3 3 2 2 4 3 +--R (5a d e + 20a b d e + 10b d e )x + (10a d e + 20a b d e + 5b d e)x +--R + +--R 2 3 2 4 2 5 2 2 4 5 2 5 +--R (10a d e + 10a b d e + b d )x + (5a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 1293 +r0:=-b^3*(A*b-a*B)/((b*d-a*e)^5*(a+b*x))+_ + 1/4*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^4)+_ + 1/3*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x)^3)+_ + 1/2*b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(d+e*x)^2)+_ + b^2*(b*B*d-4*A*b*e+3*a*B*e)/((b*d-a*e)^5*(d+e*x))+_ + b^3*(b*B*d-5*A*b*e+4*a*B*e)*log(a+b*x)/(b*d-a*e)^6-_ + b^3*(b*B*d-5*A*b*e+4*a*B*e)*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (582) +--R 5 4 5 5 4 5 +--R ((60A b - 48B a b )e - 12B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((60A a b - 48B a b )e + (240A b - 204B a b )d e - 48B b d e )x +--R + +--R 4 2 3 4 5 4 2 3 +--R (240A a b - 192B a b )d e + (360A b - 336B a b )d e +--R + +--R 5 3 2 +--R - 72B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (360A a b - 288B a b )d e + (240A b - 264B a b )d e +--R + +--R 5 4 +--R - 48B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 4 4 5 5 +--R ((240A a b - 192B a b )d e + (60A b - 96B a b )d e - 12B b d )x +--R + +--R 4 2 3 4 4 5 +--R (60A a b - 48B a b )d e - 12B a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((- 60A b + 48B a b )e + 12B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 60A a b + 48B a b )e + (- 240A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 4 5 4 2 3 +--R (- 240A a b + 192B a b )d e + (- 360A b + 336B a b )d e +--R + +--R 5 3 2 +--R 72B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 360A a b + 288B a b )d e + (- 240A b + 264B a b )d e +--R + +--R 5 4 +--R 48B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 240A a b + 192B a b )d e + (- 60A b + 96B a b )d e +--R + +--R 5 5 +--R 12B b d +--R * +--R x +--R + +--R 4 2 3 4 4 5 +--R (- 60A a b + 48B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((60A a b - 48B a b )e + (- 60A b + 36B a b )d e + 12B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (30A a b - 24B a b )e + (180A a b - 150B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 210A b + 132B a b )d e + 42B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 10A a b + 8B a b)e + (120A a b - 94B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (150A a b - 144B a b )d e + (- 260A b + 178B a b )d e + 52B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b - 4B a )e + (- 40A a b + 31B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 136B a b )d e + (- 20A a b - 20B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 125A b + 104B a b )d e + 25B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 3A a e + (20A a b - B a )d e + (- 60A a b + 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (120A a b - 36B a b )d e + (- 65A a b - 8B a b )d e +--R + +--R 5 4 5 +--R (- 12A b + 37B a b )d +--R / +--R 6 10 5 2 9 4 3 2 8 3 4 3 7 2 5 4 6 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 6 5 5 7 6 4 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 3 4 4 6 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 2 5 5 5 6 6 4 7 7 3 +--R 648a b d e - 276a b d e + 48b d e +--R * +--R 4 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 3 4 5 5 +--R 48a d e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 2 5 6 4 6 7 3 7 8 2 +--R 792a b d e - 384a b d e + 72b d e +--R * +--R 3 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 3 4 6 4 +--R 72a d e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 2 5 7 3 6 8 2 7 9 +--R 288a b d e - 216a b d e + 48b d e +--R * +--R 2 +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 3 4 7 3 +--R 48a d e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 5 8 2 6 9 7 10 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R x +--R + +--R 7 4 6 6 5 5 5 2 6 4 4 3 7 3 3 4 8 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 2 5 9 6 10 +--R - 72a b d e + 12a b d +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (583) +--R 5 4 5 5 4 5 +--R ((60A b - 48B a b )e - 12B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((60A a b - 48B a b )e + (240A b - 204B a b )d e - 48B b d e )x +--R + +--R 4 2 3 4 5 4 2 3 +--R (240A a b - 192B a b )d e + (360A b - 336B a b )d e +--R + +--R 5 3 2 +--R - 72B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (360A a b - 288B a b )d e + (240A b - 264B a b )d e +--R + +--R 5 4 +--R - 48B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 4 4 5 5 +--R ((240A a b - 192B a b )d e + (60A b - 96B a b )d e - 12B b d )x +--R + +--R 4 2 3 4 4 5 +--R (60A a b - 48B a b )d e - 12B a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((- 60A b + 48B a b )e + 12B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 60A a b + 48B a b )e + (- 240A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 4 5 4 2 3 +--R (- 240A a b + 192B a b )d e + (- 360A b + 336B a b )d e +--R + +--R 5 3 2 +--R 72B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 360A a b + 288B a b )d e + (- 240A b + 264B a b )d e +--R + +--R 5 4 +--R 48B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 240A a b + 192B a b )d e + (- 60A b + 96B a b )d e +--R + +--R 5 5 +--R 12B b d +--R * +--R x +--R + +--R 4 2 3 4 4 5 +--R (- 60A a b + 48B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((60A a b - 48B a b )e + (- 60A b + 36B a b )d e + 12B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (30A a b - 24B a b )e + (180A a b - 150B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 210A b + 132B a b )d e + 42B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 10A a b + 8B a b)e + (120A a b - 94B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (150A a b - 144B a b )d e + (- 260A b + 178B a b )d e + 52B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b - 4B a )e + (- 40A a b + 31B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 136B a b )d e + (- 20A a b - 20B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 125A b + 104B a b )d e + 25B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 3A a e + (20A a b - B a )d e + (- 60A a b + 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (120A a b - 36B a b )d e + (- 65A a b - 8B a b )d e +--R + +--R 5 4 5 +--R (- 12A b + 37B a b )d +--R / +--R 6 10 5 2 9 4 3 2 8 3 4 3 7 2 5 4 6 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 6 5 5 7 6 4 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 3 4 4 6 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 2 5 5 5 6 6 4 7 7 3 +--R 648a b d e - 276a b d e + 48b d e +--R * +--R 4 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 3 4 5 5 +--R 48a d e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 2 5 6 4 6 7 3 7 8 2 +--R 792a b d e - 384a b d e + 72b d e +--R * +--R 3 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 3 4 6 4 +--R 72a d e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 2 5 7 3 6 8 2 7 9 +--R 288a b d e - 216a b d e + 48b d e +--R * +--R 2 +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 3 4 7 3 +--R 48a d e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 5 8 2 6 9 7 10 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R x +--R + +--R 7 4 6 6 5 5 5 2 6 4 4 3 7 3 3 4 8 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 2 5 9 6 10 +--R - 72a b d e + 12a b d +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1293 +m0:=a0-r0 +--R +--R +--R (584) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1293 +d0:=D(m0,x) +--R +--R +--R (585) 0 +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1293 +t0:=(A+B*x)*(d+e*x)^5/(a+b*x)^3 +--R +--R +--R (586) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1293 +r0:=10*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*x/b^6-_ + 1/2*(A*b-a*B)*(b*d-a*e)^5/(b^7*(a+b*x)^2)-_ + (b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)/(b^7*(a+b*x))+_ + 5/2*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^2/b^7+_ + 1/3*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^3/b^7+_ + 1/4*B*e^5*(a+b*x)^4/b^7+5*e*(b*d-a*e)^3*_ + (b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^7 +--R +--R +--R (587) +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 120A a b + 180B a b )e + (360A a b - 600B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 360A a b + 720B a b )d e + (120A b - 360B a b )d e +--R + +--R 6 4 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 360B a b)e + (720A a b - 1200B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 720A a b + 1440B a b )d e + (240A a b - 720B a b )d e +--R + +--R 5 4 +--R 120B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 120A a b + 180B a )e + (360A a b - 600B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 360A a b + 720B a b )d e + (120A a b - 360B a b )d e +--R + +--R 2 4 4 +--R 60B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 3B b e x + ((4A b - 6B a b )e + 20B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 10A a b + 15B a b )e + (30A b - 50B a b )d e + 60B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (40A a b - 60B a b )e + (- 120A a b + 200B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (120A b - 240B a b )d e + 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (100A a b - 135B a b )e + (- 300A a b + 500B a b )d e +--R + +--R 5 2 4 2 3 5 3 2 +--R (240A a b - 600B a b )d e + 240B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 40A a b + 90B a b)e + (120A a b - 200B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 240A a b + 240B a b )d e + (240A a b - 240B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 60A b + 120B a b )d e - 12B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 80A a b + 135B a )e + (240A a b - 400B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 300A a b + 480B a b )d e + (180A a b - 300B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 30A a b + 90B a b )d e + (- 6A b - 6B a b )d +--R / +--R 9 2 8 2 7 +--R 12b x + 24a b x + 12a b +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (588) +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 120A a b + 180B a b )e + (360A a b - 600B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 360A a b + 720B a b )d e + (120A b - 360B a b )d e +--R + +--R 6 4 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 360B a b)e + (720A a b - 1200B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 720A a b + 1440B a b )d e + (240A a b - 720B a b )d e +--R + +--R 5 4 +--R 120B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 120A a b + 180B a )e + (360A a b - 600B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 360A a b + 720B a b )d e + (120A a b - 360B a b )d e +--R + +--R 2 4 4 +--R 60B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 3B b e x + ((4A b - 6B a b )e + 20B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 10A a b + 15B a b )e + (30A b - 50B a b )d e + 60B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (40A a b - 60B a b )e + (- 120A a b + 200B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (120A b - 240B a b )d e + 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (126A a b - 204B a b )e + (- 330A a b + 630B a b )d e +--R + +--R 5 2 4 2 3 5 3 2 +--R (240A a b - 660B a b )d e + 240B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (12A a b - 48B a b)e + (60A a b + 60B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 240A a b + 120B a b )d e + (240A a b - 240B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 60A b + 120B a b )d e - 12B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 54A a b + 66B a )e + (210A a b - 270B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 300A a b + 420B a b )d e + (180A a b - 300B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 30A a b + 90B a b )d e + (- 6A b - 6B a b )d +--R / +--R 9 2 8 2 7 +--R 12b x + 24a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1293 +m0:=a0-r0 +--R +--R +--R 3 4 5 2 2 3 4 2 2 2 3 +--R (26A a b - 69B a )e + (- 30A a b + 130B a b)d e - 60B a b d e +--R (589) ----------------------------------------------------------------- +--R 7 +--R 12b +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1293 +d0:=D(m0,x) +--R +--R +--R (590) 0 +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1293 +t0:=(A+B*x)*(d+e*x)^4/(a+b*x)^3 +--R +--R +--R (591) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 1293 +r0:=2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*x/b^5-_ + 1/2*(A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x)^2)-_ + (b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/(b^6*(a+b*x))+_ + 1/2*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^2/b^6+_ + 1/3*B*e^4*(a+b*x)^3/b^6+2*e*(b*d-a*e)^2*_ + (2*b*B*d+3*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (592) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 30A a b + 50B a b )e + (48A a b - 120B a b )d e + 72B a b d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A a b - 20B a b)e + (- 48A a b + 48B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (72A a b - 72B a b )d e + (- 24A b + 48B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (24A a b - 40B a )e + (- 60A a b + 96B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (54A a b - 90B a b )d e + (- 12A a b + 36B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (593) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 33A a b + 63B a b )e + (48A a b - 132B a b )d e + 72B a b d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6A a b + 6B a b)e + (- 48A a b + 24B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (72A a b - 72B a b )d e + (- 24A b + 48B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (21A a b - 27B a )e + (- 60A a b + 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (54A a b - 90B a b )d e + (- 12A a b + 36B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 1293 +m0:=a0-r0 +--R +--R +--R 2 3 4 2 3 +--R (- 3A a b + 13B a )e - 12B a b d e +--R (594) ------------------------------------ +--R 6 +--R 6b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1293 +d0:=D(m0,x) +--R +--R +--R (595) 0 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1293 +t0:=(A+B*x)*(d+e*x)^3/(a+b*x)^3 +--R +--R +--R (596) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 596 + +--S 597 of 1293 +r0:=e^2*(3*b*B*d+A*b*e-3*a*B*e)*x/b^4+1/2*B*e^3*x^2/b^3-_ + 1/2*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)^2)-_ + (b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)/(b^5*(a+b*x))+_ + 3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (597) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((4A a b - 11B a b )e + 12B a b d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 4A a b + 2B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 12B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 5A a b + 7B a )e + (9A a b - 15B a b)d e + (- 3A a b + 9B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (598) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((4A a b - 11B a b )e + 12B a b d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 4A a b + 2B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 12B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 5A a b + 7B a )e + (9A a b - 15B a b)d e + (- 3A a b + 9B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 1293 +m0:=a0-r0 +--R +--R +--R (599) 0 +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1293 +d0:=D(m0,x) +--R +--R +--R (600) 0 +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1293 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (601) ---------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 of 1293 +r0:=B*e^2*x/b^3-1/2*(A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x)^2)-_ + (b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)/(b^4*(a+b*x))+_ + e*(2*b*B*d+A*b*e-3*a*B*e)*log(a+b*x)/b^4 +--R +--R +--R (602) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 2 +--R 2B b e x + 4B a b e x +--R + +--R 2 2 2 3 2 3 2 +--R ((4A a b - 4B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (3A a b - 5B a )e + (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (603) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 2 +--R 2B b e x + 4B a b e x +--R + +--R 2 2 2 3 2 3 2 +--R ((4A a b - 4B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (3A a b - 5B a )e + (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 1293 +m0:=a0-r0 +--R +--R +--R (604) 0 +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1293 +d0:=D(m0,x) +--R +--R +--R (605) 0 +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1293 +t0:=(A+B*x)*(d+e*x)/(a+b*x)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (606) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 606 + +--S 607 of 1293 +r0:=-1/2*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^2)+_ + (-b*B*d-A*b*e+2*a*B*e)/(b^3*(a+b*x))+B*e*log(a+b*x)/b^3 +--R +--R +--R (607) +--R 2 2 2 +--R (2B b e x + 4B a b e x + 2B a e)log(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2A b + 4B a b)e - 2B b d)x + (- A a b + 3B a )e + (- A b - B a b)d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (608) +--R 2 2 2 +--R (2B b e x + 4B a b e x + 2B a e)log(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2A b + 4B a b)e - 2B b d)x + (- A a b + 3B a )e + (- A b - B a b)d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 1293 +m0:=a0-r0 +--R +--R +--R (609) 0 +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1293 +d0:=D(m0,x) +--R +--R +--R (610) 0 +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1293 +t0:=(A+B*x)/(a+b*x)^3 +--R +--R +--R B x + A +--R (611) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 611 + +--S 612 of 1293 +r0:=-1/2*(A+B*x)^2/((A*b-a*B)*(a+b*x)^2) +--R +--R +--R 1 2 2 1 2 +--R - - B x - A B x - - A +--R 2 2 +--R (612) ------------------------------------------------------ +--R 3 2 2 2 2 2 3 +--R (A b - B a b )x + (2A a b - 2B a b)x + A a b - B a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 612 + +--S 613 of 1293 +a0:=integrate(t0,x) +--R +--R +--R - 2B b x - A b - B a +--R (613) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 1293 +m0:=a0-r0 +--R +--R +--R 2 +--R B +--R (614) --------------- +--R 3 2 +--R 2A b - 2B a b +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1293 +d0:=D(m0,x) +--R +--R +--R (615) 0 +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)) +--R +--R +--R (616) +--R B x + A +--R ----------------------------------------------------------------------- +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 of 1293 +r0:=1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2)+(-B*d+A*e)/((b*d-a*e)^2*(a+b*x))-_ + e*(B*d-A*e)*log(a+b*x)/(b*d-a*e)^3+e*(B*d-A*e)*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (617) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 3 4 2 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a b e - 6a b d e +--R + +--R 3 3 2 2 4 3 +--R 6a b d e - 2a b d +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (618) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 3 4 2 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a b e - 6a b d e +--R + +--R 3 3 2 2 4 3 +--R 6a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 1293 +m0:=a0-r0 +--R +--R +--R (619) 0 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1293 +d0:=D(m0,x) +--R +--R +--R (620) 0 +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^2) +--R +--R +--R (621) +--R B x + A +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 621 + +--S 622 of 1293 +r0:=1/2*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^2)+_ + (-b*B*d+2*A*b*e-a*B*e)/((b*d-a*e)^3*(a+b*x))-_ + e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x))-_ + e*(2*b*B*d-3*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^4+_ + e*(2*b*B*d-3*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (622) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (623) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 623 + +--S 624 of 1293 +m0:=a0-r0 +--R +--R +--R (624) 0 +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1293 +d0:=D(m0,x) +--R +--R +--R (625) 0 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^3) +--R +--R +--R (626) +--R B x + A +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 626 + +--S 627 of 1293 +r0:=-1/2*b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x)^2)-_ + b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(a+b*x))-_ + 1/2*e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x)^2)-_ + e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(d+e*x))-_ + 3*b*e*(b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^5+_ + 3*b*e*(b*B*d-2*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (627) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 4 2 2 3 +--R ((12A a b - 6B a b )e - 12A b d e + 6B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (18A a b - 9B a b)e - 9B a b d e + (- 18A b + 9B a b )d e +--R + +--R 4 3 +--R 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (4A a b - 2B a )e + (24A a b - 14B a b)d e - 24A a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 14B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 3 2 2 3 2 2 3 +--R - A a e + (8A a b - B a )d e - 9B a b d e + (- 8A a b + 9B a b )d e +--R + +--R 4 3 4 +--R (A b + B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (628) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 4 2 2 3 +--R ((12A a b - 6B a b )e - 12A b d e + 6B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (18A a b - 9B a b)e - 9B a b d e + (- 18A b + 9B a b )d e +--R + +--R 4 3 +--R 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (4A a b - 2B a )e + (24A a b - 14B a b)d e - 24A a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 14B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 3 2 2 3 2 2 3 +--R - A a e + (8A a b - B a )d e - 9B a b d e + (- 8A a b + 9B a b )d e +--R + +--R 4 3 4 +--R (A b + B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 628 + +--S 629 of 1293 +m0:=a0-r0 +--R +--R +--R (629) 0 +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1293 +d0:=D(m0,x) +--R +--R +--R (630) 0 +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^4) +--R +--R +--R (631) +--R B x + A +--R / +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 631 + +--S 632 of 1293 +r0:=-1/2*b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x)^2)-_ + b^2*(b*B*d-4*A*b*e+3*a*B*e)/((b*d-a*e)^5*(a+b*x))-_ + 1/3*e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x)^3)-_ + 1/2*e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(d+e*x)^2)-_ + 3*b*e*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^5*(d+e*x))-_ + 2*b^2*e*(2*b*B*d-5*A*b*e+3*a*B*e)*log(a+b*x)/(b*d-a*e)^6+_ + 2*b^2*e*(2*b*B*d-5*A*b*e+3*a*B*e)*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (632) +--R 5 4 5 5 4 5 +--R ((- 60A b + 36B a b )e + 24B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 120A a b + 72B a b )e + (- 180A b + 156B a b )d e +--R + +--R 5 2 3 +--R 72B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 60A a b + 36B a b )e + (- 360A a b + 240B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 180A b + 252B a b )d e + 72B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 2 3 +--R (- 180A a b + 108B a b )d e + (- 360A a b + 288B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (- 60A b + 180B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 180A a b + 108B a b )d e + (- 120A a b + 144B a b )d e +--R + +--R 4 4 +--R 48B a b d e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 3 4 +--R (- 60A a b + 36B a b )d e + 24B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 36B a b )e - 24B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((120A a b - 72B a b )e + (180A b - 156B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (60A a b - 36B a b )e + (360A a b - 240B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (180A b - 252B a b )d e - 72B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 2 3 +--R (180A a b - 108B a b )d e + (360A a b - 288B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (60A b - 180B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 108B a b )d e + (120A a b - 144B a b )d e +--R + +--R 4 4 +--R - 48B a b d e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 3 4 +--R (60A a b - 36B a b )d e - 24B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 36B a b )e + (60A b - 12B a b )d e - 24B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 90A a b + 54B a b )e + (- 60A a b + 72B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (150A b - 66B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 20A a b + 12B a b)e + (- 210A a b + 134B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b + 12B a b )d e + (110A b - 114B a b )d e - 44B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b - 3B a )e + (- 60A a b + 34B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 120A a b + 96B a b )d e + (160A a b - 48B a b )d e +--R + +--R 5 4 4 5 5 +--R (15A b - 73B a b )d e - 6B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 2A a e + (15A a b - B a )d e + (- 60A a b + 12B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (20A a b + 36B a b )d e + (30A a b - 44B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - 3B a b )d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (633) +--R 5 4 5 5 4 5 +--R ((- 60A b + 36B a b )e + 24B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 120A a b + 72B a b )e + (- 180A b + 156B a b )d e +--R + +--R 5 2 3 +--R 72B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 60A a b + 36B a b )e + (- 360A a b + 240B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 180A b + 252B a b )d e + 72B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 2 3 +--R (- 180A a b + 108B a b )d e + (- 360A a b + 288B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (- 60A b + 180B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 180A a b + 108B a b )d e + (- 120A a b + 144B a b )d e +--R + +--R 4 4 +--R 48B a b d e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 3 4 +--R (- 60A a b + 36B a b )d e + 24B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 36B a b )e - 24B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((120A a b - 72B a b )e + (180A b - 156B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (60A a b - 36B a b )e + (360A a b - 240B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (180A b - 252B a b )d e - 72B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 2 3 +--R (180A a b - 108B a b )d e + (360A a b - 288B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (60A b - 180B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 108B a b )d e + (120A a b - 144B a b )d e +--R + +--R 4 4 +--R - 48B a b d e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 3 4 +--R (60A a b - 36B a b )d e - 24B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 36B a b )e + (60A b - 12B a b )d e - 24B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 90A a b + 54B a b )e + (- 60A a b + 72B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (150A b - 66B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 20A a b + 12B a b)e + (- 210A a b + 134B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b + 12B a b )d e + (110A b - 114B a b )d e - 44B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b - 3B a )e + (- 60A a b + 34B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 120A a b + 96B a b )d e + (160A a b - 48B a b )d e +--R + +--R 5 4 4 5 5 +--R (15A b - 73B a b )d e - 6B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 2A a e + (15A a b - B a )d e + (- 60A a b + 12B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (20A a b + 36B a b )d e + (30A a b - 44B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - 3B a b )d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Union(Expression(Integer),...) +--E 633 + +--S 634 of 1293 +m0:=a0-r0 +--R +--R +--R (634) 0 +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1293 +d0:=D(m0,x) +--R +--R +--R (635) 0 +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1293 +t0:=(a+b*x)*(A+B*x)*(d+e*x)^(7/2) +--R +--R +--R (636) +--R 3 5 3 2 4 +--R B b e x + ((A b + B a)e + 3B b d e )x +--R + +--R 3 2 2 3 +--R (A a e + (3A b + 3B a)d e + 3B b d e)x +--R + +--R 2 2 3 2 2 3 +--R (3A a d e + (3A b + 3B a)d e + B b d )x + (3A a d e + (A b + B a)d )x +--R + +--R 3 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1293 +r0:=2/9*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(9/2)/e^3-_ + 2/11*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)/e^3+2/13*b*B*(d+e*x)^(13/2)/e^3 +--R +--R +--R (637) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (638) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Union(Expression(Integer),...) +--E 638 + +--S 639 of 1293 +m0:=a0-r0 +--R +--R +--R (639) 0 +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1293 +d0:=D(m0,x) +--R +--R +--R (640) 0 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1293 +t0:=(a+b*x)*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (641) +--R 2 4 2 3 +--R B b e x + ((A b + B a)e + 2B b d e)x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + B b d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1293 +r0:=2/7*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(7/2)/e^3-_ + 2/9*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)/e^3+2/11*b*B*(d+e*x)^(11/2)/e^3 +--R +--R +--R (642) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (643) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1293 +m0:=a0-r0 +--R +--R +--R (644) 0 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1293 +d0:=D(m0,x) +--R +--R +--R (645) 0 +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1293 +t0:=(a+b*x)*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (646) +--R 3 2 +--R (B b e x + ((A b + B a)e + B b d)x + (A a e + (A b + B a)d)x + A a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1293 +r0:=2/5*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(5/2)/e^3-_ + 2/7*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)/e^3+2/9*b*B*(d+e*x)^(9/2)/e^3 +--R +--R +--R (647) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (648) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 1293 +m0:=a0-r0 +--R +--R +--R (649) 0 +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1293 +d0:=D(m0,x) +--R +--R +--R (650) 0 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1293 +t0:=(a+b*x)*(A+B*x)*sqrt(d+e*x) +--R +--R +--R 2 +-------+ +--R (651) (B b x + (A b + B a)x + A a)\|e x + d +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1293 +r0:=2/3*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(3/2)/e^3-_ + 2/5*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)/e^3+2/7*b*B*(d+e*x)^(7/2)/e^3 +--R +--R +--R (652) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (653) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 1293 +m0:=a0-r0 +--R +--R +--R (654) 0 +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1293 +d0:=D(m0,x) +--R +--R +--R (655) 0 +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1293 +t0:=(a+b*x)*(A+B*x)/sqrt(d+e*x) +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (656) --------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1293 +r0:=-2/3*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/e^3+_ + 2/5*b*B*(d+e*x)^(5/2)/e^3+2*(b*d-a*e)*(B*d-A*e)*sqrt(d+e*x)/e^3 +--R +--R +--R (657) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15e +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (658) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15e +--R Type: Union(Expression(Integer),...) +--E 658 + +--S 659 of 1293 +m0:=a0-r0 +--R +--R +--R (659) 0 +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1293 +d0:=D(m0,x) +--R +--R +--R (660) 0 +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1293 +t0:=(a+b*x)*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (661) --------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1293 +r0:=2/3*b*B*(d+e*x)^(3/2)/e^3-2*(b*d-a*e)*(B*d-A*e)/(e^3*sqrt(d+e*x))-_ + 2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/e^3 +--R +--R +--R (662) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e + (12A b + 12B a)d e +--R + +--R 2 +--R - 16B b d +--R / +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (663) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e + (12A b + 12B a)d e +--R + +--R 2 +--R - 16B b d +--R / +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 1293 +m0:=a0-r0 +--R +--R +--R (664) 0 +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1293 +d0:=D(m0,x) +--R +--R +--R (665) 0 +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1293 +t0:=(a+b*x)*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (666) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1293 +r0:=-2/3*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^(3/2))+_ + 2*(2*b*B*d-A*b*e-a*B*e)/(e^3*sqrt(d+e*x))+2*b*B*sqrt(d+e*x)/e^3 +--R +--R +--R (667) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R / +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (668) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R / +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 1293 +m0:=a0-r0 +--R +--R +--R (669) 0 +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1293 +d0:=D(m0,x) +--R +--R +--R (670) 0 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1293 +t0:=(a+b*x)*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (671) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1293 +r0:=-2/5*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^(5/2))+_ + 2/3*(2*b*B*d-A*b*e-a*B*e)/(e^3*(d+e*x)^(3/2))-2*b*B/(e^3*sqrt(d+e*x)) +--R +--R +--R (672) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R / +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (673) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R / +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 673 + +--S 674 of 1293 +m0:=a0-r0 +--R +--R +--R (674) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1293 +d0:=D(m0,x) +--R +--R +--R (675) 0 +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1293 +t0:=(a+b*x)^2*(A+B*x)*(d+e*x)^(7/2) +--R +--R +--R (676) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1293 +r0:=-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+_ + 2/11*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^4-_ + 2/13*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^4+_ + 2/15*b^2*B*(d+e*x)^(15/2)/e^4 +--R +--R +--R (677) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (678) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 678 + +--S 679 of 1293 +m0:=a0-r0 +--R +--R +--R (679) 0 +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1293 +d0:=D(m0,x) +--R +--R +--R (680) 0 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1293 +t0:=(a+b*x)^2*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (681) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1293 +r0:=-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+_ + 2/9*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^4-_ + 2/11*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^4+_ + 2/13*b^2*B*(d+e*x)^(13/2)/e^4 +--R +--R +--R (682) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (683) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 1293 +m0:=a0-r0 +--R +--R +--R (684) 0 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1293 +d0:=D(m0,x) +--R +--R +--R (685) 0 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1293 +t0:=(a+b*x)^2*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (686) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1293 +r0:=-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+_ + 2/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^4-_ + 2/9*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^4+_ + 2/11*b^2*B*(d+e*x)^(11/2)/e^4 +--R +--R +--R (687) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (688) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 1293 +m0:=a0-r0 +--R +--R +--R (689) 0 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1293 +d0:=D(m0,x) +--R +--R +--R (690) 0 +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1293 +t0:=(a+b*x)^2*(A+B*x)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (691) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1293 +r0:=-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+_ + 2/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^4-_ + 2/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^4+_ + 2/9*b^2*B*(d+e*x)^(9/2)/e^4 +--R +--R +--R (692) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (693) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 1293 +m0:=a0-r0 +--R +--R +--R (694) 0 +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1293 +d0:=D(m0,x) +--R +--R +--R (695) 0 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1293 +t0:=(a+b*x)^2*(A+B*x)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (696) ---------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1293 +r0:=2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^4-_ + 2/5*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^4+_ + 2/7*b^2*B*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^2*(B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (697) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (698) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 1293 +m0:=a0-r0 +--R +--R +--R (699) 0 +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1293 +d0:=D(m0,x) +--R +--R +--R (700) 0 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1293 +t0:=(a+b*x)^2*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (701) ---------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1293 +r0:=-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+_ + 2/5*b^2*B*(d+e*x)^(5/2)/e^4+2*(b*d-a*e)^2*(B*d-A*e)/(e^4*sqrt(d+e*x))+_ + 2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (702) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (703) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1293 +m0:=a0-r0 +--R +--R +--R (704) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1293 +d0:=D(m0,x) +--R +--R +--R (705) 0 +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1293 +t0:=(a+b*x)^2*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (706) ---------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1293 +r0:=2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+_ + 2/3*b^2*B*(d+e*x)^(3/2)/e^4-_ + 2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*sqrt(d+e*x))-_ + 2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (707) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (708) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 1293 +m0:=a0-r0 +--R +--R +--R (709) 0 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1293 +d0:=D(m0,x) +--R +--R +--R (710) 0 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1293 +t0:=(a+b*x)^2*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (711) ---------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1293 +r0:=2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-_ + 2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^(3/2))+_ + 2*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*sqrt(d+e*x))+2*b^2*B*sqrt(d+e*x)/e^4 +--R +--R +--R (712) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (713) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 1293 +m0:=a0-r0 +--R +--R +--R (714) 0 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1293 +d0:=D(m0,x) +--R +--R +--R (715) 0 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1293 +t0:=(a+b*x)^3*(A+B*x)*(d+e*x)^(7/2) +--R +--R +--R (716) +--R 3 3 7 3 2 3 3 2 6 +--R B b e x + ((A b + 3B a b )e + 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 5 +--R ((3A a b + 3B a b)e + (3A b + 9B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b + B a )e + (9A a b + 9B a b)d e + (3A b + 9B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 3 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1293 +r0:=2/9*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(9/2)/e^5-_ + 2/11*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^5+_ + 6/13*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(13/2)/e^5-_ + 2/15*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^5+_ + 2/17*b^3*B*(d+e*x)^(17/2)/e^5 +--R +--R +--R (717) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 109395e +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (718) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 109395e +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 1293 +m0:=a0-r0 +--R +--R +--R (719) 0 +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1293 +d0:=D(m0,x) +--R +--R +--R (720) 0 +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1293 +t0:=(a+b*x)^3*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (721) +--R 3 2 6 3 2 2 3 5 +--R B b e x + ((A b + 3B a b )e + 2B b d e)x +--R + +--R 2 2 2 3 2 3 2 4 +--R ((3A a b + 3B a b)e + (2A b + 6B a b )d e + B b d )x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R ((3A a b + B a )e + (6A a b + 6B a b)d e + (A b + 3B a b )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1293 +r0:=2/7*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(7/2)/e^5-_ + 2/9*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^5+_ + 6/11*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)/e^5-_ + 2/13*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^5+_ + 2/15*b^3*B*(d+e*x)^(15/2)/e^5 +--R +--R +--R (722) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (723) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 1293 +m0:=a0-r0 +--R +--R +--R (724) 0 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1293 +d0:=D(m0,x) +--R +--R +--R (725) 0 +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1293 +t0:=(a+b*x)^3*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (726) +--R 3 5 3 2 3 4 +--R B b e x + ((A b + 3B a b )e + B b d)x +--R + +--R 2 2 3 2 3 +--R ((3A a b + 3B a b)e + (A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 3 2 3 +--R ((3A a b + B a )e + (3A a b + 3B a b)d)x + (A a e + (3A a b + B a )d)x +--R + +--R 3 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1293 +r0:=2/5*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(5/2)/e^5-2/7*(b*d-a*e)^2*(4*b*B*d-_ + 3*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^5+_ + 2/3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)/e^5-_ + 2/11*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(11/2)/e^5+_ + 2/13*b^3*B*(d+e*x)^(13/2)/e^5 +--R +--R +--R (727) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 15015e +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (728) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 15015e +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 1293 +m0:=a0-r0 +--R +--R +--R (729) 0 +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1293 +d0:=D(m0,x) +--R +--R +--R (730) 0 +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1293 +t0:=(a+b*x)^3*(A+B*x)*sqrt(d+e*x) +--R +--R +--R (731) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1293 +r0:=2/3*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(3/2)/e^5-2/5*(b*d-a*e)^2*(4*b*B*d-_ + 3*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^5+_ + 6/7*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)/e^5-_ + 2/9*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^5+_ + 2/11*b^3*B*(d+e*x)^(11/2)/e^5 +--R +--R +--R (732) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (733) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 1293 +m0:=a0-r0 +--R +--R +--R (734) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1293 +d0:=D(m0,x) +--R +--R +--R (735) 0 +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1293 +t0:=(a+b*x)^3*(A+B*x)/sqrt(d+e*x) +--R +--R +--R (736) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1293 +r0:=-2/3*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^5+_ + 6/5*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)/e^5-_ + 2/7*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^5+_ + 2/9*b^3*B*(d+e*x)^(9/2)/e^5+2*(b*d-a*e)^3*(B*d-A*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (737) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (738) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 738 + +--S 739 of 1293 +m0:=a0-r0 +--R +--R +--R (739) 0 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1293 +d0:=D(m0,x) +--R +--R +--R (740) 0 +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1293 +t0:=(a+b*x)^3*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R (741) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1293 +r0:=2*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/e^5-_ + 2/5*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^5+_ + 2/7*b^3*B*(d+e*x)^(7/2)/e^5-2*(b*d-a*e)^3*(B*d-A*e)/(e^5*sqrt(d+e*x))-_ + 2*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (742) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R / +--R 5 +-------+ +--R 35e \|e x + d +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (743) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R / +--R 5 +-------+ +--R 35e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 1293 +m0:=a0-r0 +--R +--R +--R (744) 0 +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1293 +d0:=D(m0,x) +--R +--R +--R (745) 0 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1293 +t0:=(a+b*x)^3*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R (746) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1293 +r0:=-2/3*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(3/2))-_ + 2/3*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^5+_ + 2/5*b^3*B*(d+e*x)^(5/2)/e^5+2*(b*d-a*e)^2*_ + (4*b*B*d-3*A*b*e-a*B*e)/(e^5*sqrt(d+e*x))+6*b*(b*d-a*e)*_ + (2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (747) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (748) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 748 + +--S 749 of 1293 +m0:=a0-r0 +--R +--R +--R (749) 0 +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1293 +d0:=D(m0,x) +--R +--R +--R (750) 0 +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1293 +t0:=(a+b*x)^3*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R (751) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1293 +r0:=-2/5*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(5/2))+_ + 2/3*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*(d+e*x)^(3/2))+_ + 2/3*b^3*B*(d+e*x)^(3/2)/e^5-6*b*(b*d-a*e)*_ + (2*b*B*d-A*b*e-a*B*e)/(e^5*sqrt(d+e*x))-_ + 2*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (752) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (753) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 1293 +m0:=a0-r0 +--R +--R +--R (754) 0 +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1293 +d0:=D(m0,x) +--R +--R +--R (755) 0 +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1293 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+b*x) +--R +--R +--R (756) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1293 +r0:=2/3*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^(3/2)/b^4+_ + 2/5*(A*b-a*B)*(b*d-a*e)*(d+e*x)^(5/2)/b^3+_ + 2/7*(A*b-a*B)*(d+e*x)^(7/2)/b^2+2/9*B*(d+e*x)^(9/2)/(b*e)-_ + 2*(A*b-a*B)*(b*d-a*e)^(7/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+2*(A*b-a*B)*_ + (b*d-a*e)^3*sqrt(d+e*x)/b^5 +--R +--R +--R (757) +--R 3 4 4 2 2 3 3 +--R (630A a b - 630B a )e + (- 1890A a b + 1890B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1890A a b - 1890B a b )d e + (- 630A b + 630B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 70B b e x + ((90A b - 90B a b )e + 280B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 126A a b + 126B a b )e + (396A b - 396B a b )d e +--R + +--R 4 2 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (210A a b - 210B a b)e + (- 672A a b + 672B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (732A b - 732B a b )d e + 280B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 630A a b + 630B a )e + (2100A a b - 2100B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 2436A a b + 2436B a b )d e + (1056A b - 1056B a b )d e + 70B b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 +-+ +--R 315b e\|b +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (758) +--R [ +--R 3 4 4 2 2 3 3 +--R (- 315A a b + 315B a )e + (945A a b - 945B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 945A a b + 945B a b )d e + (315A b - 315B a b )d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 70B b e x + ((90A b - 90B a b )e + 280B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 126A a b + 126B a b )e + (396A b - 396B a b )d e +--R + +--R 4 2 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (210A a b - 210B a b)e + (- 672A a b + 672B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (732A b - 732B a b )d e + 280B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 630A a b + 630B a )e + (2100A a b - 2100B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2436A a b + 2436B a b )d e + (1056A b - 1056B a b )d e +--R + +--R 4 4 +--R 70B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315b e +--R , +--R +--R 3 4 4 2 2 3 3 +--R (630A a b - 630B a )e + (- 1890A a b + 1890B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1890A a b - 1890B a b )d e + (- 630A b + 630B a b )d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 70B b e x + ((90A b - 90B a b )e + 280B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 126A a b + 126B a b )e + (396A b - 396B a b )d e +--R + +--R 4 2 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (210A a b - 210B a b)e + (- 672A a b + 672B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (732A b - 732B a b )d e + 280B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 630A a b + 630B a )e + (2100A a b - 2100B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2436A a b + 2436B a b )d e + (1056A b - 1056B a b )d e +--R + +--R 4 4 +--R 70B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 758 + +--S 759 of 1293 +m0:=a0.1-r0 +--R +--R +--R (759) +--R 3 4 3 2 2 3 2 +--R (- A a b + B a )e + (3A a b - 3B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b + 3B a b )d e + (A b - B a b )d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 3 4 3 2 2 3 2 +--R (- 2A a b + 2B a )e + (6A a b - 6B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 6A a b + 6B a b )d e + (2A b - 2B a b )d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1293 +d0:=D(m0,x) +--R +--R +--R (760) 0 +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1293 +m0:=a0.2-r0 +--R +--R +--R (761) +--R 3 4 3 2 2 3 2 +--R (- 2A a b + 2B a )e + (6A a b - 6B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 6A a b + 6B a b )d e + (2A b - 2B a b )d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 4 3 2 2 3 2 +--R (2A a b - 2B a )e + (- 6A a b + 6B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (6A a b - 6B a b )d e + (- 2A b + 2B a b )d +--R * +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1293 +d0:=D(m0,x) +--R +--R +--R (762) 0 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (763) ---------------------------------------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1293 +r0:=2/3*(A*b-a*B)*(b*d-a*e)*(d+e*x)^(3/2)/b^3+_ + 2/5*(A*b-a*B)*(d+e*x)^(5/2)/b^2+2/7*B*(d+e*x)^(7/2)/(b*e)-_ + 2*(A*b-a*B)*(b*d-a*e)^(5/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+2*(A*b-a*B)*_ + (b*d-a*e)^2*sqrt(d+e*x)/b^4 +--R +--R +--R (764) +--R 2 3 3 2 2 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 +--R (- 210A b + 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 +-+ +--R 105b e\|b +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (765) +--R [ +--R 2 3 3 2 2 2 +--R (- 105A a b + 105B a )e + (210A a b - 210B a b)d e +--R + +--R 3 2 2 +--R (- 105A b + 105B a b )d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b e +--R , +--R +--R 2 3 3 2 2 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 +--R (- 210A b + 210B a b )d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 765 + +--S 766 of 1293 +m0:=a0.1-r0 +--R +--R +--R (766) +--R 2 3 2 2 2 3 2 2 +--R ((- A a b + B a )e + (2A a b - 2B a b)d e + (- A b + B a b )d ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 2 2 2 3 2 2 +--R ((2A a b - 2B a )e + (- 4A a b + 4B a b)d e + (2A b - 2B a b )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1293 +d0:=D(m0,x) +--R +--R +--R (767) 0 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1293 +m0:=a0.2-r0 +--R +--R +--R (768) +--R 2 3 2 2 2 3 2 2 +--R ((2A a b - 2B a )e + (- 4A a b + 4B a b)d e + (2A b - 2B a b )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A a b + 2B a )e + (4A a b - 4B a b)d e + (- 2A b + 2B a b )d ) +--R * +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1293 +d0:=D(m0,x) +--R +--R +--R (769) 0 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (770) --------------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1293 +r0:=2/3*(A*b-a*B)*(d+e*x)^(3/2)/b^2+2/5*B*(d+e*x)^(5/2)/(b*e)-_ + 2*(A*b-a*B)*(b*d-a*e)^(3/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(7/2)+2*(A*b-a*B)*(b*d-a*e)*sqrt(d+e*x)/b^3 +--R +--R +--R (771) +--R 2 2 2 +-----------+ +--R ((30A a b - 30B a )e + (- 30A b + 30B a b)d e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 3 +-+ +--R 15b e\|b +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (772) +--R [ +--R +-----------+ +--R 2 2 2 |- a e + b d +--R ((- 15A a b + 15B a )e + (15A b - 15B a b)d e) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b e +--R , +--R +--R +---------+ +--R 2 2 2 |a e - b d +--R ((30A a b - 30B a )e + (- 30A b + 30B a b)d e) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 772 + +--S 773 of 1293 +m0:=a0.1-r0 +--R +--R +--R (773) +--R +-----------+ +--R 2 2 |- a e + b d +-+ +--R ((- A a b + B a )e + (A b - B a b)d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 +-----------+ +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1293 +d0:=D(m0,x) +--R +--R +--R (774) 0 +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1293 +m0:=a0.2-r0 +--R +--R +--R (775) +--R 2 2 +-----------+ +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 2 +-+ |a e - b d \|e x + d +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1293 +d0:=D(m0,x) +--R +--R +--R (776) 0 +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (777) ------------------- +--R b x + a +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1293 +r0:=2/3*B*(d+e*x)^(3/2)/(b*e)-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(5/2)+2*(A*b-a*B)*sqrt(d+e*x)/b^2 +--R +--R +--R (778) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 6A b + 6B a)e\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|b \|e x + d +--R / +--R 2 +-+ +--R 3b e\|b +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (779) +--R [ +--R +-----------+ +--R |- a e + b d +--R (3A b - 3B a)e |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|e x + d +--R / +--R 2 +--R 3b e +--R , +--R +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R (- 6A b + 6B a)e |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|e x + d +--R / +--R 2 +--R 3b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 779 + +--S 780 of 1293 +m0:=a0.1-r0 +--R +--R +--R (780) +--R +-----------+ +--R |- a e + b d +-+ +--R (A b - B a) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (2A b - 2B a)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1293 +d0:=D(m0,x) +--R +--R +--R (781) 0 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1293 +m0:=a0.2-r0 +--R +--R +--R (782) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (2A b - 2B a)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R (- 2A b + 2B a)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1293 +d0:=D(m0,x) +--R +--R +--R (783) 0 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1293 +t0:=(A+B*x)/((a+b*x)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (784) ------------------- +--R +-------+ +--R (b x + a)\|e x + d +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1293 +r0:=-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + sqrt(b*d-a*e))+2*B*sqrt(d+e*x)/(b*e) +--R +--R +--R (785) +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- 2A b + 2B a)e atanh(--------------) + 2B\|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R ----------------------------------------------------------------------- +--R +-----------+ +-+ +--R b e\|- a e + b d \|b +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (786) +--R [ +--R (A b - B a)e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R 2B\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R | 2 +--R b e\|- a b e + b d +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b e - b d \|e x + d | 2 +-------+ +--R (2A b - 2B a)e atan(------------------------) + 2B\|a b e - b d \|e x + d +--R a e - b d +--R --------------------------------------------------------------------------] +--R +-----------+ +--R | 2 +--R b e\|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 786 + +--S 787 of 1293 +m0:=a0.1-r0 +--R +--R +--R (787) +--R +-----------+ +-+ +--R (A b - B a)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R (2A b - 2B a)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +--R b\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1293 +d0:=D(m0,x) +--R +--R +--R (788) 0 +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1293 +m0:=a0.2-r0 +--R +--R +--R (789) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R (2A b - 2B a)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R (2A b - 2B a)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R b\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1293 +d0:=D(m0,x) +--R +--R +--R (790) 0 +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R B x + A +--R (791) --------------------------------------- +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1293 +r0:=-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(3/2)*sqrt(b))-2*(B*d-A*e)/(e*(b*d-a*e)*sqrt(d+e*x)) +--R +--R +--R (792) +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R (2A b - 2B a)e\|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R (- 2A e + 2B d)\|- a e + b d \|b +--R / +--R 2 +-----------+ +-+ +-------+ +--R (a e - b d e)\|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (793) +--R [ +--R +-------+ +--R (A b - B a)e\|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +--R (- 2A e + 2B d)\|- a b e + b d +--R / +--R +-------------+ +--R 2 | 2 +-------+ +--R (a e - b d e)\|- a b e + b d \|e x + d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R (- 2A b + 2B a)e\|e x + d atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +--R (- 2A e + 2B d)\|a b e - b d +--R / +--R +-----------+ +--R 2 | 2 +-------+ +--R (a e - b d e)\|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 793 + +--S 794 of 1293 +m0:=a0.1-r0 +--R +--R +--R (794) +--R +-----------+ +-+ +--R (A b - B a)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R (- 2A b + 2B a)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +--R (a e - b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1293 +d0:=D(m0,x) +--R +--R +--R (795) 0 +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1293 +m0:=a0.2-r0 +--R +--R +--R (796) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R (- 2A b + 2B a)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R (- 2A b + 2B a)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R (a e - b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1293 +d0:=D(m0,x) +--R +--R +--R (797) 0 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R B x + A +--R (798) ---------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1293 +r0:=-2/3*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(3/2))-2*(A*b-a*B)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/_ + (b*d-a*e)^(5/2)+2*(A*b-a*B)/((b*d-a*e)^2*sqrt(d+e*x)) +--R +--R +--R (799) +--R 2 +-+ +-------+ +--R ((- 6A b + 6B a)e x + (- 6A b + 6B a)d e)\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +-----------+ +--R ((6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d )\|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (800) +--R [ +--R +-----------+ +--R 2 | b +-------+ +--R ((3A b - 3B a)e x + (3A b - 3B a)d e) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R (6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e)\|e x + d +--R , +--R +--R +---------+ +--R 2 | b +-------+ +--R ((6A b - 6B a)e x + (6A b - 6B a)d e) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 +--R (6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e)\|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 800 + +--S 801 of 1293 +m0:=a0.1-r0 +--R +--R +--R (801) +--R +-----------+ +--R +-----------+ | b +--R (A b - B a)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R (2A b - 2B a)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 2 2 2 +-----------+ +--R (a e - 2a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1293 +d0:=D(m0,x) +--R +--R +--R (802) 0 +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1293 +m0:=a0.2-r0 +--R +--R +--R (803) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R (2A b - 2B a)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|e x + d +--R (2A b - 2B a)\|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 2 2 2 2 +-----------+ +--R (a e - 2a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1293 +d0:=D(m0,x) +--R +--R +--R (804) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^(7/2)) +--R +--R +--R (805) +--R B x + A +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1293 +r0:=-2/5*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(5/2))+2/3*(A*b-a*B)/_ + ((b*d-a*e)^2*(d+e*x)^(3/2))-2*b^(3/2)*(A*b-a*B)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(7/2)+_ + 2*b*(A*b-a*B)/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (806) +--R 2 3 2 2 2 +--R (30A b - 30B a b)e x + (60A b - 60B a b)d e x +--R + +--R 2 2 +--R (30A b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (807) +--R [ +--R 2 3 2 2 2 +--R (15A b - 15B a b)e x + (30A b - 30B a b)d e x +--R + +--R 2 2 +--R (15A b - 15B a b)d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 3 2 2 2 +--R (- 30A b + 30B a b)e x + (- 60A b + 60B a b)d e x +--R + +--R 2 2 +--R (- 30A b + 30B a b)d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 807 + +--S 808 of 1293 +m0:=a0.1-r0 +--R +--R +--R (808) +--R +-----------+ +--R 2 +-----------+ | b +--R (A b - B a b)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R (- 2A b + 2B a b)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1293 +d0:=D(m0,x) +--R +--R +--R (809) 0 +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1293 +m0:=a0.2-r0 +--R +--R +--R (810) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R (- 2A b + 2B a b)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|e x + d +--R (- 2A b + 2B a b)\|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1293 +d0:=D(m0,x) +--R +--R +--R (811) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1293 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^2 +--R +--R +--R (812) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1293 +r0:=1/3*(b*d-a*e)*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ + 1/5*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/b^3+_ + 1/7*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x))-_ + (b*d-a*e)^(5/2)*(2*b*B*d+7*A*b*e-9*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+(b*d-a*e)^2*_ + (2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (813) +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 5 +-+ +--R (105b x + 105a b )\|b +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (814) +--R [ +--R 2 2 3 3 3 2 2 2 +--R (735A a b - 945B a b)e + (- 1470A a b + 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (735A b - 1365B a b )d e + 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1470A a b + 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (735A a b - 1365B a b )d e + 210B a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 60B b e x + ((84A b - 108B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 196A a b + 252B a b )e + (448A b - 632B a b )d e +--R + +--R 4 2 +--R 488B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (980A a b - 1260B a b)e + (- 2352A a b + 3304B a b )d e +--R + +--R 4 3 2 4 3 +--R (1624A b - 2760B a b )d e + 704B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (1470A a b - 1890B a )e + (- 3430A a b + 4830B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (2254A a b - 3878B a b )d e + (- 210A b + 914B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 5 +--R 210b x + 210a b +--R , +--R +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 5 +--R 105b x + 105a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 814 + +--S 815 of 1293 +m0:=a0.1-r0 +--R +--R +--R (815) +--R 2 3 3 2 2 2 +--R (7A a b - 9B a )e + (- 14A a b + 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (7A b - 13B a b )d e + 2B b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 18B a )e + (- 28A a b + 40B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b - 26B a b )d e + 4B b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1293 +d0:=D(m0,x) +--R +--R +--R (816) 0 +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1293 +m0:=a0.2-r0 +--R +--R +--R (817) +--R 2 3 3 2 2 2 +--R (7A a b - 9B a )e + (- 14A a b + 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (7A b - 13B a b )d e + 2B b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 3 2 2 2 +--R (- 7A a b + 9B a )e + (14A a b - 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 7A b + 13B a b )d e - 2B b d +--R * +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1293 +d0:=D(m0,x) +--R +--R +--R (818) 0 +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (819) ---------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1293 +r0:=1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+_ + 1/5*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x))-_ + (b*d-a*e)^(3/2)*(2*b*B*d+5*A*b*e-7*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+_ + (b*d-a*e)*(2*b*B*d+5*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (820) +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 4 +-+ +--R (15b x + 15a b )\|b +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (821) +--R [ +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 12B b e x + ((20A b - 28B a b )e + 44B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 100A a b + 140B a b)e + (140A b - 236B a b )d e + 92B b d )x +--R + +--R 2 3 2 2 2 +--R (- 150A a b + 210B a )e + (200A a b - 340B a b)d e +--R + +--R 3 2 2 +--R (- 30A b + 122B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 30b x + 30a b +--R , +--R +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 15b x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 821 + +--S 822 of 1293 +m0:=a0.1-r0 +--R +--R +--R (822) +--R +-----------+ +--R 2 2 2 2 2 |- a e + b d +--R ((5A a b - 7B a )e + (- 5A b + 9B a b)d e - 2B b d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R +-+ \| b +--R \|b log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 +--R ((- 10A a b + 14B a )e + (10A b - 18B a b)d e + 4B b d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1293 +d0:=D(m0,x) +--R +--R +--R (823) 0 +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1293 +m0:=a0.2-r0 +--R +--R +--R (824) +--R 2 2 2 2 2 +-----------+ +--R ((- 5A a b + 7B a )e + (5A b - 9B a b)d e + 2B b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 2 2 +-+ |a e - b d +--R ((5A a b - 7B a )e + (- 5A b + 9B a b)d e - 2B b d )\|b |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1293 +d0:=D(m0,x) +--R +--R +--R (825) 0 +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (826) --------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1293 +r0:=1/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x))-_ + (2*b*B*d+3*A*b*e-5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + (2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3 +--R +--R +--R (827) +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (828) +--R [ +--R 2 2 2 +--R (((9A b - 15B a b)e + 6B b d)x + (9A a b - 15B a )e + 6B a b d) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 2 2 2 2 +--R 4B b e x + ((12A b - 20B a b)e + 16B b d)x + (18A a b - 30B a )e +--R + +--R 2 +--R (- 6A b + 22B a b)d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 828 + +--S 829 of 1293 +m0:=a0.1-r0 +--R +--R +--R (829) +--R +-----------+ +--R |- a e + b d +-+ +--R ((3A b - 5B a)e + 2B b d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R ((6A b - 10B a)e + 4B b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1293 +d0:=D(m0,x) +--R +--R +--R (830) 0 +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1293 +m0:=a0.2-r0 +--R +--R +--R (831) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R ((3A b - 5B a)e + 2B b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R ((- 3A b + 5B a)e - 2B b d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1293 +d0:=D(m0,x) +--R +--R +--R (832) 0 +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (833) ------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1293 +r0:=-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-_ + (2*b*B*d+A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))+(2*b*B*d+A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)) +--R +--R +--R (834) +--R 2 2 2 +--R (((- A b + 3B a b)e - 2B b d)x + (- A a b + 3B a )e - 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x - A b + 3B a)\|- a e + b d \|b \|e x + d +--R / +--R 3 2 +-----------+ +-+ +--R (b x + a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (835) +--R [ +--R 2 2 2 +--R (((A b - 3B a b)e + 2B b d)x + (A a b - 3B a )e + 2B a b d) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (4B b x - 2A b + 6B a)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 3 2 | 2 +--R (2b x + 2a b )\|- a b e + b d +--R , +--R +--R 2 2 2 +--R (((A b - 3B a b)e + 2B b d)x + (A a b - 3B a )e + 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (2B b x - A b + 3B a)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 3 2 | 2 +--R (b x + a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 835 + +--S 836 of 1293 +m0:=a0.1-r0 +--R +--R +--R (836) +--R +-----------+ +-+ +--R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((2A b - 6B a)e + 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R 2b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1293 +d0:=D(m0,x) +--R +--R +--R (837) 0 +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1293 +m0:=a0.2-r0 +--R +--R +--R (838) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((A b - 3B a)e + 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1293 +d0:=D(m0,x) +--R +--R +--R (839) 0 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1293 +t0:=(A+B*x)/((a+b*x)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (840) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1293 +r0:=-(2*b*B*d-A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*(b*d-a*e)^(3/2))-(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (841) +--R 2 2 2 +--R (((- A b - B a b)e + 2B b d)x + (- A a b - B a )e + 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (A b - B a)\|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 2 +-----------+ +-+ +--R ((a b e - b d)x + a b e - a b d)\|- a e + b d \|b +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (842) +--R [ +--R 2 2 2 +--R (((A b + B a b)e - 2B b d)x + (A a b + B a )e - 2B a b d) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (2A b - 2B a)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 2 3 2 2 | 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|- a b e + b d +--R , +--R +--R 2 2 2 +--R (((A b + B a b)e - 2B b d)x + (A a b + B a )e - 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (A b - B a)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 2 3 2 2 | 2 +--R ((a b e - b d)x + a b e - a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 842 + +--S 843 of 1293 +m0:=a0.1-r0 +--R +--R +--R (843) +--R +-----------+ +-+ +--R ((A b + B a)e - 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((2A b + 2B a)e - 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R (2a b e - 2b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1293 +d0:=D(m0,x) +--R +--R +--R (844) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1293 +m0:=a0.2-r0 +--R +--R +--R (845) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((A b + B a)e - 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b + B a)e - 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R (a b e - b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1293 +d0:=D(m0,x) +--R +--R +--R (846) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^(3/2)) +--R +--R +--R B x + A +--R (847) ------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1293 +r0:=-(2*b*B*d-3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(5/2)*sqrt(b))+(2*b*B*d-3*A*b*e+a*B*e)/_ + (b*(b*d-a*e)^2*sqrt(d+e*x))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (848) +--R 2 2 2 +-------+ +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d)\|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|- a e + b d \|b +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (849) +--R [ +--R 2 2 2 +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d) +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R (((- 6A b + 2B a)e + 4B b d)x - 4A a e + (- 2A b + 6B a)d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 2 2 2 +--R (((- 3A b + B a b)e + 2B b d)x + (- 3A a b + B a )e + 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|a b e - b d +--R / +--R +-----------+ +--R 2 2 2 3 2 3 2 2 2 2 | 2 +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|a b e - b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 849 + +--S 850 of 1293 +m0:=a0.1-r0 +--R +--R +--R (850) +--R +-----------+ +-+ +--R ((3A b - B a)e - 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((- 6A b + 2B a)e + 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-----------+ +-+ +--R (2a e - 4a b d e + 2b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1293 +d0:=D(m0,x) +--R +--R +--R (851) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1293 +m0:=a0.2-r0 +--R +--R +--R (852) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((- 3A b + B a)e + 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((- 3A b + B a)e + 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 2 +-----------+ +-+ | 2 +--R (a e - 2a b d e + b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1293 +d0:=D(m0,x) +--R +--R +--R (853) 0 +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^(5/2)) +--R +--R +--R (854) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1293 +r0:=1/3*(2*b*B*d-5*A*b*e+3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+_ + (-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2))-_ + (2*b*B*d-5*A*b*e+3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/(b*d-a*e)^(7/2)+(2*b*B*d-5*A*b*e+3*a*B*e)/_ + ((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (855) +--R 2 2 2 2 +--R ((- 15A b + 9B a b)e + 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 15A a b + 9B a )e + (- 15A b + 15B a b)d e + 6B b d )x +--R + +--R 2 2 +--R (- 15A a b + 9B a )d e + 6B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (856) +--R [ +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((15A a b - 9B a )e + (15A b - 15B a b)d e - 6B b d )x +--R + +--R 2 2 +--R (15A a b - 9B a )d e - 6B a b d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R ((30A b - 18B a b)e - 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((20A a b - 12B a )e + (40A b - 32B a b)d e - 16B b d )x - 4A a e +--R + +--R 2 2 2 +--R (28A a b - 8B a )d e + (6A b - 22B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b e - 18a b d e + 18a b d e - 6b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (6a e - 12a b d e + 12a b d e - 6b d )x + 6a d e - 18a b d e +--R + +--R 2 2 3 3 4 +--R 18a b d e - 6a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((15A a b - 9B a )e + (15A b - 15B a b)d e - 6B b d )x +--R + +--R 2 2 +--R (15A a b - 9B a )d e - 6B a b d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 856 + +--S 857 of 1293 +m0:=a0.1-r0 +--R +--R +--R (857) +--R +-----------+ +--R +-----------+ | b +--R ((5A b - 3B a)e - 2B b d)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R ((10A b - 6B a)e - 4B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (2a e - 6a b d e + 6a b d e - 2b d )\|- a e + b d +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1293 +d0:=D(m0,x) +--R +--R +--R (858) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1293 +m0:=a0.2-r0 +--R +--R +--R (859) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R ((5A b - 3B a)e - 2B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R +-----------+ | b +--R ((5A b - 3B a)e - 2B b d)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1293 +d0:=D(m0,x) +--R +--R +--R (860) 0 +--R Type: Expression(Integer) +--E 860 + +--S 861 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^(7/2)) +--R +--R +--R (861) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1293 +r0:=1/5*(2*b*B*d-7*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + (-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2))+_ + 1/3*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2))-_ + b^(3/2)*(2*b*B*d-7*A*b*e+5*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+_ + b*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (862) +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e +--R + +--R 3 2 +--R 70B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (863) +--R [ +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((- 210A b + 150B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 140A a b + 100B a b)e + (- 490A b + 390B a b )d e +--R + +--R 3 2 +--R 140B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (28A a b - 20B a )e + (- 336A a b + 232B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 322A b + 326B a b )d e + 92B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 12A a e + (64A a b - 8B a )d e + (- 232A a b + 96B a b)d e +--R + +--R 3 2 3 +--R (- 30A b + 122B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (30a b e - 120a b d e + 180a b d e - 120a b d e + 30b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 30a e - 60a b d e - 60a b d e + 240a b d e - 210a b d e +--R + +--R 5 5 +--R 60b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 60a d e - 210a b d e + 240a b d e - 60a b d e - 60a b d e +--R + +--R 5 6 +--R 30b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 30a d e - 120a b d e + 180a b d e - 120a b d e + 30a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 105A a b + 75B a b)e + (- 210A b + 180B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 3 2 2 +--R (- 210A a b + 150B a b)d e + (- 105A b + 135B a b )d e +--R + +--R 3 3 +--R 30B b d +--R * +--R x +--R + +--R 2 2 2 2 3 +--R (- 105A a b + 75B a b)d e + 30B a b d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e + 70B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 863 + +--S 864 of 1293 +m0:=a0.1-r0 +--R +--R +--R (864) +--R +-----------+ +--R 2 2 +-----------+ | b +--R ((7A b - 5B a b)e - 2B b d)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R ((- 14A b + 10B a b)e + 4B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (2a e - 8a b d e + 12a b d e - 8a b d e + 2b d )\|- a e + b d +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1293 +d0:=D(m0,x) +--R +--R +--R (865) 0 +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1293 +m0:=a0.2-r0 +--R +--R +--R (866) +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R ((- 7A b + 5B a b)e + 2B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 +-----------+ | b +--R ((- 7A b + 5B a b)e + 2B b d)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (a e - 4a b d e + 6a b d e - 4a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1293 +d0:=D(m0,x) +--R +--R +--R (867) 0 +--R Type: Expression(Integer) +--E 867 + +--S 868 of 1293 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^3 +--R +--R +--R (868) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1293 +r0:=7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ + 7/20*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e))-_ + 1/4*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x))-_ + 1/2*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 7/4*e*(b*d-a*e)^(3/2)*(4*b*B*d+5*A*b*e-9*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+_ + 7/4*e*(b*d-a*e)*(4*b*B*d+5*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (869) +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 7 2 6 2 5 +-+ +--R (60b x + 120a b x + 60a b )\|b +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (870) +--R [ +--R 3 2 2 3 4 3 2 +--R (- 525A a b + 945B a b )e + (525A b - 1365B a b )d e +--R + +--R 4 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1050A a b + 1890B a b)e + (1050A a b - 2730B a b )d e +--R + +--R 3 2 +--R 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 525A a b + 945B a )e + (525A a b - 1365B a b)d e + 420B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 48B b e x + ((80A b - 144B a b )e + 256B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 560A a b + 1008B a b )e + (800A b - 1888B a b )d e +--R + +--R 4 2 +--R 928B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1750A a b + 3150B a b)e + (2380A a b - 5684B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 390A b + 2606B a b )d e - 120B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 1050A a b + 1890B a )e + (1400A a b - 3360B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 210A a b + 1498B a b )d e + (- 60A b - 60B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 120b x + 240a b x + 120a b +--R , +--R +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 60b x + 120a b x + 60a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 870 + +--S 871 of 1293 +m0:=a0.1-r0 +--R +--R +--R (871) +--R 2 3 2 2 2 2 +--R ((- 35A a b + 63B a )e + (35A b - 91B a b)d e + 28B b d e) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 2 2 2 2 +--R ((- 70A a b + 126B a )e + (70A b - 182B a b)d e + 56B b d e) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1293 +d0:=D(m0,x) +--R +--R +--R (872) 0 +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1293 +m0:=a0.2-r0 +--R +--R +--R (873) +--R 2 3 2 2 2 2 +--R ((- 35A a b + 63B a )e + (35A b - 91B a b)d e + 28B b d e) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 2 2 2 +-+ +--R ((35A a b - 63B a )e + (- 35A b + 91B a b)d e - 28B b d e)\|b +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1293 +d0:=D(m0,x) +--R +--R +--R (874) 0 +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (875) ---------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1293 +r0:=5/12*e*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e))-_ + 1/4*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x))-_ + 1/2*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(9/2)+5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + sqrt(d+e*x)/b^4 +--R +--R +--R (876) +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 2 5 2 4 +-+ +--R (12b x + 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (877) +--R [ +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x +--R + +--R 2 3 2 2 +--R (- 45A a b + 105B a )e - 60B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 16B b e x + ((48A b - 112B a b )e + 112B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((150A a b - 350B a b)e + (- 54A b + 326B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (90A a b - 210B a )e + (- 30A a b + 190B a b)d e +--R + +--R 3 2 2 +--R (- 12A b - 12B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 24b x + 48a b x + 24a b +--R , +--R +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x +--R + +--R 2 3 2 2 +--R (- 45A a b + 105B a )e - 60B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 12b x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 877 + +--S 878 of 1293 +m0:=a0.1-r0 +--R +--R +--R (878) +--R +-----------+ +--R 2 |- a e + b d +-+ +--R ((- 15A b + 35B a)e - 20B b d e) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-----------+ \|b \|e x + d +--R ((30A b - 70B a)e + 40B b d e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1293 +d0:=D(m0,x) +--R +--R +--R (879) 0 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1293 +m0:=a0.2-r0 +--R +--R +--R (880) +--R +-+ +-------+ +--R 2 +-----------+ \|b \|e x + d +--R ((15A b - 35B a)e + 20B b d e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-+ |a e - b d \|e x + d +--R ((- 15A b + 35B a)e - 20B b d e)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1293 +d0:=D(m0,x) +--R +--R +--R (881) 0 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (882) --------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1293 +r0:=-1/4*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x))-_ + 1/2*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e))+3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*_ + sqrt(d+e*x)/(b^3*(b*d-a*e)) +--R +--R +--R (883) +--R 3 2 2 3 2 +--R ((- 3A b + 15B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b + 30B a b)e - 24B a b d e)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 5 2 4 2 3 +-----------+ +-+ +--R (4b x + 8a b x + 4a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (884) +--R [ +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R 16B b e x + ((- 10A b + 50B a b)e - 8B b d)x +--R + +--R 2 2 +--R (- 6A a b + 30B a )e + (- 4A b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 5 2 4 2 3 | 2 +--R (8b x + 16a b x + 8a b )\|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 2 3 | 2 +--R (4b x + 8a b x + 4a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 884 + +--S 885 of 1293 +m0:=a0.1-r0 +--R +--R +--R (885) +--R 2 +-----------+ +-+ +--R ((3A b - 15B a)e + 12B b d e)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((6A b - 30B a)e + 24B b d e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 | 2 +-----------+ +-+ +--R 8b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1293 +d0:=D(m0,x) +--R +--R +--R (886) 0 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1293 +m0:=a0.2-r0 +--R +--R +--R (887) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((3A b - 15B a)e + 12B b d e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 +-----------+ +-+ +--R ((3A b - 15B a)e + 12B b d e)\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 +-----------+ +-+ | 2 +--R 4b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1293 +d0:=D(m0,x) +--R +--R +--R (888) 0 +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (889) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1293 +r0:=-1/2*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 1/4*e*(4*b*B*d-A*b*e-3*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2))-_ + 1/4*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)*(a+b*x)) +--R +--R +--R (890) +--R 3 2 2 3 2 +--R ((- A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 2A a b - 6B a b)e + 8B a b d e)x + (- A a b - 3B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e + (2A b + 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +-----------+ +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|- a e + b d +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (891) +--R [ +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R ((2A b - 10B a b)e + 8B b d)x + (- 2A a b - 6B a )e +--R + +--R 2 +--R (4A b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((8a b e - 8b d)x + (16a b e - 16a b d)x + 8a b e - 8a b d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 +--R ((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e +--R + +--R 2 +--R (2A b + 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 4 5 2 2 3 4 3 2 2 3 | 2 +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 891 + +--S 892 of 1293 +m0:=a0.1-r0 +--R +--R +--R (892) +--R 2 +-----------+ +-+ +--R ((A b + 3B a)e - 4B b d e)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((2A b + 6B a)e - 8B b d e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 3 | 2 +-----------+ +-+ +--R (8a b e - 8b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1293 +d0:=D(m0,x) +--R +--R +--R (893) 0 +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1293 +m0:=a0.2-r0 +--R +--R +--R (894) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((A b + 3B a)e - 4B b d e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b + 3B a)e - 4B b d e)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 3 +-----------+ +-+ | 2 +--R (4a b e - 4b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1293 +d0:=D(m0,x) +--R +--R +--R (895) 0 +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1293 +t0:=(A+B*x)/((a+b*x)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (896) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1293 +r0:=1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2))-_ + 1/2*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 1/4*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (897) +--R 3 2 2 3 2 +--R ((- 3A b - B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b - 2B a b)e + 8B a b d e)x + (- 3A a b - B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((3A b + B a b)e - 4B b d)x + (5A a b - B a )e + (- 2A b - 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 4a b e - 8a b d e + 4a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (898) +--R [ +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R ((6A b + 2B a b)e - 8B b d)x + (10A a b - 2B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 8a b e - 16a b d e + 8a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 +--R ((3A b + B a b)e - 4B b d)x + (5A a b - B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 4a b e - 8a b d e + 4a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 898 + +--S 899 of 1293 +m0:=a0.1-r0 +--R +--R +--R (899) +--R 2 +-----------+ +-+ +--R ((3A b + B a)e - 4B b d e)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((6A b + 2B a)e - 8B b d e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 3 2 | 2 +-----------+ +-+ +--R (8a b e - 16a b d e + 8b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1293 +d0:=D(m0,x) +--R +--R +--R (900) 0 +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1293 +m0:=a0.2-r0 +--R +--R +--R (901) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((3A b + B a)e - 4B b d e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R ((3A b + B a)e - 4B b d e)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 3 2 +-----------+ +-+ | 2 +--R (4a b e - 8a b d e + 4b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1293 +d0:=D(m0,x) +--R +--R +--R (902) 0 +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^(3/2)) +--R +--R +--R (903) +--R B x + A +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1293 +r0:=3/4*e*(4*b*B*d-5*A*b*e+a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(b))-_ + 3/4*e*(4*b*B*d-5*A*b*e+a*B*e)/(b*(b*d-a*e)^3*sqrt(d+e*x))+_ + 1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*sqrt(d+e*x))+_ + 1/4*(-4*b*B*d+5*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (904) +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x - 8A a e +--R + +--R 2 2 2 +--R (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (905) +--R [ +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R ((- 30A b + 6B a b)e + 24B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 50A a b + 10B a )e + (- 10A b + 42B a b)d e + 8B b d )x +--R + +--R 2 2 2 2 2 +--R - 16A a e + (- 18A a b + 26B a )d e + (4A b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (16a b e - 48a b d e + 48a b d e - 16a b d )x + 8a e - 24a b d e +--R + +--R 3 2 2 2 3 3 +--R 24a b d e - 8a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 3 2 2 3 2 +--R ((- 15A b + 3B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 30A a b + 6B a b)e + 24B a b d e)x + (- 15A a b + 3B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x +--R + +--R 2 2 2 2 2 +--R - 8A a e + (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 905 + +--S 906 of 1293 +m0:=a0.1-r0 +--R +--R +--R (906) +--R 2 +-----------+ +-+ +--R ((15A b - 3B a)e - 12B b d e)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((- 30A b + 6B a)e + 24B b d e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 3 2 2 2 2 3 3 | 2 +-----------+ +-+ +--R (8a e - 24a b d e + 24a b d e - 8b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1293 +d0:=D(m0,x) +--R +--R +--R (907) 0 +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1293 +m0:=a0.2-r0 +--R +--R +--R (908) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((- 15A b + 3B a)e + 12B b d e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 +-----------+ +-+ +--R ((- 15A b + 3B a)e + 12B b d e)\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 3 2 2 2 2 3 3 +-----------+ +-+ | 2 +--R (4a e - 12a b d e + 12a b d e - 4b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1293 +d0:=D(m0,x) +--R +--R +--R (909) 0 +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^(5/2)) +--R +--R +--R (910) +--R B x + A +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1293 +r0:=-5/12*e*(4*b*B*d-7*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(d+e*x)^(3/2))+_ + 1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*(d+e*x)^(3/2))+_ + 1/4*(-4*b*B*d+7*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2))+_ + 5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(9/2)-_ + 5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (911) +--R 3 2 3 3 2 3 +--R ((- 105A b + 45B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 210A a b + 90B a b)e + (- 105A b + 165B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 105A a b + 45B a )e + (- 210A a b + 150B a b)d e +--R + +--R 2 2 +--R 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (- 105A a b + 45B a )d e + 60B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e + 24a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (912) +--R [ +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (105A a b - 45B a )e + (210A a b - 150B a b)d e +--R + +--R 2 2 +--R - 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((210A b - 90B a b )e - 120B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((350A a b - 150B a b)e + (280A b - 320B a b )d e - 160B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (112A a b - 48B a )e + (476A a b - 268B a b)d e +--R + +--R 3 2 2 3 3 +--R (42A b - 290B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 16A a e + (160A a b - 32B a )d e + (78A a b - 166B a b)d e +--R + +--R 3 2 3 +--R (- 12A b - 12B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b e - 168a b d e + 192a b d e - 48a b d e - 48a b d e +--R + +--R 6 5 +--R 24b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a e - 48a b d e - 48a b d e + 192a b d e - 168a b d e +--R + +--R 5 5 +--R 48a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a d e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (105A a b - 45B a )e + (210A a b - 150B a b)d e +--R + +--R 2 2 +--R - 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e +--R + +--R 5 5 +--R 24a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 912 + +--S 913 of 1293 +m0:=a0.1-r0 +--R +--R +--R (913) +--R +-----------+ +--R 2 +-----------+ | b +--R ((35A b - 15B a)e - 20B b d e)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R ((70A b - 30B a)e - 40B b d e)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (8a e - 32a b d e + 48a b d e - 32a b d e + 8b d )\|- a e + b d +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1293 +d0:=D(m0,x) +--R +--R +--R (914) 0 +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1293 +m0:=a0.2-r0 +--R +--R +--R (915) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R ((35A b - 15B a)e - 20B b d e)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 +-----------+ | b +--R ((35A b - 15B a)e - 20B b d e)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (4a e - 16a b d e + 24a b d e - 16a b d e + 4b d )\|- a e + b d +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1293 +d0:=D(m0,x) +--R +--R +--R (916) 0 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^(7/2)) +--R +--R +--R (917) +--R B x + A +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1293 +r0:=-7/20*e*(4*b*B*d-9*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(d+e*x)^(5/2))+_ + 1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*(d+e*x)^(5/2))+_ + 1/4*(-4*b*B*d+9*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2))-_ + 7/12*e*(4*b*B*d-9*A*b*e+5*a*B*e)/((b*d-a*e)^4*(d+e*x)^(3/2))+_ + 7/4*b^(3/2)*e*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(11/2)-_ + 7/4*b*e*(4*b*B*d-9*A*b*e+5*a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (918) +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 2 +--R - 60b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 120a b e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 7 6 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a e - 60a b d e - 540a b d e + 1500a b d e - 1500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 540a b d e + 60a b d e - 60b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 120a d e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 6 7 +--R - 120a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 5 7 +--R - 60a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (919) +--R [ +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 1050B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3150A a b + 1750B a b )e + (- 4410A b + 3850B a b )d e +--R + +--R 4 2 2 +--R 1960B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 1008A a b + 560B a b)e + (- 7434A a b + 4578B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 2898A b + 4914B a b )d e + 1288B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 80B a )e + (- 2448A a b + 1296B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 4986A a b + 3858B a b )d e + (- 270A b + 2366B a b )d e +--R + +--R 4 4 +--R 120B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 48A a e + (336A a b - 32B a )d e + (- 1728A a b + 544B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 510A a b + 1318B a b )d e + (60A b + 60B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 120a b e - 600a b d e + 1200a b d e - 1200a b d e +--R + +--R 6 4 3 7 5 2 +--R 600a b d e - 120b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 +--R 240a b e - 960a b d e + 1200a b d e - 1200a b d e +--R + +--R 6 5 2 7 6 +--R 960a b d e - 240b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 120a e - 120a b d e - 1080a b d e + 3000a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 3000a b d e + 1080a b d e + 120a b d e - 120b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 +--R 240a d e - 960a b d e + 1200a b d e - 1200a b d e +--R + +--R 2 5 6 6 7 +--R 960a b d e - 240a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 120a d e - 600a b d e + 1200a b d e - 1200a b d e + 600a b d e +--R + +--R 2 5 7 +--R - 120a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1890A a b + 1050B a b )e + (- 1890A b + 1890B a b )d e +--R + +--R 4 2 2 +--R 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 525B a b)e + (- 3780A a b + 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 945A b + 2205B a b )d e + 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 +--R (- 1890A a b + 1050B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 1890A a b + 1890B a b )d e + 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 945A a b + 525B a b)d e + 420B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 2 +--R - 60b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 120a b e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 7 6 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a e - 60a b d e - 540a b d e + 1500a b d e - 1500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 540a b d e + 60a b d e - 60b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 120a d e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 6 7 +--R - 120a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 5 7 +--R - 60a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 919 + +--S 920 of 1293 +m0:=a0.1-r0 +--R +--R +--R (920) +--R +-----------+ +--R 2 2 2 +-----------+ | b +--R ((63A b - 35B a b)e - 28B b d e)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 +-+ \|b \|e x + d +--R ((- 126A b + 70B a b)e + 56B b d e)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (8a e - 40a b d e + 80a b d e - 80a b d e + 40a b d e - 8b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1293 +d0:=D(m0,x) +--R +--R +--R (921) 0 +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1293 +m0:=a0.2-r0 +--R +--R +--R (922) +--R +-+ +-------+ +--R 2 2 2 +-+ \|b \|e x + d +--R ((- 63A b + 35B a b)e + 28B b d e)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 +-----------+ | b +--R ((- 63A b + 35B a b)e + 28B b d e)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (4a e - 20a b d e + 40a b d e - 40a b d e + 20a b d e - 4b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1293 +d0:=D(m0,x) +--R +--R +--R (923) 0 +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)*sqrt(a+b*x) +--R +--R +--R (924) +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1293 +r0:=-1/48*(b*d-a*e)*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*_ + (d+e*x)^(3/2)/(b^3*e)-1/40*(3*b*B*d-10*A*b*e+7*a*B*e)*_ + (a+b*x)^(3/2)*(d+e*x)^(5/2)/(b^2*e)+1/5*B*(a+b*x)^(3/2)*_ + (d+e*x)^(7/2)/(b*e)+1/128*(b*d-a*e)^4*(3*b*B*d-10*A*b*e+7*a*B*e)*_ + atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(5/2))-_ + 1/64*(b*d-a*e)^2*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*_ + sqrt(d+e*x)/(b^4*e)-1/128*(b*d-a*e)^3*(3*b*B*d-10*A*b*e+7*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e^2) +--R +--R +--R (925) +--R 4 5 5 3 2 4 4 +--R (- 150A a b + 105B a )e + (600A a b - 375B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 900A a b + 450B a b )d e + (600A a b - 150B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 150A b - 75B a b )d e + 45B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 384B b e x + ((480A b + 48B a b )e + 1008B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (80A a b - 56B a b )e + (1360A b + 176B a b )d e +--R + +--R 4 2 2 +--R 744B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 100A a b + 70B a b)e + (360A a b - 222B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (1180A b + 218B a b )d e + 30B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (150A a b - 105B a )e + (- 550A a b + 340B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (730A a b - 346B a b )d e + (150A b + 60B a b )d e - 45B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 2 +-+ +-+ +--R 1920b e \|b \|e +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1293 +--a0:=integrate(t0,x) +--E 926 + +--S 927 of 1293 +--m0:=a0-r0 +--E 927 + +--S 928 of 1293 +--d0:=D(m0,x) +--E 928 + +--S 929 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)*sqrt(a+b*x) +--R +--R +--R 2 +-------+ +-------+ +--R (926) (B e x + (A e + B d)x + A d)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1293 +r0:=-1/24*(3*b*B*d-8*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2)/(b^2*e)+_ + 1/4*B*(a+b*x)^(3/2)*(d+e*x)^(5/2)/(b*e)+1/64*(b*d-a*e)^3*_ + (3*b*B*d-8*A*b*e+5*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*e^(5/2))-1/32*(b*d-a*e)*_ + (3*b*B*d-8*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e)-_ + 1/64*(b*d-a*e)^2*(3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(b^3*e^2) +--R +--R +--R (927) +--R 3 4 4 2 2 3 3 +--R (24A a b - 15B a )e + (- 72A a b + 36B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (72A a b - 18B a b )d e + (- 24A b - 12B a b )d e + 9B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B b e x + ((64A b + 8B a b )e + 72B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((16A a b - 10B a b)e + (112A b + 20B a b )d e + 6B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (- 24A a b + 15B a )e + (64A a b - 31B a b)d e +--R + +--R 3 2 2 3 3 +--R (24A b + 9B a b )d e - 9B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 2 +-+ +-+ +--R 192b e \|b \|e +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1293 +--a0:=integrate(t0,x) +--E 931 + +--S 932 of 1293 +--m0:=a0-r0 +--E 932 + +--S 933 of 1293 +--d0:=D(m0,x) +--E 933 + +--S 934 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)*sqrt(d+e*x) +--R +--R +--R +-------+ +-------+ +--R (928) (B x + A)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1293 +r0:=1/3*B*(a+b*x)^(3/2)*(d+e*x)^(3/2)/(b*e)-1/8*(b*d-a*e)^2*_ + (2*A*b*e-B*(b*d+a*e))*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(5/2))+1/4*(2*A*b*e-B*(b*d+a*e))*_ + (a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e)+1/8*(b*d-a*e)*_ + (2*A*b*e-B*(b*d+a*e))*sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^2) +--R +--R +--R (929) +--R 2 3 3 2 2 2 +--R (- 6A a b + 3B a )e + (12A a b - 3B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 6A b - 3B a b )d e + 3B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 2 2 2 +--R 8B b e x + ((12A b + 2B a b)e + 2B b d e)x + (6A a b - 3B a )e +--R + +--R 2 2 2 +--R (6A b + 2B a b)d e - 3B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 2 2 +-+ +-+ +--R 24b e \|b \|e +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1293 +--a0:=integrate(t0,x) +--E 936 + +--S 937 of 1293 +--m0:=a0-r0 +--E 937 + +--S 938 of 1293 +--d0:=D(m0,x) +--E 938 + +--S 939 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/sqrt(d+e*x) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (930) ------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1293 +r0:=1/4*(b*d-a*e)*(3*b*B*d-4*A*b*e+a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(5/2))+1/2*B*(a+b*x)^(3/2)*_ + sqrt(d+e*x)/(b*e)-1/4*(3*b*B*d-4*A*b*e+a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b*e^2) +--R +--R +--R (931) +--R 2 2 2 2 2 +--R ((4A a b - B a )e + (- 4A b - 2B a b)d e + 3B b d ) +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2B b e x + (4A b + B a)e - 3B b d)\|b \|e \|b x + a \|e x + d +--R / +--R 2 +-+ +-+ +--R 4b e \|b \|e +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1293 +--a0:=integrate(t0,x) +--E 941 + +--S 942 of 1293 +--m0:=a0-r0 +--E 942 + +--S 943 of 1293 +--d0:=D(m0,x) +--E 943 + +--S 944 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (932) ------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1293 +r0:=-(3*b*B*d-2*A*b*e-a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(e^(5/2)*sqrt(b))-2*(B*d-A*e)*_ + (a+b*x)^(3/2)/(e*(b*d-a*e)*sqrt(d+e*x))+(3*b*B*d-2*A*b*e-a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(e^2*(b*d-a*e)) +--R +--R +--R (933) +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R ((2A b + B a)e - 3B b d)\|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +--R (B e x - 2A e + 3B d)\|b \|e \|b x + a +--R / +--R 2 +-+ +-+ +-------+ +--R e \|b \|e \|e x + d +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1293 +--a0:=integrate(t0,x) +--E 946 + +--S 947 of 1293 +--m0:=a0-r0 +--E 947 + +--S 948 of 1293 +--d0:=D(m0,x) +--E 948 + +--S 949 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (934) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1293 +r0:=-2/3*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ + 2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(5/2)-_ + 2*B*sqrt(a+b*x)/(e^2*sqrt(d+e*x)) +--R +--R +--R (935) +--R 2 2 +-+ +-------+ +--R ((6B a e - 6B b d e)x + 6B a d e - 6B b d )\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 +-+ +--R (((- 2A b - 6B a)e + 8B b d e)x - 2A a e - 4B a d e + 6B b d )\|e +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 3 3 2 2 +-+ +-------+ +--R ((3a e - 3b d e )x + 3a d e - 3b d e )\|e \|e x + d +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1293 +--a0:=integrate(t0,x) +--E 951 + +--S 952 of 1293 +--m0:=a0-r0 +--E 952 + +--S 953 of 1293 +--d0:=D(m0,x) +--E 953 + +--S 954 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(7/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (936) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1293 +r0:=-2/5*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))+_ + 2/15*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^(3/2)) +--R +--R +--R (937) +--R 2 2 2 +--R ((4A b - 10B a b)e + 6B b d)x +--R + +--R 2 2 2 +--R ((- 2A a b - 10B a )e + (10A b + 2B a b)d)x - 6A a e +--R + +--R 2 +--R (10A a b - 4B a )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +--R (15a e - 30a b d e + 15b d e )x + (30a d e - 60a b d e + 30b d e)x +--R + +--R 2 2 2 3 2 4 +--R 15a d e - 30a b d e + 15b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (938) +--R 2 3 2 4 2 +--R ((8A b - 20B a b)d e + 12B b d )x +--R + +--R 2 3 2 4 2 3 +--R ((- 4A a b - 20B a )d e + (20A b + 4B a b)d )x - 12A a d e +--R + +--R 2 4 +--R (20A a b - 8B a )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 3 4 2 2 2 3 3 3 +--R ((3A a d + 12A a )e + ((- 5A a b + 2B a )d + (- 20A a b + 8B a )d)e )x +--R + +--R 2 2 3 3 +--R (9A a d + 36A a d)e +--R + +--R 2 3 2 3 2 2 +--R ((- 15A a b + 6B a )d + (- 60A a b + 24B a )d )e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 +--R (9A a d + 36A a d )e +--R + +--R 2 4 2 3 3 +--R ((- 15A a b + 6B a )d + (- 60A a b + 24B a )d )e +--R * +--R x +--R + +--R 2 4 3 3 2 5 2 3 4 +--R (3A a d + 12A a d )e + (- 5A a b + 2B a )d + (- 20A a b + 8B a )d +--R / +--R 2 3 5 4 4 2 5 3 3 +--R (30a d e - 60a b d e + 30b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 +--R (90a d e - 180a b d e + 90b d e )x +--R + +--R 2 5 3 6 2 2 7 2 6 2 7 2 8 +--R (90a d e - 180a b d e + 90b d e)x + 30a d e - 60a b d e + 30b d +--R Type: Union(Expression(Integer),...) +--E 956 + +--S 957 of 1293 +m0:=a0-r0 +--R +--R +--R 2 3 2 2 2 3 +--R (3A a d + 12A a )e + (- 5A a b + 2B a )d + (- 20A a b + 8B a )d +--R (939) ---------------------------------------------------------------- +--R 2 3 2 4 2 5 +--R 30a d e - 60a b d e + 30b d +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1293 +d0:=D(m0,x) +--R +--R +--R (940) 0 +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(9/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (941) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1293 +r0:=-2/7*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ + 2/35*(3*b*B*d+4*A*b*e-7*a*B*e)*(a+b*x)^(3/2)/_ + (e*(b*d-a*e)^2*(d+e*x)^(5/2))+4/105*b*(3*b*B*d+4*A*b*e-7*a*B*e)*_ + (a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(3/2)) +--R +--R +--R (942) +--R 3 2 2 3 3 +--R ((- 16A b + 28B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 2 +--R ((8A a b - 14B a b)e + (- 56A b + 104B a b )d e - 42B b d )x +--R + +--R 2 3 2 2 2 +--R (- 6A a b - 42B a )e + (28A a b + 104B a b)d e +--R + +--R 3 2 2 +--R (- 70A b - 14B a b )d +--R * +--R x +--R + +--R 3 2 2 3 2 2 2 +--R - 30A a e + (84A a b - 12B a )d e + (- 70A a b + 28B a b)d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (105a e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (315a d e - 945a b d e + 945a b d e - 315b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (315a d e - 945a b d e + 945a b d e - 315b d e)x + 105a d e +--R + +--R 2 4 2 2 5 3 6 +--R - 315a b d e + 315a b d e - 105b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (943) +--R 3 2 4 2 3 5 3 +--R ((- 64A b + 112B a b )d e - 48B b d e)x +--R + +--R 2 2 4 2 3 2 5 3 6 2 +--R ((32A a b - 56B a b)d e + (- 224A b + 416B a b )d e - 168B b d )x +--R + +--R 2 3 4 2 2 2 5 +--R (- 24A a b - 168B a )d e + (112A a b + 416B a b)d e +--R + +--R 3 2 6 +--R (- 280A b - 56B a b )d +--R * +--R x +--R + +--R 3 4 2 2 3 5 2 2 6 +--R - 120A a d e + (336A a b - 48B a )d e + (- 280A a b + 112B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 4 6 +--R (15A a d + 240A a )e +--R + +--R 2 3 2 3 4 5 +--R ((- 42A a b + 6B a )d + (- 672A a b + 96B a )d)e +--R + +--R 2 2 3 2 2 3 2 4 +--R ((35A a b - 14B a b)d + (560A a b - 224B a b)d )e +--R * +--R 4 +--R x +--R + +--R 3 2 4 5 +--R (60A a d + 960A a d)e +--R + +--R 2 3 3 3 4 2 4 +--R ((- 168A a b + 24B a )d + (- 2688A a b + 384B a )d )e +--R + +--R 2 2 4 2 2 3 3 3 +--R ((140A a b - 56B a b)d + (2240A a b - 896B a b)d )e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 +--R (90A a d + 1440A a d )e +--R + +--R 2 3 4 3 4 3 3 +--R ((- 252A a b + 36B a )d + (- 4032A a b + 576B a )d )e +--R + +--R 2 2 5 2 2 3 4 2 +--R ((210A a b - 84B a b)d + (3360A a b - 1344B a b)d )e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 3 +--R (60A a d + 960A a d )e +--R + +--R 2 3 5 3 4 4 2 +--R ((- 168A a b + 24B a )d + (- 2688A a b + 384B a )d )e +--R + +--R 2 2 6 2 2 3 5 +--R ((140A a b - 56B a b)d + (2240A a b - 896B a b)d )e 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- 210210B a b )d +--R + +--R 2 5 3 4 9 +--R (4729725A a b - 1891890B a b )d +--R * +--R 3 +--R e +--R * +--R 3 +--R x +--R + +--R 6 6 7 5 7 +--R (- 72765A a d - 654885A a d )e +--R + +--R 5 6 7 6 7 6 6 +--R ((429975A a b - 13230B a )d + (3869775A a b - 119070B a )d )e +--R + +--R 4 2 5 8 +--R (- 1051050A a b + 76440B a b)d +--R + +--R 5 2 6 7 +--R (- 9459450A a b + 687960B a b)d +--R * +--R 5 +--R e +--R + +--R 3 3 4 2 9 +--R (1351350A a b - 180180B a b )d +--R + +--R 4 3 5 2 8 +--R (12162150A a b - 1621620B a b )d +--R * +--R 4 +--R e +--R + +--R 2 4 3 3 10 +--R (- 945945A a b + 216216B a b )d +--R + +--R 3 4 4 3 9 +--R (- 8513505A a b + 1945944B a b )d +--R * +--R 3 +--R e +--R + +--R 5 2 4 11 +--R (315315A a b - 126126B a b )d +--R + +--R 2 5 3 4 10 +--R (2837835A a b - 1135134B a b )d +--R * +--R 2 +--R e +--R * +--R 2 +--R x +--R + +--R 6 7 7 6 6 +--R (- 24255A a d - 218295A a d )e +--R + +--R 5 6 8 6 7 7 5 +--R ((143325A a b - 4410B a )d + (1289925A a b - 39690B a )d )e +--R + +--R 4 2 5 9 +--R (- 350350A a b + 25480B a b)d +--R + +--R 5 2 6 8 +--R (- 3153150A a b + 229320B a b)d +--R * +--R 4 +--R e +--R + +--R 3 3 4 2 10 +--R (450450A a b - 60060B a b )d +--R + +--R 4 3 5 2 9 +--R (4054050A a b - 540540B a b )d +--R * +--R 3 +--R e +--R + +--R 2 4 3 3 11 +--R (- 315315A a b + 72072B a b )d +--R + +--R 3 4 4 3 10 +--R (- 2837835A a b + 648648B a b )d +--R * +--R 2 +--R e +--R + +--R 5 2 4 12 2 5 3 4 11 +--R ((105105A a b - 42042B a b )d + (945945A a b - 378378B a b )d )e +--R * +--R x +--R + +--R 6 8 7 7 5 +--R (- 3465A a d - 31185A a d )e +--R + +--R 5 6 9 6 7 8 4 +--R ((20475A a b - 630B a )d + (184275A a b - 5670B a )d )e +--R + +--R 4 2 5 10 5 2 6 9 3 +--R ((- 50050A a b + 3640B a b)d + (- 450450A a b + 32760B a b)d )e +--R + +--R 3 3 4 2 11 4 3 5 2 10 2 +--R ((64350A a b - 8580B a b )d + (579150A a b - 77220B a b )d )e +--R + +--R 2 4 3 3 12 3 4 4 3 11 +--R ((- 45045A a b + 10296B a b )d + (- 405405A a b + 92664B a b )d )e +--R + +--R 5 2 4 13 2 5 3 4 12 +--R (15015A a b - 6006B a b )d + (135135A a b - 54054B a b )d +--R / +--R 6 7 13 5 8 12 4 2 9 11 +--R 135135a d e - 810810a b d e + 2027025a b d e +--R + +--R 3 3 10 10 2 4 11 9 5 12 8 +--R - 2702700a b d e + 2027025a b d e - 810810a b d e +--R + +--R 6 13 7 +--R 135135b d e +--R * +--R 7 +--R x +--R + +--R 6 8 12 5 9 11 4 2 10 10 +--R 945945a d e - 5675670a b d e + 14189175a b d e +--R + +--R 3 3 11 9 2 4 12 8 5 13 7 +--R - 18918900a b d e + 14189175a b d e - 5675670a b d e +--R + +--R 6 14 6 +--R 945945b d e +--R * +--R 6 +--R x +--R + +--R 6 9 11 5 10 10 4 2 11 9 +--R 2837835a d e - 17027010a b d e + 42567525a b d e +--R + +--R 3 3 12 8 2 4 13 7 5 14 6 +--R - 56756700a b d e + 42567525a b d e - 17027010a b d e +--R + +--R 6 15 5 +--R 2837835b d e +--R * +--R 5 +--R x +--R + +--R 6 10 10 5 11 9 4 2 12 8 +--R 4729725a d e - 28378350a b d e + 70945875a b d e +--R + +--R 3 3 13 7 2 4 14 6 5 15 5 +--R - 94594500a b d e + 70945875a b d e - 28378350a b d e +--R + +--R 6 16 4 +--R 4729725b d e +--R * +--R 4 +--R x +--R + +--R 6 11 9 5 12 8 4 2 13 7 +--R 4729725a d e - 28378350a b d e + 70945875a b d e +--R + +--R 3 3 14 6 2 4 15 5 5 16 4 +--R - 94594500a b d e + 70945875a b d e - 28378350a b d e +--R + +--R 6 17 3 +--R 4729725b d e +--R * +--R 3 +--R x +--R + +--R 6 12 8 5 13 7 4 2 14 6 +--R 2837835a d e - 17027010a b d e + 42567525a b d e +--R + +--R 3 3 15 5 2 4 16 4 5 17 3 +--R - 56756700a b d e + 42567525a b d e - 17027010a b d e +--R + +--R 6 18 2 +--R 2837835b d e +--R * +--R 2 +--R x +--R + +--R 6 13 7 5 14 6 4 2 15 5 +--R 945945a d e - 5675670a b d e + 14189175a b d e +--R + +--R 3 3 16 4 2 4 17 3 5 18 2 +--R - 18918900a b d e + 14189175a b d e - 5675670a b d e +--R + +--R 6 19 +--R 945945b d e +--R * +--R x +--R + +--R 6 14 6 5 15 5 4 2 16 4 3 3 17 3 +--R 135135a d e - 810810a b d e + 2027025a b d e - 2702700a b d e +--R + +--R 2 4 18 2 5 19 6 20 +--R 2027025a b d e - 810810a b d e + 135135b d +--R Type: Union(Expression(Integer),...) +--E 976 + +--S 977 of 1293 +m0:=a0-r0 +--R +--R +--R (959) +--R 6 7 5 +--R (- 3465A a d - 31185A a )e +--R + +--R 5 6 2 6 7 4 +--R ((20475A a b - 630B a )d + (184275A a b - 5670B a )d)e +--R + +--R 4 2 5 3 5 2 6 2 3 +--R ((- 50050A a b + 3640B a b)d + (- 450450A a b + 32760B a b)d )e +--R + +--R 3 3 4 2 4 4 3 5 2 3 2 +--R ((64350A a b - 8580B a b )d + (579150A a b - 77220B a b )d )e +--R + +--R 2 4 3 3 5 3 4 4 3 4 +--R ((- 45045A a b + 10296B a b )d + (- 405405A a b + 92664B a b )d )e +--R + +--R 5 2 4 6 2 5 3 4 5 +--R (15015A a b - 6006B a b )d + (135135A a b - 54054B a b )d +--R / +--R 6 7 6 5 8 5 4 2 9 4 3 3 10 3 +--R 135135a d e - 810810a b d e + 2027025a b d e - 2702700a b d e +--R + +--R 2 4 11 2 5 12 6 13 +--R 2027025a b d e - 810810a b d e + 135135b d +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1293 +d0:=D(m0,x) +--R +--R +--R (960) 0 +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (961) +--R 2 4 2 3 +--R B b e x + ((A b + B a)e + 2B b d e)x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + B b d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1293 +r0:=-1/96*(b*d-a*e)*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*_ + (d+e*x)^(3/2)/(b^3*e)-1/60*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*_ + (d+e*x)^(5/2)/(b^2*e)+1/6*B*(a+b*x)^(5/2)*(d+e*x)^(7/2)/(b*e)-_ + 1/512*(b*d-a*e)^5*(5*b*B*d-12*A*b*e+7*a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(7/2))-_ + 1/768*(b*d-a*e)^3*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*_ + sqrt(d+e*x)/(b^4*e^2)-1/192*(b*d-a*e)^2*(5*b*B*d-_ + 12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^4*e)+_ + 1/512*(b*d-a*e)^4*(5*b*B*d-12*A*b*e+7*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(b^4*e^3) +--R +--R +--R (962) +--R 5 6 6 4 2 5 5 +--R (- 180A a b + 105B a )e + (900A a b - 450B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 1800A a b + 675B a b )d e + (1800A a b - 300B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 900A a b - 225B a b )d e + (180A b + 270B a b )d e - 75B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 1280B b e x + ((1536A b + 1664B a b )e + 3200B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (2112A a b + 48B a b )e + (4032A b + 4448B a b )d e +--R + +--R 5 2 3 +--R 2160B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (96A a b - 56B a b )e + (6144A a b + 216B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (2976A b + 3384B a b )d e + 40B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 120A a b + 70B a b)e + (552A a b - 272B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (5592A a b + 348B a b )d e + (120A b + 160B a b )d e +--R + +--R 5 4 +--R - 50B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (180A a b - 105B a )e + (- 840A a b + 415B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (1536A a b - 546B a b )d e + (840A a b + 150B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 180A b - 245B a b )d e + 75B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 3 +-+ +-+ +--R 7680b e \|b \|e +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1293 +--a0:=integrate(t0,x) +--E 981 + +--S 982 of 1293 +--m0:=a0-r0 +--E 982 + +--S 983 of 1293 +--d0:=D(m0,x) +--E 983 + +--S 984 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (963) +--R 3 2 +--R (B b e x + ((A b + B a)e + B b d)x + (A a e + (A b + B a)d)x + A a d) +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1293 +r0:=1/8*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b^2*e)+_ + 1/5*B*(a+b*x)^(5/2)*(d+e*x)^(5/2)/(b*e)+3/128*(b*d-a*e)^4*_ + (2*A*b*e-B*(b*d+a*e))*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(d+e*x)))/(b^(7/2)*e^(7/2))+1/64*(b*d-a*e)^2*(2*A*b*e-_ + B*(b*d+a*e))*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e^2)+1/16*(b*d-a*e)*_ + (2*A*b*e-B*(b*d+a*e))*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^3*e)-_ + 3/128*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e^3) +--R +--R +--R (964) +--R 4 5 5 3 2 4 4 +--R (30A a b - 15B a )e + (- 120A a b + 45B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 30B a b )d e + (- 120A a b - 30B a b )d e +--R + +--R 5 4 4 5 5 +--R (30A b + 45B a b )d e - 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 128B b e x + ((160A b + 176B a b )e + 176B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((240A a b + 8B a b )e + (240A b + 272B a b )d e + 8B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (20A a b - 10B a b)e + (440A a b + 26B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (20A b + 26B a b )d e - 10B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 30A a b + 15B a )e + (110A a b - 40B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (110A a b + 18B a b )d e + (- 30A b - 40B a b )d e + 15B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 3 +-+ +-+ +--R 640b e \|b \|e +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1293 +--a0:=integrate(t0,x) +--E 986 + +--S 987 of 1293 +--m0:=a0-r0 +--E 987 + +--S 988 of 1293 +--d0:=D(m0,x) +--E 988 + +--S 989 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)*sqrt(d+e*x) +--R +--R +--R 2 +-------+ +-------+ +--R (965) (B b x + (A b + B a)x + A a)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1293 +r0:=1/4*B*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b*e)-1/64*(b*d-a*e)^3*_ + (5*b*B*d-8*A*b*e+3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(7/2))-1/96*(b*d-a*e)*_ + (5*b*B*d-8*A*b*e+3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e^2)-_ + 1/24*(5*b*B*d-8*A*b*e+3*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^2*e)+_ + 1/64*(b*d-a*e)^2*(5*b*B*d-8*A*b*e+3*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(b^2*e^3) +--R +--R +--R (966) +--R 3 4 4 2 2 3 3 +--R (- 24A a b + 9B a )e + (72A a b - 12B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 72A a b - 18B a b )d e + (24A b + 36B a b )d e - 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B b e x + ((64A b + 72B a b )e + 8B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((112A a b + 6B a b)e + (16A b + 20B a b )d e - 10B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (24A a b - 9B a )e + (64A a b + 9B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 24A b - 31B a b )d e + 15B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 2 3 +-+ +-+ +--R 192b e \|b \|e +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1293 +--a0:=integrate(t0,x) +--E 991 + +--S 992 of 1293 +--m0:=a0-r0 +--E 992 + +--S 993 of 1293 +--d0:=D(m0,x) +--E 993 + +--S 994 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/sqrt(d+e*x) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (967) --------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1293 +r0:=-1/8*(b*d-a*e)^2*(5*b*B*d-6*A*b*e+a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(7/2))-1/12*(5*b*B*d-6*A*b*e+a*B*e)*_ + (a+b*x)^(3/2)*sqrt(d+e*x)/(b*e^2)+1/3*B*(a+b*x)^(5/2)*_ + sqrt(d+e*x)/(b*e)+1/8*(b*d-a*e)*(5*b*B*d-6*A*b*e+a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b*e^3) +--R +--R +--R (968) +--R 2 3 3 2 2 2 +--R (18A a b - 3B a )e + (- 36A a b - 9B a b)d e +--R + +--R 3 2 2 3 3 +--R (18A b + 27B a b )d e - 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 2 2 2 +--R 8B b e x + ((12A b + 14B a b)e - 10B b d e)x + (30A a b + 3B a )e +--R + +--R 2 2 2 +--R (- 18A b - 22B a b)d e + 15B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 +-+ +-+ +--R 24b e \|b \|e +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1293 +--a0:=integrate(t0,x) +--E 996 + +--S 997 of 1293 +--m0:=a0-r0 +--E 997 + +--S 998 of 1293 +--d0:=D(m0,x) +--E 998 + +--S 999 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (969) --------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1293 +r0:=3/4*(b*d-a*e)*(5*b*B*d-4*A*b*e-a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(7/2)*sqrt(b))-_ + 2*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*sqrt(d+e*x))+_ + 1/2*(5*b*B*d-4*A*b*e-a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(e^2*(b*d-a*e))-_ + 3/4*(5*b*B*d-4*A*b*e-a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^3 +--R +--R +--R (970) +--R 2 2 2 2 2 +-------+ +--R ((12A a b + 3B a )e + (- 12A b - 18B a b)d e + 15B b d )\|e x + d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 +--R 2B b e x + ((4A b + 5B a)e - 5B b d e)x - 8A a e +--R + +--R 2 +--R (12A b + 13B a)d e - 15B b d +--R * +--R +-+ +-+ +-------+ +--R \|b \|e \|b x + a +--R / +--R 3 +-+ +-+ +-------+ +--R 4e \|b \|e \|e x + d +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1293 +--a0:=integrate(t0,x) +--E 1001 + +--S 1002 of 1293 +--m0:=a0-r0 +--E 1002 + +--S 1003 of 1293 +--d0:=D(m0,x) +--E 1003 + +--S 1004 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (971) --------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1293 +r0:=-2/3*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))-_ + (5*b*B*d-2*A*b*e-3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(7/2)-2/3*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (a+b*x)^(3/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+b*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(e^3*(b*d-a*e)) +--R +--R +--R (972) +--R 2 2 +-+ +--R (((6A b + 9B a)e - 15B b d e)x + (6A b + 9B a)d e - 15B b d )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 +--R 3B b e x + ((- 8A b - 6B a)e + 20B b d e)x - 2A a e +--R + +--R 2 +--R (- 6A b - 4B a)d e + 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 4 3 +-+ +-------+ +--R (3e x + 3d e )\|e \|e x + d +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1293 +--a0:=integrate(t0,x) +--E 1006 + +--S 1007 of 1293 +--m0:=a0-r0 +--E 1007 + +--S 1008 of 1293 +--d0:=D(m0,x) +--E 1008 + +--S 1009 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (973) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1293 +r0:=-2/5*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-_ + 2/3*B*(a+b*x)^(3/2)/(e^2*(d+e*x)^(3/2))+2*b^(3/2)*_ + B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/e^(7/2)-_ + 2*b*B*sqrt(a+b*x)/(e^3*sqrt(d+e*x)) +--R +--R +--R (974) +--R 3 2 2 2 2 2 2 +--R (30B a b e - 30B b d e )x + (60B a b d e - 60B b d e)x +--R + +--R 2 2 3 +--R 30B a b d e - 30B b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|b \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 3 2 2 2 +--R ((- 6A b - 40B a b)e + 46B b d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 12A a b - 10B a )e - 48B a b d e + 70B b d e)x - 6A a e +--R + +--R 2 2 2 2 3 +--R - 4B a d e - 20B a b d e + 30B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 6 5 2 5 2 4 2 4 3 3 +--R ((15a e - 15b d e )x + (30a d e - 30b d e )x + 15a d e - 15b d e ) +--R * +--R +-+ +-------+ +--R \|e \|e x + d +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1293 +--a0:=integrate(t0,x) +--E 1011 + +--S 1012 of 1293 +--m0:=a0-r0 +--E 1012 + +--S 1013 of 1293 +--d0:=D(m0,x) +--E 1013 + +--S 1014 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(9/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (975) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1293 +r0:=-2/7*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ + 2/35*(5*b*B*d+2*A*b*e-7*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^(5/2)) +--R +--R +--R (976) +--R 3 2 3 3 +--R ((4A b - 14B a b )e + 10B b d)x +--R + +--R 2 2 3 2 2 +--R ((- 2A a b - 28B a b)e + (14A b + 16B a b )d)x +--R + +--R 2 3 2 2 3 +--R ((- 16A a b - 14B a )e + (28A a b + 2B a b)d)x - 10A a e +--R + +--R 2 3 +--R (14A a b - 4B a )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 5 4 2 2 3 3 +--R (35a e - 70a b d e + 35b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (105a d e - 210a b d e + 105b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (105a d e - 210a b d e + 105b d e)x + 35a d e - 70a b d e + 35b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (977) +--R 3 2 4 3 5 3 +--R ((20A b - 70B a b )d e + 50B b d )x +--R + +--R 2 2 4 3 2 5 2 +--R ((- 10A a b - 140B a b)d e + (70A b + 80B a b )d )x +--R + +--R 2 3 4 2 2 5 3 4 +--R ((- 80A a b - 70B a )d e + (140A a b + 10B a b)d )x - 50A a d e +--R + +--R 2 3 5 +--R (70A a b - 20B a )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 4 5 +--R (- 5A a d - 125A a )e +--R + +--R 2 3 2 3 4 4 +--R ((7A a b - 2B a )d + (175A a b - 50B a )d)e +--R * +--R 4 +--R x +--R + +--R 3 2 4 4 +--R (- 20A a d - 500A a d)e +--R + +--R 2 3 3 3 4 2 3 +--R ((28A a b - 8B a )d + (700A a b - 200B a )d )e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 3 +--R (- 30A a d - 750A a d )e +--R + +--R 2 3 4 3 4 3 2 +--R ((42A a b - 12B a )d + (1050A a b - 300B a )d )e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 2 +--R (- 20A a d - 500A a d )e +--R + +--R 2 3 5 3 4 4 +--R ((28A a b - 8B a )d + (700A a b - 200B a )d )e +--R * +--R x +--R + +--R 3 5 4 4 2 3 6 3 4 5 +--R (- 5A a d - 125A a d )e + (7A a b - 2B a )d + (175A a b - 50B a )d +--R / +--R 2 4 6 5 5 2 6 4 4 +--R (175a d e - 350a b d e + 175b d e )x +--R + +--R 2 5 5 6 4 2 7 3 3 +--R (700a d e - 1400a b d e + 700b d e )x +--R + +--R 2 6 4 7 3 2 8 2 2 +--R (1050a d e - 2100a b d e + 1050b d e )x +--R + +--R 2 7 3 8 2 2 9 2 8 2 9 2 10 +--R (700a d e - 1400a b d e + 700b d e)x + 175a d e - 350a b d e + 175b d +--R Type: Union(Expression(Integer),...) +--E 1016 + +--S 1017 of 1293 +m0:=a0-r0 +--R +--R +--R 3 4 2 3 2 3 4 +--R (- 5A a d - 125A a )e + (7A a b - 2B a )d + (175A a b - 50B a )d +--R (978) ----------------------------------------------------------------- +--R 2 4 2 5 2 6 +--R 175a d e - 350a b d e + 175b d +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1293 +d0:=D(m0,x) +--R +--R +--R (979) 0 +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(11/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (980) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1293 +r0:=-2/9*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ + 2/63*(5*b*B*d+4*A*b*e-9*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(7/2))+4/315*b*(5*b*B*d+4*A*b*e-9*a*B*e)*(a+b*x)^(5/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(5/2)) +--R +--R +--R (981) +--R 4 3 2 4 4 +--R ((- 16A b + 36B a b )e - 20B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 3 +--R ((8A a b - 18B a b )e + (- 72A b + 172B a b )d e - 90B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 6A a b - 144B a b)e + (36A a b + 384B a b )d e +--R + +--R 4 3 2 +--R (- 126A b - 144B a b )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 100A a b - 90B a )e + (288A a b + 172B a b)d e +--R + +--R 3 2 2 2 +--R (- 252A a b - 18B a b )d +--R * +--R x +--R + +--R 4 2 3 4 2 2 3 2 +--R - 70A a e + (180A a b - 20B a )d e + (- 126A a b + 36B a b)d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (315a e - 945a b d e + 945a b d e - 315b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (1260a d e - 3780a b d e + 3780a b d e - 1260b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (1890a d e - 5670a b d e + 5670a b d e - 1890b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (1260a d e - 3780a b d e + 3780a b d e - 1260b d e)x + 315a d e +--R + +--R 2 5 2 2 6 3 7 +--R - 945a b d e + 945a b d e - 315b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (982) +--R 4 3 5 2 4 6 4 +--R ((- 48A b + 108B a b )d e - 60B b d e)x +--R + +--R 3 2 2 5 2 4 3 6 +--R (24A a b - 54B a b )d e + (- 216A b + 516B a b )d e +--R + +--R 4 7 +--R - 270B b d +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (- 18A a b - 432B a b)d e + (108A a b + 1152B a b )d e +--R + +--R 4 3 7 +--R (- 378A b - 432B a b )d +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 2 3 6 +--R (- 300A a b - 270B a )d e + (864A a b + 516B a b)d e +--R + +--R 3 2 2 7 +--R (- 756A a b - 54B a b )d +--R * +--R x +--R + +--R 4 5 2 3 4 6 2 2 3 7 +--R - 210A a d e + (540A a b - 60B a )d e + (- 378A a b + 108B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 7 +--R (- 35A a d - 315A a )e +--R + +--R 3 4 2 4 5 6 +--R ((90A a b - 10B a )d + (810A a b - 90B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 5 +--R ((- 63A a b + 18B a b)d + (- 567A a b + 162B a b)d )e +--R * +--R 5 +--R x +--R + +--R 4 2 5 6 +--R (- 175A a d - 1575A a d)e +--R + +--R 3 4 3 4 5 2 5 +--R ((450A a b - 50B a )d + (4050A a b - 450B a )d )e +--R + +--R 2 2 3 4 3 2 4 3 4 +--R ((- 315A a b + 90B a b)d + (- 2835A a b + 810B a b)d )e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 5 +--R (- 350A a d - 3150A a d )e +--R + +--R 3 4 4 4 5 3 4 +--R ((900A a b - 100B a )d + (8100A a b - 900B a )d )e +--R + +--R 2 2 3 5 3 2 4 4 3 +--R ((- 630A a b + 180B a b)d + (- 5670A a b + 1620B a b)d )e +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 4 +--R (- 350A a d - 3150A a d )e +--R + +--R 3 4 5 4 5 4 3 +--R ((900A a b - 100B a )d + (8100A a b - 900B a )d )e +--R + +--R 2 2 3 6 3 2 4 5 2 +--R ((- 630A a b + 180B a b)d + (- 5670A a b + 1620B a b)d )e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 3 +--R (- 175A a d - 1575A a d )e +--R + +--R 3 4 6 4 5 5 2 +--R ((450A a b - 50B a )d + (4050A a b - 450B a )d )e +--R + +--R 2 2 3 7 3 2 4 6 +--R ((- 315A a b + 90B a b)d + (- 2835A a b + 810B a b)d )e +--R * +--R x +--R + +--R 4 6 5 5 2 +--R (- 35A a d - 315A a d )e +--R + +--R 3 4 7 4 5 6 +--R ((90A a b - 10B a )d + (810A a b - 90B a )d )e +--R + +--R 2 2 3 8 3 2 4 7 +--R (- 63A a b + 18B a b)d + (- 567A a b + 162B a b)d +--R / +--R 3 5 8 2 6 7 2 7 6 3 8 5 5 +--R (945a d e - 2835a b d e + 2835a b d e - 945b d e )x +--R + +--R 3 6 7 2 7 6 2 8 5 3 9 4 4 +--R (4725a d e - 14175a b d e + 14175a b d e - 4725b d e )x +--R + +--R 3 7 6 2 8 5 2 9 4 3 10 3 3 +--R (9450a d e - 28350a b d e + 28350a b d e - 9450b d e )x +--R + +--R 3 8 5 2 9 4 2 10 3 3 11 2 2 +--R (9450a d e - 28350a b d e + 28350a b d e - 9450b d e )x +--R + +--R 3 9 4 2 10 3 2 11 2 3 12 3 10 3 +--R (4725a d e - 14175a b d e + 14175a b d e - 4725b d e)x + 945a d e +--R + +--R 2 11 2 2 12 3 13 +--R - 2835a b d e + 2835a b d e - 945b d +--R Type: Union(Expression(Integer),...) +--E 1021 + +--S 1022 of 1293 +m0:=a0-r0 +--R +--R +--R (983) +--R 4 5 2 3 4 2 4 5 +--R (- 35A a d - 315A a )e + ((90A a b - 10B a )d + (810A a b - 90B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 63A a b + 18B a b)d + (- 567A a b + 162B a b)d +--R / +--R 3 5 3 2 6 2 2 7 3 8 +--R 945a d e - 2835a b d e + 2835a b d e - 945b d +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1293 +d0:=D(m0,x) +--R +--R +--R (984) 0 +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(13/2) +--R +--R +--R (985) +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1293 +r0:=-2/11*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ + 2/99*(5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(9/2))+8/693*b*(5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(7/2))+16/3465*b^2*_ + (5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^(5/2)) +--R +--R +--R (986) +--R 5 4 3 5 2 5 +--R ((96A b - 176B a b )e + 80B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 4 +--R ((- 48A a b + 88B a b )e + (528A b - 1008B a b )d e + 440B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (36A a b - 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a b + 630B a )d )e +--R + +--R 3 2 4 9 4 2 5 8 +--R ((1485A a b - 220B a b)d + (13365A a b - 1980B a b)d )e +--R + +--R 2 3 3 2 10 3 3 4 2 9 +--R (- 693A a b + 198B a b )d + (- 6237A a b + 1782B a b )d +--R / +--R 4 6 10 3 7 9 2 2 8 8 3 9 7 +--R 10395a d e - 41580a b d e + 62370a b d e - 41580a b d e +--R + +--R 4 10 6 +--R 10395b d e +--R * +--R 6 +--R x +--R + +--R 4 7 9 3 8 8 2 2 9 7 3 10 6 +--R 62370a d e - 249480a b d e + 374220a b d e - 249480a b d e +--R + +--R 4 11 5 +--R 62370b d e +--R * +--R 5 +--R x +--R + +--R 4 8 8 3 9 7 2 2 10 6 3 11 5 +--R 155925a d e - 623700a b d e + 935550a b d e - 623700a b d e +--R + +--R 4 12 4 +--R 155925b d e +--R * +--R 4 +--R x +--R + +--R 4 9 7 3 10 6 2 2 11 5 3 12 4 +--R 207900a d e - 831600a b d e + 1247400a b d e - 831600a b d e +--R + +--R 4 13 3 +--R 207900b d e +--R * +--R 3 +--R x +--R + +--R 4 10 6 3 11 5 2 2 12 4 3 13 3 +--R 155925a d e - 623700a b d e + 935550a b d e - 623700a b d e +--R + +--R 4 14 2 +--R 155925b d e +--R * +--R 2 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+--R +--R +--R (990) +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1293 +r0:=-2/13*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ + 2/143*(5*b*B*d+8*A*b*e-13*a*B*e)*(a+b*x)^(5/2)/(e*_ + (b*d-a*e)^2*(d+e*x)^(11/2))+4/429*b*(5*b*B*d+8*A*b*e-13*a*B*e)*_ + (a+b*x)^(5/2)/(e*(b*d-a*e)^3*(d+e*x)^(9/2))+16/3003*b^2*_ + (5*b*B*d+8*A*b*e-13*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^4*_ + (d+e*x)^(7/2))+32/15015*b^3*(5*b*B*d+8*A*b*e-13*a*B*e)*_ + (a+b*x)^(5/2)/(e*(b*d-a*e)^5*(d+e*x)^(5/2)) +--R +--R +--R (991) +--R 6 5 4 6 3 6 +--R ((- 256A b + 416B a b )e - 160B b d e )x +--R + +--R 5 2 4 4 6 5 3 +--R (128A a b - 208B a b )e + (- 1664A b + 2784B a b )d e +--R + +--R 6 2 2 +--R - 1040B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 96A a b + 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a b + 1820B a b)d e + (17160A a b - 2860B a b )d e +--R + +--R 2 4 3 3 4 +--R (- 6006A a b + 1716B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 11 4 10 3 2 2 9 2 3 3 8 +--R 15015a e - 75075a b d e + 150150a b d e - 150150a b d e +--R + +--R 4 4 7 5 5 6 +--R 75075a b d e - 15015b d e +--R * +--R 6 +--R x +--R + +--R 5 10 4 2 9 3 2 3 8 2 3 4 7 +--R 90090a d e - 450450a b d e + 900900a b d e - 900900a b d e +--R + +--R 4 5 6 5 6 5 +--R 450450a b d e - 90090b d e +--R * +--R 5 +--R x +--R + +--R 5 2 9 4 3 8 3 2 4 7 2 3 5 6 +--R 225225a d e - 1126125a b d e + 2252250a b d e - 2252250a b d e +--R + +--R 4 6 5 5 7 4 +--R 1126125a b d e - 225225b d e +--R * +--R 4 +--R x +--R + +--R 5 3 8 4 4 7 3 2 5 6 2 3 6 5 +--R 300300a d e - 1501500a b d e + 3003000a b d e - 3003000a b d e +--R + +--R 4 7 4 5 8 3 +--R 1501500a b d e - 300300b d e +--R * +--R 3 +--R x +--R + +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 +--R 225225a d e - 1126125a b d e + 2252250a b d e - 2252250a b d e +--R + +--R 4 8 3 5 9 2 +--R 1126125a b d e - 225225b d e +--R * +--R 2 +--R x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 90090a d e - 450450a b d e + 900900a b d e - 900900a b d e +--R + +--R 4 9 2 5 10 +--R 450450a b d e - 90090b d e +--R * +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 15015a d e - 75075a b d e + 150150a b d e - 150150a b d e +--R + +--R 4 10 5 11 +--R 75075a b d e - 15015b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (992) +--R 6 5 7 4 6 8 3 6 +--R ((- 1024A b + 1664B a b )d e - 640B b d e )x +--R + +--R 5 2 4 7 4 6 5 8 3 +--R (512A a b - 832B a b )d e + (- 6656A b + 11136B a b )d e +--R + +--R 6 9 2 +--R - 4160B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 4 5 2 4 8 3 +--R (- 384A a b + 624B a b )d e + (3328A a b - 5648B a b )d e +--R + +--R 6 5 9 2 6 10 +--R (- 18304A b + 31824B a b )d e - 11440B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 4 2 4 3 3 8 3 +--R (320A a b - 520B a 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4 2 4 19 3 5 20 2 +--R - 36036000a b d e + 27027000a b d e - 10810800a b d e +--R + +--R 6 21 +--R 1801800b d e +--R * +--R x +--R + +--R 6 16 6 5 17 5 4 2 18 4 3 3 19 3 +--R 225225a d e - 1351350a b d e + 3378375a b d e - 4504500a b d e +--R + +--R 2 4 20 2 5 21 6 22 +--R 3378375a b d e - 1351350a b d e + 225225b d +--R Type: Union(Expression(Integer),...) +--E 1036 + +--S 1037 of 1293 +m0:=a0-r0 +--R +--R +--R (998) +--R 7 8 5 +--R (- 3003A a d - 75075A a )e +--R + +--R 6 7 2 7 8 4 +--R ((17325A a b - 462B a )d + (433125A a b - 11550B a )d)e +--R + +--R 5 2 6 3 6 2 7 2 3 +--R ((- 40950A a b + 2520B a b)d + (- 1023750A a b + 63000B a b)d )e +--R + +--R 4 3 5 2 4 5 3 6 2 3 2 +--R ((50050A a b - 5460B a b )d + (1251250A a b - 136500B a b )d )e +--R + +--R 3 4 4 3 5 4 4 5 3 4 +--R ((- 32175A a b + 5720B a b )d + (- 804375A a b + 143000B a b )d )e +--R + +--R 2 5 3 4 6 3 5 4 4 5 +--R (9009A a b - 2574B a b )d + (225225A a b - 64350B a b )d +--R / +--R 6 8 6 5 9 5 4 2 10 4 3 3 11 3 +--R 225225a d e - 1351350a b d e + 3378375a b d e - 4504500a b d e +--R + +--R 2 4 12 2 5 13 6 14 +--R 3378375a b d e - 1351350a b d e + 225225b d +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1293 +d0:=D(m0,x) +--R +--R +--R (999) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (1000) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1293 +r0:=1/24*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(7/2)*(d+e*x)^(3/2)/_ + (b^3*e)+1/12*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(7/2)*(d+e*x)^(5/2)/_ + (b^2*e)+1/7*B*(a+b*x)^(7/2)*(d+e*x)^(7/2)/(b*e)-5/1024*(b*d-a*e)^6*_ + 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5 5 6 6 +--R (- 1190A a b - 791B a b )d e + (210A b + 490B a b )d e - 105B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 4 +-+ +-+ +--R 21504b e \|b \|e +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1293 +--a0:=integrate(t0,x) +--E 1041 + +--S 1042 of 1293 +--m0:=a0-r0 +--E 1042 + +--S 1043 of 1293 +--d0:=D(m0,x) +--E 1043 + +--S 1044 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (1002) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1293 +r0:=-1/60*(7*b*B*d-12*A*b*e+5*a*B*e)*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b^2*e)+_ + 1/6*B*(a+b*x)^(7/2)*(d+e*x)^(5/2)/(b*e)+1/512*(b*d-a*e)^5*(7*b*B*d-_ + 12*A*b*e+5*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(d+e*x)))/(b^(7/2)*e^(9/2))+1/768*(b*d-a*e)^3*(7*b*B*d-_ + 12*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e^3)-_ + 1/960*(b*d-a*e)^2*(7*b*B*d-12*A*b*e+5*a*B*e)*(a+b*x)^(5/2)*_ + sqrt(d+e*x)/(b^3*e^2)-1/160*(b*d-a*e)*(7*b*B*d-12*A*b*e+5*a*B*e)*_ + (a+b*x)^(7/2)*sqrt(d+e*x)/(b^3*e)-1/512*(b*d-a*e)^4*_ + (7*b*B*d-12*A*b*e+5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e^4) +--R +--R +--R (1003) +--R 5 6 6 4 2 5 5 +--R (180A a b - 75B a )e + (- 900A a b + 270B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (1800A a b - 225B a b )d e + (- 1800A a b - 300B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (900A a b + 675B a b )d e + (- 180A b - 450B a b )d e + 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 1280B b e x + ((1536A b + 3200B a b )e + 1664B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (4032A a b + 2160B a b )e + (2112A b + 4448B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (2976A a b + 40B a b )e + (6144A a b + 3384B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (96A b + 216B a b )d e - 56B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (120A a b - 50B a b)e + (5592A a b + 160B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (552A a b + 348B a b )d e + (- 120A b - 272B a b )d e +--R + +--R 5 4 +--R 70B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 180A a b + 75B a )e + (840A a b - 245B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (1536A a b + 150B a b )d e + (- 840A a b - 546B a b )d e +--R + +--R 5 4 4 5 5 +--R (180A b + 415B a b )d e - 105B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 4 +-+ +-+ +--R 7680b e \|b \|e +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1293 +--a0:=integrate(t0,x) +--E 1046 + +--S 1047 of 1293 +--m0:=a0-r0 +--E 1047 + +--S 1048 of 1293 +--d0:=D(m0,x) +--E 1048 + +--S 1049 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)*sqrt(d+e*x) +--R +--R +--R (1004) +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1293 +r0:=1/5*B*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b*e)+1/128*(b*d-a*e)^4*_ + (7*b*B*d-10*A*b*e+3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(9/2))+1/192*(b*d-a*e)^2*_ + (7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e^3)-_ + 1/240*(b*d-a*e)*(7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/_ + (b^2*e^2)-1/40*(7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(7/2)*_ + sqrt(d+e*x)/(b^2*e)-1/128*(b*d-a*e)^3*(7*b*B*d-10*A*b*e+3*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^4) +--R +--R +--R (1005) +--R 4 5 5 3 2 4 4 +--R (- 150A a b + 45B a )e + (600A a b - 75B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 900A a b - 150B a b )d e + (600A a b + 450B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 150A b - 375B a b )d e + 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 384B b e x + ((480A b + 1008B a b )e + 48B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1360A a b + 744B a b )e + (80A b + 176B a b )d e +--R + +--R 4 2 2 +--R - 56B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (1180A a b + 30B a b)e + (360A a b + 218B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 100A b - 222B a b )d e + 70B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (150A a b - 45B a )e + (730A a b + 60B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 550A a b - 346B a b )d e + (150A b + 340B a b )d e - 105B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 2 4 +-+ +-+ +--R 1920b e \|b \|e +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1293 +--a0:=integrate(t0,x) +--E 1051 + +--S 1052 of 1293 +--m0:=a0-r0 +--E 1052 + +--S 1053 of 1293 +--d0:=D(m0,x) +--E 1053 + +--S 1054 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1006) ---------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1293 +r0:=5/64*(b*d-a*e)^3*(7*b*B*d-8*A*b*e+a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(9/2))+5/96*(b*d-a*e)*_ + (7*b*B*d-8*A*b*e+a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b*e^3)-_ + 1/24*(7*b*B*d-8*A*b*e+a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b*e^2)+_ + 1/4*B*(a+b*x)^(7/2)*sqrt(d+e*x)/(b*e)-5/64*(b*d-a*e)^2*_ + (7*b*B*d-8*A*b*e+a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b*e^4) +--R +--R +--R (1007) +--R 3 4 4 2 2 3 3 +--R (120A a b - 15B a )e + (- 360A a b - 60B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (360A a b + 270B a b )d e + (- 120A b - 300B a b )d e + 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B b e x + ((64A b + 136B a b )e - 56B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((208A a b + 118B a b)e + (- 80A b - 172B a b )d e + 70B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (264A a b + 15B a )e + (- 320A a b - 191B a b)d e +--R + +--R 3 2 2 3 3 +--R (120A b + 265B a b )d e - 105B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 +-+ +-+ +--R 192b e \|b \|e +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1293 +--a0:=integrate(t0,x) +--E 1056 + +--S 1057 of 1293 +--m0:=a0-r0 +--E 1057 + +--S 1058 of 1293 +--d0:=D(m0,x) +--E 1058 + +--S 1059 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1008) ---------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1293 +r0:=-5/8*(b*d-a*e)^2*(7*b*B*d-6*A*b*e-a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(9/2)*sqrt(b))-_ + 2*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*sqrt(d+e*x))-_ + 5/12*(7*b*B*d-6*A*b*e-a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/e^3+_ + 1/3*(7*b*B*d-6*A*b*e-a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(e^2*(b*d-a*e))+_ + 5/8*(b*d-a*e)*(7*b*B*d-6*A*b*e-a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^4 +--R +--R +--R (1009) +--R 2 3 3 2 2 2 +--R (90A a b + 15B a )e + (- 180A a b - 135B a b)d e +--R + +--R 3 2 2 3 3 +--R (90A b + 225B a b )d e - 105B b d +--R * +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 3 3 2 3 2 2 2 +--R 8B b e x + ((12A b + 26B a b)e - 14B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((54A a b + 33B a )e + (- 30A b - 68B a b)d e + 35B b d e)x +--R + +--R 2 3 2 2 2 2 +--R - 48A a e + (150A a b + 81B a )d e + (- 90A b - 190B a b)d e +--R + +--R 2 3 +--R 105B b d +--R * +--R +-+ +-+ +-------+ +--R \|b \|e \|b x + a +--R / +--R 4 +-+ +-+ +-------+ +--R 24e \|b \|e \|e x + d +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1293 +--a0:=integrate(t0,x) +--E 1061 + +--S 1062 of 1293 +--m0:=a0-r0 +--E 1062 + +--S 1063 of 1293 +--d0:=D(m0,x) +--E 1063 + +--S 1064 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1010) ---------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1293 +r0:=-2/3*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ + 5/4*(b*d-a*e)*(7*b*B*d-4*A*b*e-3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(9/2)-2/3*(7*b*B*d-4*A*b*e-3*a*B*e)*_ + (a+b*x)^(5/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+5/6*b*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(e^3*(b*d-a*e))-_ + 5/4*b*(7*b*B*d-4*A*b*e-3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^4 +--R +--R +--R (1011) +--R 2 3 2 2 2 2 +--R ((60A a b + 45B a )e + (- 60A b - 150B a b)d e + 105B b d e)x +--R + +--R 2 2 2 2 2 3 +--R (60A a b + 45B a )d e + (- 60A b - 150B a b)d e + 105B b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|b \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((12A b + 27B a b)e - 21B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 56A a b - 24B a )e + (80A b + 158B a b)d e - 140B b d e)x +--R + +--R 2 3 2 2 2 2 +--R - 8A a e + (- 40A a b - 16B a )d e + (60A b + 115B a b)d e +--R + +--R 2 3 +--R - 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 5 4 +-+ +-------+ +--R (12e x + 12d e )\|e \|e x + d +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1293 +--a0:=integrate(t0,x) +--E 1066 + +--S 1067 of 1293 +--m0:=a0-r0 +--E 1067 + +--S 1068 of 1293 +--d0:=D(m0,x) +--E 1068 + +--S 1069 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1012) ---------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1293 +r0:=-2/5*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-_ + 2/15*(7*b*B*d-2*A*b*e-5*a*B*e)*(a+b*x)^(5/2)/(e^2*(b*d-a*e)*_ + (d+e*x)^(3/2))-b^(3/2)*(7*b*B*d-2*A*b*e-5*a*B*e)*_ + atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/e^(9/2)-_ + 2/3*b*(7*b*B*d-2*A*b*e-5*a*B*e)*(a+b*x)^(3/2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+b^2*(7*b*B*d-2*A*b*e-5*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(e^4*(b*d-a*e)) +--R +--R +--R (1013) +--R 2 3 2 2 2 +--R ((30A b + 75B a b)e - 105B b d e )x +--R + +--R 2 2 2 2 2 2 +--R ((60A b + 150B a b)d e - 210B b d e)x + (30A b + 75B a b)d e +--R + +--R 2 3 +--R - 105B b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|b \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 3 3 2 3 2 2 2 +--R 15B b e x + ((- 46A b - 70B a b)e + 161B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 22A a b - 10B a )e + (- 70A b - 98B a b)d e + 245B b d e)x +--R + +--R 2 3 2 2 2 2 +--R - 6A a e + (- 10A a b - 4B a )d e + (- 30A b - 40B a b)d e +--R + +--R 2 3 +--R 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 6 2 5 2 4 +-+ +-------+ +--R (15e x + 30d e x + 15d e )\|e \|e x + d +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1293 +--a0:=integrate(t0,x) +--E 1071 + +--S 1072 of 1293 +--m0:=a0-r0 +--E 1072 + +--S 1073 of 1293 +--d0:=D(m0,x) +--E 1073 + +--S 1074 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(9/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1014) ---------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1293 +r0:=-2/7*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))-_ + 2/5*B*(a+b*x)^(5/2)/(e^2*(d+e*x)^(5/2))-2/3*b*B*(a+b*x)^(3/2)/_ + (e^3*(d+e*x)^(3/2))+2*b^(5/2)*B*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/e^(9/2)-2*b^2*B*sqrt(a+b*x)/(e^4*sqrt(d+e*x)) +--R +--R +--R (1015) +--R 2 4 3 3 3 2 3 3 2 2 2 +--R (210B a b e - 210B b d e )x + (630B a b d e - 630B b d e )x +--R + +--R 2 2 2 3 3 2 3 3 4 +--R (630B a b d e - 630B b d e)x + 210B a b d e - 210B b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|b \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 2 4 3 3 3 +--R ((- 30A b - 322B a b )e + 352B b d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 90A a b - 154B a b)e - 568B a b d e + 812B b d e )x +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 90A a b - 42B a )e - 92B a b d e - 476B a b d e + 700B b d e)x +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 +--R - 30A a e - 12B a d e - 28B a b d e - 140B a b d e + 210B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 8 7 3 7 2 6 2 +--R (105a e - 105b d e )x + (315a d e - 315b d e )x +--R + +--R 2 6 3 5 3 5 4 4 +--R (315a d e - 315b d e )x + 105a d e - 105b d e +--R * +--R +-+ +-------+ +--R \|e \|e x + d +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1293 +--a0:=integrate(t0,x) +--E 1076 + +--S 1077 of 1293 +--m0:=a0-r0 +--E 1077 + +--S 1078 of 1293 +--d0:=D(m0,x) +--E 1078 + +--S 1079 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(11/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1016) ---------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1293 +r0:=-2/9*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ + 2/63*(7*b*B*d+2*A*b*e-9*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*(d+e*x)^(7/2)) +--R +--R +--R (1017) +--R 4 3 4 4 +--R ((4A b - 18B a b )e + 14B b d)x +--R + +--R 3 2 2 4 3 3 +--R ((- 2A a b - 54B a b )e + (18A b + 38B a b )d)x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 30A a b - 54B a b)e + (54A a b + 30B a b )d)x +--R + +--R 3 4 2 2 3 4 +--R ((- 38A a b - 18B a )e + (54A a b + 2B a b)d)x - 14A a e +--R + +--R 3 4 +--R (18A a b - 4B a )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 6 5 2 2 4 4 +--R (63a e - 126a b d e + 63b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (252a d e - 504a b d e + 252b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (378a d e - 756a b d e + 378b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (252a d e - 504a b d e + 252b d e)x + 63a d e - 126a b d e + 63b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1018) +--R 4 3 5 4 6 4 +--R ((12A b - 54B a b )d e + 42B b d )x +--R + +--R 3 2 2 5 4 3 6 3 +--R ((- 6A a b - 162B a b )d e + (54A b + 114B a b )d )x +--R + +--R 2 2 3 5 3 2 2 6 2 +--R ((- 90A a b - 162B a b)d e + (162A a b + 90B a b )d )x +--R + +--R 3 4 5 2 2 3 6 4 5 +--R ((- 114A a b - 54B a )d e + (162A a b + 6B a b)d )x - 42A a d e +--R + +--R 3 4 6 +--R (54A a b - 12B a )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 6 3 4 2 4 5 5 5 +--R ((- 7A a d - 63A a )e + ((9A a b - 2B a )d + (81A a b - 18B a )d)e )x +--R + +--R 4 2 5 5 +--R (- 35A a d - 315A a d)e +--R + +--R 3 4 3 4 5 2 4 +--R ((45A a b - 10B a )d + (405A a b - 90B a )d )e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 4 +--R (- 70A a d - 630A a d )e +--R + +--R 3 4 4 4 5 3 3 +--R ((90A a b - 20B a )d + (810A a b - 180B a )d )e +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 3 +--R (- 70A a d - 630A a d )e +--R + +--R 3 4 5 4 5 4 2 +--R ((90A a b - 20B a )d + (810A a b - 180B a )d )e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 2 +--R (- 35A a d - 315A a d )e +--R + +--R 3 4 6 4 5 5 +--R ((45A a b - 10B a )d + (405A a b - 90B a )d )e +--R * +--R x +--R + +--R 4 6 5 5 3 4 7 4 5 6 +--R (- 7A a d - 63A a d )e + (9A a b - 2B a )d + (81A a b - 18B a )d +--R / +--R 2 5 7 6 6 2 7 5 5 +--R (189a d e - 378a b d e + 189b d e )x +--R + +--R 2 6 6 7 5 2 8 4 4 +--R (945a d e - 1890a b d e + 945b d e )x +--R + +--R 2 7 5 8 4 2 9 3 3 +--R (1890a d e - 3780a b d e + 1890b d e )x +--R + +--R 2 8 4 9 3 2 10 2 2 +--R (1890a d e - 3780a b d e + 1890b d e )x +--R + +--R 2 9 3 10 2 2 11 2 10 2 11 +--R (945a d e - 1890a b d e + 945b d e)x + 189a d e - 378a b d e +--R + +--R 2 12 +--R 189b d +--R Type: Union(Expression(Integer),...) +--E 1081 + +--S 1082 of 1293 +m0:=a0-r0 +--R +--R +--R 4 5 3 4 2 4 5 +--R (- 7A a d - 63A a )e + (9A a b - 2B a )d + (81A a b - 18B a )d +--R (1019) --------------------------------------------------------------- +--R 2 5 2 6 2 7 +--R 189a d e - 378a b d e + 189b d +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1293 +d0:=D(m0,x) +--R +--R +--R (1020) 0 +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(13/2) +--R +--R +--R (1021) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1293 +r0:=-2/11*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ + 2/99*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(9/2))+4/693*b*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^(7/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(7/2)) +--R +--R +--R (1022) +--R 5 4 2 5 5 +--R ((- 16A b + 44B a b )e - 28B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 4 +--R ((8A a b - 22B a b )e + (- 88A b + 256B a b )d e - 154B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (- 6A a b - 330B a b )e + (44A a b + 908B a b )d e +--R + +--R 5 4 2 +--R (- 198A b - 418B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 226A a b - 418B a b)e + (660A a b + 908B a b )d e +--R + +--R 4 2 3 2 +--R (- 594A a b - 330B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 322A a b - 154B a )e + (836A a b + 256B a b)d e +--R + +--R 2 3 3 2 2 +--R (- 594A a b - 22B a b )d +--R * +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R - 126A a e + (308A a b - 28B a )d e + (- 198A a b + 44B a b)d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 8 2 7 2 2 6 3 3 5 5 +--R (693a e - 2079a b d e + 2079a b d e - 693b d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 4 +--R (3465a d e - 10395a b d e + 10395a b d e - 3465b d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 3 +--R (6930a d e - 20790a b d e + 20790a b d e - 6930b d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 2 +--R (6930a d e - 20790a b d e + 20790a b d e - 6930b d e )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 3 5 3 +--R (3465a d e - 10395a b d e + 10395a b d e - 3465b d e)x + 693a d e +--R + +--R 2 6 2 2 7 3 8 +--R - 2079a b d e + 2079a b d e - 693b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1023) +--R 5 4 6 2 5 7 5 +--R ((- 16A b + 44B a b )d e - 28B b d e)x +--R + +--R 4 2 3 6 2 5 4 7 5 8 4 +--R ((8A a b - 22B a b )d e + (- 88A b + 256B a b )d e - 154B b d )x +--R + +--R 2 3 3 2 6 2 4 2 3 7 +--R (- 6A a b - 330B a b )d e + (44A a b + 908B a b )d e +--R + +--R 5 4 8 +--R (- 198A b - 418B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 2 3 3 2 7 +--R (- 226A a b - 418B a b)d e + (660A a b + 908B a b )d e +--R + +--R 4 2 3 8 +--R (- 594A a b - 330B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 6 2 3 2 4 7 +--R (- 322A a b - 154B a )d e + (836A a b + 256B a b)d e +--R + +--R 2 3 3 2 8 +--R (- 594A a b - 22B a b )d +--R * +--R x +--R + +--R 5 6 2 4 5 7 3 2 4 8 +--R - 126A a d e + (308A a b - 28B a )d e + (- 198A a b + 44B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 5 6 8 +--R (63A a d + 63A a )e +--R + +--R 4 5 2 5 6 7 +--R ((- 154A a b + 14B a )d + (- 154A a b + 14B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 6 +--R ((99A a b - 22B a b)d + (99A a b - 22B a b)d )e +--R * +--R 6 +--R x +--R + +--R 5 2 6 7 +--R (378A a d + 378A a d)e +--R + +--R 4 5 3 5 6 2 6 +--R ((- 924A a b + 84B a )d + (- 924A a b + 84B a )d )e +--R + +--R 3 2 4 4 4 2 5 3 5 +--R ((594A a b - 132B a b)d + (594A a b - 132B a b)d )e +--R * +--R 5 +--R x +--R + +--R 5 3 6 2 6 +--R (945A a d + 945A a d )e +--R + +--R 4 5 4 5 6 3 5 +--R ((- 2310A a b + 210B a )d + (- 2310A a b + 210B a )d )e +--R + +--R 3 2 4 5 4 2 5 4 4 +--R ((1485A a b - 330B a b)d + (1485A a b - 330B a b)d )e +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 5 +--R (1260A a d + 1260A a d )e +--R + +--R 4 5 5 5 6 4 4 +--R ((- 3080A a b + 280B a )d + (- 3080A a b + 280B a )d )e +--R + +--R 3 2 4 6 4 2 5 5 3 +--R ((1980A a b - 440B a b)d + (1980A a b - 440B a b)d )e +--R * +--R 3 +--R x +--R + +--R 5 5 6 4 4 +--R (945A a d + 945A a d )e +--R + +--R 4 5 6 5 6 5 3 +--R ((- 2310A a b + 210B a )d + (- 2310A a b + 210B a )d )e +--R + +--R 3 2 4 7 4 2 5 6 2 +--R ((1485A a b - 330B a b)d + (1485A a b - 330B a b)d )e +--R * +--R 2 +--R x +--R + +--R 5 6 6 5 3 +--R (378A a d + 378A a d )e +--R + +--R 4 5 7 5 6 6 2 +--R ((- 924A a b + 84B a )d + (- 924A a b + 84B a )d )e +--R + +--R 3 2 4 8 4 2 5 7 +--R ((594A a b - 132B a b)d + (594A a b - 132B a b)d )e +--R * +--R x +--R + +--R 5 7 6 6 2 +--R (63A a d + 63A a d )e +--R + +--R 4 5 8 5 6 7 +--R ((- 154A a b + 14B a )d + (- 154A a b + 14B a )d )e +--R + +--R 3 2 4 9 4 2 5 8 +--R (99A a b - 22B a b)d + (99A a b - 22B a b)d +--R / +--R 3 6 9 2 7 8 2 8 7 3 9 6 6 +--R (693a d e - 2079a b d e + 2079a b d e - 693b d e )x +--R + +--R 3 7 8 2 8 7 2 9 6 3 10 5 5 +--R (4158a d e - 12474a b d e + 12474a b d e - 4158b d e )x +--R + +--R 3 8 7 2 9 6 2 10 5 3 11 4 4 +--R (10395a d e - 31185a b d e + 31185a b d e - 10395b d e )x +--R + +--R 3 9 6 2 10 5 2 11 4 3 12 3 3 +--R (13860a d e - 41580a b d e + 41580a b d e - 13860b d e )x +--R + +--R 3 10 5 2 11 4 2 12 3 3 13 2 2 +--R (10395a d e - 31185a b d e + 31185a b d e - 10395b d e )x +--R + +--R 3 11 4 2 12 3 2 13 2 3 14 +--R (4158a d e - 12474a b d e + 12474a b d e - 4158b d e)x +--R + +--R 3 12 3 2 13 2 2 14 3 15 +--R 693a d e - 2079a b d e + 2079a b d e - 693b d +--R Type: Union(Expression(Integer),...) +--E 1086 + +--S 1087 of 1293 +m0:=a0-r0 +--R +--R +--R (1024) +--R 5 6 2 +--R (63A a d + 63A a )e +--R + +--R 4 5 2 5 6 +--R ((- 154A a b + 14B a )d + (- 154A a b + 14B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 +--R (99A a b - 22B a b)d + (99A a b - 22B a b)d +--R / +--R 3 6 3 2 7 2 2 8 3 9 +--R 693a d e - 2079a b d e + 2079a b d e - 693b d +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1293 +d0:=D(m0,x) +--R +--R +--R (1025) 0 +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(15/2) +--R +--R +--R (1026) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1293 +r0:=-2/13*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ + 2/143*(7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(11/2))+8/1287*b*(7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(9/2))+16/9009*b^2*_ + (7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^4*(d+e*x)^(7/2)) +--R +--R +--R (1027) +--R 6 5 3 6 2 6 +--R ((96A b - 208B a b )e + 112B b d e )x +--R + +--R 5 2 4 3 6 5 2 +--R (- 48A a b + 104B a b )e + (624A b - 1408B a b )d e +--R + +--R 6 2 +--R 728B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (36A a b - 78B a b )e + (- 312A a b + 718B a b )d e +--R + +--R 6 5 2 6 3 +--R (1716A b - 4082B a b )d e + 2002B b d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 30A a b - 2938B a b )e + (234A a b + 11470B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 858A a b - 15886B a b )d e + (2574A b + 5434B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 2226A a b - 4186B a b)e + (8814A a b + 14342B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 12870A a b - 15886B a b )d e + (7722A a b + 4290B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 3402A a b - 1638B a )e + (12558A a b + 4858B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 16302A a b - 4082B a b )d e + (7722A a b + 286B a b )d +--R * +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - 1386A a e + (4914A a b - 252B a )d e + (- 6006A a b + 728B a b)d e +--R + +--R 3 3 4 2 3 +--R (2574A a b - 572B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 10 3 9 2 2 2 8 3 3 7 +--R 9009a e - 36036a b d e + 54054a b d e - 36036a b d e +--R + +--R 4 4 6 +--R 9009b d e +--R * +--R 6 +--R x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 +--R 54054a d e - 216216a b d e + 324324a b d e - 216216a b d e +--R + +--R 4 5 5 +--R 54054b d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 +--R 135135a d e - 540540a b d e + 810810a b d e - 540540a b d e +--R + +--R 4 6 4 +--R 135135b d e +--R * +--R 4 +--R x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 6 4 +--R 180180a d e - 720720a b d e + 1081080a b d e - 720720a b d e +--R + +--R 4 7 3 +--R 180180b d e +--R * +--R 3 +--R x +--R + +--R 4 4 6 3 5 5 2 2 6 4 3 7 3 +--R 135135a d e - 540540a b d e + 810810a b d e - 540540a b d e +--R + +--R 4 8 2 +--R 135135b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 6 4 2 2 7 3 3 8 2 +--R 54054a d e - 216216a b d e + 324324a b d e - 216216a b d e +--R + +--R 4 9 +--R 54054b d e +--R * +--R x +--R + +--R 4 6 4 3 7 3 2 2 8 2 3 9 4 10 +--R 9009a d e - 36036a b d e + 54054a b d e - 36036a b d e + 9009b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1028) +--R 6 5 7 3 6 8 2 6 +--R ((288A b - 624B a b )d e + 336B b d e )x +--R + +--R 5 2 4 7 3 6 5 8 2 +--R (- 144A a b + 312B a b )d e + (1872A b - 4224B a b )d e +--R + +--R 6 9 +--R 2184B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 3 5 2 4 8 2 +--R (108A a b - 234B a b )d e + (- 936A a b + 2154B a b )d e +--R + +--R 6 5 9 6 10 +--R (5148A b - 12246B a b )d e + 6006B b d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 3 2 4 3 3 8 2 +--R (- 90A a b - 8814B a b )d e + (702A a b + 34410B a b )d e +--R + +--R 5 2 4 9 6 5 10 +--R (- 2574A a b - 47658B a b )d e + (7722A b + 16302B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 3 4 2 8 2 +--R (- 6678A a b - 12558B a b)d e + (26442A a b + 43026B a b )d e +--R + +--R 2 4 3 3 9 5 2 4 10 +--R (- 38610A a b - 47658B a b )d e + (23166A a b + 12870B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 7 3 4 2 5 8 2 +--R (- 10206A a b - 4914B a )d e + (37674A a b + 14574B a b)d e +--R + +--R 3 3 4 2 9 2 4 3 3 10 +--R (- 48906A a b - 12246B a b )d e + (23166A a b + 858B a b )d +--R * +--R x +--R + +--R 6 7 3 5 6 8 2 +--R - 4158A a d e + (14742A a b - 756B a )d e +--R + +--R 4 2 5 9 3 3 4 2 10 +--R (- 18018A a b + 2184B a b)d e + (7722A a b - 1716B a b 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7 2 4 18 6 5 19 5 +--R - 3859455600a b d e + 2894591700a b d e - 1157836680a b d e +--R + +--R 6 20 4 +--R 192972780b d e +--R * +--R 4 +--R x +--R + +--R 6 15 9 5 16 8 4 2 17 7 +--R 128648520a d e - 771891120a b d e + 1929727800a b d e +--R + +--R 3 3 18 6 2 4 19 5 5 20 4 +--R - 2572970400a b d e + 1929727800a b d e - 771891120a b d e +--R + +--R 6 21 3 +--R 128648520b d e +--R * +--R 3 +--R x +--R + +--R 6 16 8 5 17 7 4 2 18 6 +--R 55135080a d e - 330810480a b d e + 827026200a b d e +--R + +--R 3 3 19 5 2 4 20 4 5 21 3 +--R - 1102701600a b d e + 827026200a b d e - 330810480a b d e +--R + +--R 6 22 2 +--R 55135080b d e +--R * +--R 2 +--R x +--R + +--R 6 17 7 5 18 6 4 2 19 5 +--R 13783770a d e - 82702620a b d e + 206756550a b d e +--R + +--R 3 3 20 4 2 4 21 3 5 22 2 +--R - 275675400a b d e + 206756550a b d e - 82702620a b d e +--R + +--R 6 23 +--R 13783770b d e +--R * +--R x +--R + +--R 6 18 6 5 19 5 4 2 20 4 3 3 21 3 +--R 1531530a d e - 9189180a b d e + 22972950a b d e - 30630600a b d e +--R + +--R 2 4 22 2 5 23 6 24 +--R 22972950a b d e - 9189180a b d e + 1531530b d +--R Type: Union(Expression(Integer),...) +--E 1101 + +--S 1102 of 1293 +m0:=a0-r0 +--R +--R +--R (1039) +--R 8 9 5 +--R (- 45045A a d - 180180A a )e +--R + +--R 7 8 2 8 9 4 +--R ((255255A a b - 6006B a )d + (1021020A a b - 24024B a )d)e +--R + +--R 6 2 7 3 7 2 8 2 3 +--R ((- 589050A a b + 31416B a b)d + (- 2356200A a b + 125664B a b)d )e +--R + +--R 5 3 6 2 4 6 3 7 2 3 2 +--R ((696150A a b - 64260B a b )d + (2784600A a b - 257040B a b )d )e +--R + +--R 4 4 5 3 5 5 4 6 3 4 +--R ((- 425425A a b + 61880B a b )d + (- 1701700A a b + 247520B a b )d )e +--R + +--R 3 5 4 4 6 4 5 5 4 5 +--R (109395A a b - 24310B a b )d + (437580A a b - 97240B a b )d +--R / +--R 6 9 6 5 10 5 4 2 11 4 3 3 12 3 +--R 1531530a d e - 9189180a b d e + 22972950a b d e - 30630600a b d e +--R + +--R 2 4 13 2 5 14 6 15 +--R 22972950a b d e - 9189180a b d e + 1531530b d +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1293 +d0:=D(m0,x) +--R +--R +--R (1040) 0 +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(a+b*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1041) ---------------------------------------------------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1293 +r0:=-5/64*(b*d-a*e)^3*(b*B*d-8*A*b*e+7*a*B*e)*_ + atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(3/2))-_ + 5/96*(b*d-a*e)*(b*B*d-8*A*b*e+7*a*B*e)*(d+e*x)^(3/2)*_ + sqrt(a+b*x)/(b^3*e)-1/24*(b*B*d-8*A*b*e+7*a*B*e)*(d+e*x)^(5/2)*_ + sqrt(a+b*x)/(b^2*e)+1/4*B*(d+e*x)^(7/2)*sqrt(a+b*x)/(b*e)-_ + 5/64*(b*d-a*e)^2*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e) +--R +--R +--R (1042) +--R 3 4 4 2 2 3 3 +--R (- 120A a b + 105B a )e + (360A a b - 300B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 360A a b + 270B a b )d e + (120A b - 60B a b )d e - 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B b e x + ((64A b - 56B a b )e + 136B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 80A a b + 70B a b)e + (208A b - 172B a b )d e + 118B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (120A a b - 105B a )e + (- 320A a b + 265B a b)d e +--R + +--R 3 2 2 3 3 +--R (264A b - 191B a b )d e + 15B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 +-+ +-+ +--R 192b e\|b \|e +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1293 +--a0:=integrate(t0,x) +--E 1106 + +--S 1107 of 1293 +--m0:=a0-r0 +--E 1107 + +--S 1108 of 1293 +--d0:=D(m0,x) +--E 1108 + +--S 1109 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a+b*x) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1043) --------------------------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1293 +r0:=-1/8*(b*d-a*e)^2*(b*B*d-6*A*b*e+5*a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*e^(3/2))-_ + 1/12*(b*B*d-6*A*b*e+5*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/(b^2*e)+_ + 1/3*B*(d+e*x)^(5/2)*sqrt(a+b*x)/(b*e)-1/8*(b*d-a*e)*_ + (b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e) +--R +--R +--R (1044) +--R 2 3 3 2 2 2 +--R (18A a b - 15B a )e + (- 36A a b + 27B a b)d e +--R + +--R 3 2 2 3 3 +--R (18A b - 9B a b )d e - 3B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 2 +--R 8B b e x + ((12A b - 10B a b)e + 14B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 18A a b + 15B a )e + (30A b - 22B a b)d e + 3B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 +-+ +-+ +--R 24b e\|b \|e +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1293 +--a0:=integrate(t0,x) +--E 1111 + +--S 1112 of 1293 +--m0:=a0-r0 +--E 1112 + +--S 1113 of 1293 +--d0:=D(m0,x) +--E 1113 + +--S 1114 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a+b*x) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1045) ------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1293 +r0:=-1/4*(b*d-a*e)*(b*B*d-4*A*b*e+3*a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(3/2))+_ + 1/2*B*(d+e*x)^(3/2)*sqrt(a+b*x)/(b*e)-1/4*(b*B*d-4*A*b*e+3*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e) +--R +--R +--R (1046) +--R 2 2 2 2 2 +--R ((- 4A a b + 3B a )e + (4A b - 2B a b)d e - B b d ) +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2B b e x + (4A b - 3B a)e + B b d)\|b \|e \|b x + a \|e x + d +--R / +--R 2 +-+ +-+ +--R 4b e\|b \|e +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1293 +--a0:=integrate(t0,x) +--E 1116 + +--S 1117 of 1293 +--m0:=a0-r0 +--E 1117 + +--S 1118 of 1293 +--d0:=D(m0,x) +--E 1118 + +--S 1119 of 1293 +t0:=(A+B*x)/(sqrt(a+b*x)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1047) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1293 +r0:=(2*A*b*e-B*(b*d+a*e))*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/_ + (b^(3/2)*e^(3/2))+B*sqrt(a+b*x)*sqrt(d+e*x)/(b*e) +--R +--R +--R (1048) +--R +-+ +-------+ +--R \|e \|b x + a +-+ +-+ +-------+ +-------+ +--R ((2A b - B a)e - B b d)atanh(--------------) + B\|b \|e \|b x + a \|e x + d +--R +-+ +-------+ +--R \|b \|e x + d +--R ---------------------------------------------------------------------------- +--R +-+ +-+ +--R b e\|b \|e +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1293 +--a0:=integrate(t0,x) +--E 1121 + +--S 1122 of 1293 +--m0:=a0-r0 +--E 1122 + +--S 1123 of 1293 +--d0:=D(m0,x) +--E 1123 + +--S 1124 of 1293 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a+b*x)) +--R +--R +--R B x + A +--R (1049) ----------------------------- +--R +-------+ +-------+ +--R (e x + d)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1293 +r0:=2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(3/2)*sqrt(b))-_ + 2*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*sqrt(d+e*x)) +--R +--R +--R (1050) +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R (2B a e - 2B b d)\|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +--R (- 2A e + 2B d)\|b \|e \|b x + a +--R / +--R 2 +-+ +-+ +-------+ +--R (a e - b d e)\|b \|e \|e x + d +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1293 +--a0:=integrate(t0,x) +--E 1126 + +--S 1127 of 1293 +--m0:=a0-r0 +--E 1127 + +--S 1128 of 1293 +--d0:=D(m0,x) +--E 1128 + +--S 1129 of 1293 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(a+b*x)) +--R +--R +--R B x + A +--R (1051) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (e x + 2d e x + d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1293 +r0:=-2/3*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ + 2/3*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*sqrt(d+e*x)) +--R +--R +--R (1052) +--R +-------+ +--R (((4A b - 6B a)e + 2B b d)x - 2A a e + (6A b - 4B a)d)\|b x + a +--R ---------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d )\|e x + d +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1053) +--R 2 3 2 3 +-------+ +--R (((4A b - 6B a)d e + 2B b d )x - 2A a d e + (6A b - 4B a)d )\|b x + a +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 +--R ((- A a d - A a )e + ((3A b - 2B a)d + (3A a b - 2B a )d)e )x +--R + +--R 2 2 2 3 2 2 +--R ((- 2A a d - 2A a d)e + ((6A b - 4B a)d + (6A a b - 4B a )d )e)x +--R + +--R 3 2 2 4 2 3 +--R (- A a d - A a d )e + (3A b - 2B a)d + (3A a b - 2B a )d +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (3a d e - 6a b d e + 3b d e )x + (6a d e - 12a b d e + 6b d e)x +--R + +--R 2 4 2 5 2 6 +--R 3a d e - 6a b d e + 3b d +--R Type: Union(Expression(Integer),...) +--E 1131 + +--S 1132 of 1293 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R (- A a d - A a )e + (3A b - 2B a)d + (3A a b - 2B a )d +--R (1054) ------------------------------------------------------- +--R 2 2 2 3 2 4 +--R 3a d e - 6a b d e + 3b d +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1293 +d0:=D(m0,x) +--R +--R +--R (1055) 0 +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1293 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(a+b*x)) +--R +--R +--R B x + A +--R (1056) -------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +-------+ +--R (e x + 3d e x + 3d e x + d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1293 +r0:=-2/5*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2))+_ + 2/15*(b*B*d+4*A*b*e-5*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(3/2))+_ + 4/15*b*(b*B*d+4*A*b*e-5*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (1057) +--R 2 2 2 2 +--R ((- 16A b + 20B a b)e - 4B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((8A a b - 10B a )e + (- 40A b + 52B a b)d e - 10B b d )x - 6A a e +--R + +--R 2 2 2 +--R (20A a b - 4B a )d e + (- 30A b + 20B a b)d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e - 45a b d e +--R + +--R 2 4 3 5 +--R 45a b d e - 15b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1058) +--R 2 3 2 2 4 2 +--R ((- 48A b + 60B a b)d e - 12B b d e)x +--R + +--R 2 3 2 2 4 2 5 +--R ((24A a b - 30B a )d e + (- 120A b + 156B a b)d e - 30B b d )x +--R + +--R 2 3 2 2 4 2 5 +--R - 18A a d e + (60A a b - 12B a )d e + (- 90A b + 60B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 3 5 2 2 2 3 4 +--R (- 3A a d - 27A a )e + ((10A a b - 2B a )d + (90A a b - 18B a )d)e +--R + +--R 2 3 2 2 2 3 +--R ((- 15A b + 10B a b)d + (- 135A a b + 90B a b)d )e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 +--R (- 9A a d - 81A a d)e +--R + +--R 2 3 2 3 2 3 +--R ((30A a b - 6B a )d + (270A a b - 54B a )d )e +--R + +--R 2 4 2 2 3 2 +--R ((- 45A b + 30B a b)d + (- 405A a b + 270B a b)d )e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 3 +--R (- 9A a d - 81A a d )e +--R + +--R 2 4 2 3 3 2 +--R ((30A a b - 6B a )d + (270A a b - 54B a )d )e +--R + +--R 2 5 2 2 4 +--R ((- 45A b + 30B a b)d + (- 405A a b + 270B a b)d )e +--R * +--R x +--R + +--R 2 4 3 3 2 2 5 2 3 4 +--R (- 3A a d - 27A a d )e + ((10A a b - 2B a )d + (90A a b - 18B a )d )e +--R + +--R 2 6 2 2 5 +--R (- 15A b + 10B a b)d + (- 135A a b + 90B a b)d +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (45a d e - 135a b d e + 135a b d e - 45b d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (135a d e - 405a b d e + 405a b d e - 135b d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (135a d e - 405a b d e + 405a b d e - 135b d e)x + 45a d e +--R + +--R 2 7 2 2 8 3 9 +--R - 135a b d e + 135a b d e - 45b d +--R Type: Union(Expression(Integer),...) +--E 1136 + +--S 1137 of 1293 +m0:=a0-r0 +--R +--R +--R (1059) +--R 2 3 2 2 2 2 3 +--R (- 3A a d - 27A a )e + ((10A a b - 2B a )d + (90A a b - 18B a )d)e +--R + +--R 2 3 2 2 2 +--R (- 15A b + 10B a b)d + (- 135A a b + 90B a b)d +--R / +--R 3 3 3 2 4 2 2 5 3 6 +--R 45a d e - 135a b d e + 135a b d e - 45b d +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1293 +d0:=D(m0,x) +--R +--R +--R (1060) 0 +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1293 +t0:=(A+B*x)/((d+e*x)^(9/2)*sqrt(a+b*x)) +--R +--R +--R B x + A +--R (1061) ------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +-------+ +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1293 +r0:=-2/7*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ + 2/35*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + 8/105*b*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^3*_ + (d+e*x)^(3/2))+16/105*b^2*(b*B*d+6*A*b*e-7*a*B*e)*_ + sqrt(a+b*x)/(e*(b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (1062) +--R 3 2 3 3 2 3 +--R ((96A b - 112B a b )e + 16B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 48A a b + 56B a b)e + (336A b - 400B a b )d e + 56B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (36A a b - 42B a )e + (- 168A a b + 202B a b)d e +--R + +--R 3 2 2 3 3 +--R (420A b - 518B a b )d e + 70B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 30A a e + (126A a b - 12B a )d e + (- 210A a b + 56B a b)d e +--R + +--R 3 2 3 +--R (210A b - 140B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (105a e - 420a b d e + 630a b d e - 420a b d e + 105b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (315a d e - 1260a b d e + 1890a b d e - 1260a b d e + 315b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (315a d e - 1260a b d e + 1890a b d e - 1260a b d e + 315b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 105a d e - 420a b d e + 630a b d e - 420a b d e + 105b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1063) +--R 3 2 4 3 3 5 2 3 +--R ((384A b - 448B a b )d e + 64B b d e )x +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 192A a b + 224B a b)d e + (1344A b - 1600B a b )d e +--R + +--R 3 6 +--R 224B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 3 2 2 5 2 +--R (144A a b - 168B a )d e + (- 672A a b + 808B a b)d e +--R + +--R 3 2 6 3 7 +--R (1680A b - 2072B a b )d e + 280B b d +--R * +--R x +--R + +--R 3 4 3 2 3 5 2 2 2 6 +--R - 120A a d e + (504A a b - 48B a )d e + (- 840A a b + 224B a b)d e +--R + +--R 3 2 7 +--R (840A b - 560B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 4 7 +--R (- 15A a d - 240A a )e +--R + +--R 2 3 2 3 4 6 +--R ((63A a b - 6B a )d + (1008A a b - 96B a )d)e +--R + +--R 2 2 3 2 2 3 2 5 +--R ((- 105A a b + 28B a b)d + (- 1680A a b + 448B a b)d )e +--R + +--R 3 2 4 3 2 2 3 4 +--R ((105A b - 70B a b )d + (1680A a b - 1120B a b )d )e +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 +--R (- 60A a d - 960A a d)e +--R + +--R 2 3 3 3 4 2 5 +--R ((252A a b - 24B a )d + (4032A a b - 384B a )d )e +--R + +--R 2 2 4 2 2 3 3 4 +--R ((- 420A a b + 112B a b)d + (- 6720A a b + 1792B a b)d )e +--R + +--R 3 2 5 3 2 2 4 3 +--R ((420A b - 280B a b )d + (6720A a b - 4480B a b )d )e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 90A a d - 1440A a d )e +--R + +--R 2 3 4 3 4 3 4 +--R ((378A a b - 36B a )d + (6048A a b - 576B a )d )e +--R + +--R 2 2 5 2 2 3 4 3 +--R ((- 630A a b + 168B a b)d + (- 10080A a b + 2688B a b)d )e +--R + +--R 3 2 6 3 2 2 5 2 +--R ((630A b - 420B a b )d + (10080A a b - 6720B a b )d )e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 4 +--R (- 60A a d - 960A a d )e +--R + +--R 2 3 5 3 4 4 3 +--R ((252A a b - 24B a )d + (4032A a b - 384B a )d )e +--R + +--R 2 2 6 2 2 3 5 2 +--R ((- 420A a b + 112B a b)d + (- 6720A a b + 1792B a b)d )e +--R + +--R 3 2 7 3 2 2 6 +--R ((420A b - 280B a b )d + (6720A a b - 4480B a b )d )e +--R * +--R x +--R + +--R 3 5 4 4 3 +--R (- 15A a d - 240A a d )e +--R + +--R 2 3 6 3 4 5 2 +--R ((63A a b - 6B a )d + (1008A a b - 96B a )d )e +--R + +--R 2 2 7 2 2 3 6 +--R ((- 105A a b + 28B a b)d + (- 1680A a b + 448B a b)d )e +--R + +--R 3 2 8 3 2 2 7 +--R (105A b - 70B a b )d + (1680A a b - 1120B a b )d +--R / +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 8 4 4 +--R (420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 4 9 3 3 +--R (1680a d e - 6720a b d e + 10080a b d e - 6720a b d e + 1680b d e )x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 +--R 2520a d e - 10080a b d e + 15120a b d e - 10080a b d e +--R + +--R 4 10 2 +--R 2520b d e +--R * +--R 2 +--R x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 +--R (1680a d e - 6720a b d e + 10080a b d e - 6720a b d e + 1680b d e)x +--R + +--R 4 8 4 3 9 3 2 2 10 2 3 11 4 12 +--R 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R Type: Union(Expression(Integer),...) +--E 1141 + +--S 1142 of 1293 +m0:=a0-r0 +--R +--R +--R (1064) +--R 3 4 3 2 3 2 3 4 2 +--R (- 15A a d - 240A a )e + ((63A a b - 6B a )d + (1008A a b - 96B a )d)e +--R + +--R 2 2 3 2 2 3 2 +--R ((- 105A a b + 28B a b)d + (- 1680A a b + 448B a b)d )e +--R + +--R 3 2 4 3 2 2 3 +--R (105A b - 70B a b )d + (1680A a b - 1120B a b )d +--R / +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 8 +--R 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1293 +d0:=D(m0,x) +--R +--R +--R (1065) 0 +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1293 +t0:=(A+B*x)/((d+e*x)^(11/2)*sqrt(a+b*x)) +--R +--R +--R (1066) +--R B x + A +--R ------------------------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1293 +r0:=-2/9*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ + 2/63*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(7/2))+_ + 4/105*b*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/_ + (e*(b*d-a*e)^3*(d+e*x)^(5/2))+16/315*b^2*(b*B*d+8*A*b*e-9*a*B*e)*_ + sqrt(a+b*x)/(e*(b*d-a*e)^4*(d+e*x)^(3/2))+_ + 32/315*b^3*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (1067) +--R 4 3 4 4 3 4 +--R ((- 256A b + 288B a b )e - 32B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (128A a b - 144B a b )e + (- 1152A b + 1312B a b )d e +--R + +--R 4 2 2 +--R - 144B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 96A a b + 108B a b)e + (576A a b - 660B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 2016A b + 2340B a b )d e - 252B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (80A a b - 90B a )e + (- 432A a b + 496B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1008A a b - 1188B a b )d e + (- 1680A b + 2016B a b )d e +--R + +--R 4 4 +--R - 210B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 70A a e + (360A a b - 20B a )d e + (- 756A a b + 108B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (840A a b - 252B a b )d e + (- 630A b + 420B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 9 4 8 3 2 2 7 2 3 3 6 4 4 5 +--R 315a e - 1575a b d e + 3150a b d e - 3150a b d e + 1575a b d e +--R + +--R 5 5 4 +--R - 315b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 +--R 1260a d e - 6300a b d e + 12600a b d e - 12600a b d e +--R + +--R 4 5 4 5 6 3 +--R 6300a b d e - 1260b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 +--R 1890a d e - 9450a b d e + 18900a b d e - 18900a b d e +--R + +--R 4 6 3 5 7 2 +--R 9450a b d e - 1890b d e +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 +--R 1260a d e - 6300a b d e + 12600a b d e - 12600a b d e +--R + +--R 4 7 2 5 8 +--R 6300a b d e - 1260b d e +--R * +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 4 8 +--R 315a d e - 1575a b d e + 3150a b d e - 3150a b d e + 1575a b d e +--R + +--R 5 9 +--R - 315b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1068) +--R 4 3 5 4 4 6 3 4 +--R ((- 768A b + 864B a b )d e - 96B b d e )x +--R + +--R 3 2 2 5 4 4 3 6 3 +--R (384A a b - 432B a b )d e + (- 3456A b + 3936B a b )d e +--R + +--R 4 7 2 +--R - 432B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (- 288A a b + 324B a b)d e + (1728A a b - 1980B a b )d e +--R + +--R 4 3 7 2 4 8 +--R (- 6048A b + 7020B a b )d e - 756B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 4 2 2 3 6 3 +--R (240A a b - 270B a )d e + (- 1296A a b + 1488B a b)d e +--R + +--R 3 2 2 7 2 4 3 8 +--R (3024A a b - 3564B a b )d e + (- 5040A b + 6048B a b )d e +--R + +--R 4 9 +--R - 630B b d +--R * +--R x +--R + +--R 4 5 4 3 4 6 3 +--R - 210A a d e + (1080A a b - 60B a )d e +--R + +--R 2 2 3 7 2 3 2 2 8 +--R (- 2268A a b + 324B a b)d e + (2520A a b - 756B a b )d e +--R + +--R 4 3 9 +--R (- 1890A b + 1260B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 9 +--R (- 35A a d - 315A a )e +--R + +--R 3 4 2 4 5 8 +--R ((180A a b - 10B a )d + (1620A a b - 90B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 7 +--R ((- 378A a b + 54B a b)d + (- 3402A a b + 486B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 6 +--R ((420A a b - 126B a b )d + (3780A a b - 1134B a b )d )e +--R + +--R 4 3 5 4 2 3 4 5 +--R ((- 315A b + 210B a b )d + (- 2835A a b + 1890B a b )d )e +--R * +--R 5 +--R x +--R + +--R 4 2 5 8 +--R (- 175A a d - 1575A a d)e +--R + +--R 3 4 3 4 5 2 7 +--R ((900A a b - 50B a )d + (8100A a b - 450B a )d )e +--R + +--R 2 2 3 4 3 2 4 3 6 +--R ((- 1890A a b + 270B a b)d + (- 17010A a b + 2430B a b)d )e +--R + +--R 3 2 2 5 2 3 3 2 4 5 +--R ((2100A a b - 630B a b )d + (18900A a b - 5670B a b )d )e +--R + +--R 4 3 6 4 2 3 5 4 +--R ((- 1575A b + 1050B a b )d + (- 14175A a b + 9450B a b )d )e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (- 350A a d - 3150A a d )e +--R + +--R 3 4 4 4 5 3 6 +--R ((1800A a b - 100B a )d + (16200A a b - 900B a )d )e +--R + +--R 2 2 3 5 3 2 4 4 5 +--R ((- 3780A a b + 540B a b)d + (- 34020A a b + 4860B a b)d )e +--R + +--R 3 2 2 6 2 3 3 2 5 4 +--R ((4200A a b - 1260B a b )d + (37800A a b - 11340B a b )d )e +--R + +--R 4 3 7 4 2 3 6 3 +--R ((- 3150A b + 2100B a b )d + (- 28350A a b + 18900B a b )d )e +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 6 +--R (- 350A a d - 3150A a d )e +--R + +--R 3 4 5 4 5 4 5 +--R ((1800A a b - 100B a )d + (16200A a b - 900B a )d )e +--R + +--R 2 2 3 6 3 2 4 5 4 +--R ((- 3780A a b + 540B a b)d + (- 34020A a b + 4860B a b)d )e +--R + +--R 3 2 2 7 2 3 3 2 6 3 +--R ((4200A a b - 1260B a b )d + (37800A a b - 11340B a b )d )e +--R + +--R 4 3 8 4 2 3 7 2 +--R ((- 3150A b + 2100B a b )d + (- 28350A a b + 18900B a b )d )e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 5 +--R (- 175A a d - 1575A a d )e +--R + +--R 3 4 6 4 5 5 4 +--R ((900A a b - 50B a )d + (8100A a b - 450B a )d )e +--R + +--R 2 2 3 7 3 2 4 6 3 +--R ((- 1890A a b + 270B a b)d + (- 17010A a b + 2430B a b)d )e +--R + +--R 3 2 2 8 2 3 3 2 7 2 +--R ((2100A a b - 630B a b )d + (18900A a b - 5670B a b )d )e +--R + +--R 4 3 9 4 2 3 8 +--R ((- 1575A b + 1050B a b )d + (- 14175A a b + 9450B a b )d )e +--R * +--R x +--R + +--R 4 6 5 5 4 +--R (- 35A a d - 315A a d )e +--R + +--R 3 4 7 4 5 6 3 +--R ((180A a b - 10B a )d + (1620A a b - 90B a )d )e +--R + +--R 2 2 3 8 3 2 4 7 2 +--R ((- 378A a b + 54B a b)d + (- 3402A a b + 486B a b)d )e +--R + +--R 3 2 2 9 2 3 3 2 8 +--R ((420A a b - 126B a b )d + (3780A a b - 1134B a b )d )e +--R + +--R 4 3 10 4 2 3 9 +--R (- 315A b + 210B a b )d + (- 2835A a b + 1890B a b )d +--R / +--R 5 5 10 4 6 9 3 2 7 8 2 3 8 7 +--R 945a d e - 4725a b d e + 9450a b d e - 9450a b d e +--R + +--R 4 9 6 5 10 5 +--R 4725a b d e - 945b d e +--R * +--R 5 +--R x +--R + +--R 5 6 9 4 7 8 3 2 8 7 2 3 9 6 +--R 4725a d e - 23625a b d e + 47250a b d e - 47250a b d e +--R + +--R 4 10 5 5 11 4 +--R 23625a b d e - 4725b d e +--R * +--R 4 +--R x +--R + +--R 5 7 8 4 8 7 3 2 9 6 2 3 10 5 +--R 9450a d e - 47250a b d e + 94500a b d e - 94500a b d e +--R + +--R 4 11 4 5 12 3 +--R 47250a b d e - 9450b d e +--R * +--R 3 +--R x +--R + +--R 5 8 7 4 9 6 3 2 10 5 2 3 11 4 +--R 9450a d e - 47250a b d e + 94500a b d e - 94500a b d e +--R + +--R 4 12 3 5 13 2 +--R 47250a b d e - 9450b d e +--R * +--R 2 +--R x +--R + +--R 5 9 6 4 10 5 3 2 11 4 2 3 12 3 +--R 4725a d e - 23625a b d e + 47250a b d e - 47250a b d e +--R + +--R 4 13 2 5 14 +--R 23625a b d e - 4725b d e +--R * +--R x +--R + +--R 5 10 5 4 11 4 3 2 12 3 2 3 13 2 4 14 +--R 945a d e - 4725a b d e + 9450a b d e - 9450a b d e + 4725a b d e +--R + +--R 5 15 +--R - 945b d +--R Type: Union(Expression(Integer),...) +--E 1146 + +--S 1147 of 1293 +m0:=a0-r0 +--R +--R +--R (1069) +--R 4 5 4 +--R (- 35A a d - 315A a )e +--R + +--R 3 4 2 4 5 3 +--R ((180A a b - 10B a )d + (1620A a b - 90B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 2 +--R ((- 378A a b + 54B a b)d + (- 3402A a b + 486B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R ((420A a b - 126B a b )d + (3780A a b - 1134B a b )d )e +--R + +--R 4 3 5 4 2 3 4 +--R (- 315A b + 210B a b )d + (- 2835A a b + 1890B a b )d +--R / +--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2 4 9 +--R 945a d e - 4725a b d e + 9450a b d e - 9450a b d e + 4725a b d e +--R + +--R 5 10 +--R - 945b d +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1293 +d0:=D(m0,x) +--R +--R +--R (1070) 0 +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1071) ---------------------------------------------------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1293 +r0:=5/8*(b*d-a*e)^2*(b*B*d+6*A*b*e-7*a*B*e)*_ + atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*sqrt(e))-_ + 2*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*sqrt(a+b*x))+_ + 5/12*(b*B*d+6*A*b*e-7*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/b^3+_ + 1/3*(b*B*d+6*A*b*e-7*a*B*e)*(d+e*x)^(5/2)*sqrt(a+b*x)/(b^2*(b*d-a*e))+_ + 5/8*(b*d-a*e)*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/b^4 +--R +--R +--R (1072) +--R 2 3 3 2 2 2 +--R (90A a b - 105B a )e + (- 180A a b + 225B a b)d e +--R + +--R 3 2 2 3 3 +--R (90A b - 135B a b )d e + 15B b d +--R * +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((12A b - 14B a b )e + 26B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 30A a b + 35B a b)e + (54A b - 68B a b )d e + 33B b d )x +--R + +--R 2 3 2 2 2 +--R (- 90A a b + 105B a )e + (150A a b - 190B a b)d e +--R + +--R 3 2 2 +--R (- 48A b + 81B a b )d +--R * +--R +-+ +-+ +-------+ +--R \|b \|e \|e x + d +--R / +--R 4 +-+ +-+ +-------+ +--R 24b \|b \|e \|b x + a +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1293 +--a0:=integrate(t0,x) +--E 1151 + +--S 1152 of 1293 +--m0:=a0-r0 +--E 1152 + +--S 1153 of 1293 +--d0:=D(m0,x) +--E 1153 + +--S 1154 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1073) --------------------------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1293 +r0:=3/4*(b*d-a*e)*(b*B*d+4*A*b*e-5*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*sqrt(e))-2*(A*b-a*B)*(d+e*x)^(5/2)/_ + (b*(b*d-a*e)*sqrt(a+b*x))+1/2*(b*B*d+4*A*b*e-5*a*B*e)*(d+e*x)^(3/2)*_ + sqrt(a+b*x)/(b^2*(b*d-a*e))+3/4*(b*B*d+4*A*b*e-5*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/b^3 +--R +--R +--R (1074) +--R 2 2 2 2 2 +-------+ +--R ((- 12A a b + 15B a )e + (12A b - 18B a b)d e + 3B b d )\|b x + a +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((4A b - 5B a b)e + 5B b d)x + (12A a b - 15B a )e +--R + +--R 2 +--R (- 8A b + 13B a b)d +--R * +--R +-+ +-+ +-------+ +--R \|b \|e \|e x + d +--R / +--R 3 +-+ +-+ +-------+ +--R 4b \|b \|e \|b x + a +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1293 +--a0:=integrate(t0,x) +--E 1156 + +--S 1157 of 1293 +--m0:=a0-r0 +--E 1157 + +--S 1158 of 1293 +--d0:=D(m0,x) +--E 1158 + +--S 1159 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1075) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1293 +r0:=(b*B*d+2*A*b*e-3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*sqrt(e))-2*(A*b-a*B)*(d+e*x)^(3/2)/_ + (b*(b*d-a*e)*sqrt(a+b*x))+(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)) +--R +--R +--R (1076) +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R ((2A b - 3B a)e + B b d)\|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +--R (B b x - 2A b + 3B a)\|b \|e \|e x + d +--R / +--R 2 +-+ +-+ +-------+ +--R b \|b \|e \|b x + a +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1293 +--a0:=integrate(t0,x) +--E 1161 + +--S 1162 of 1293 +--m0:=a0-r0 +--E 1162 + +--S 1163 of 1293 +--d0:=D(m0,x) +--E 1163 + +--S 1164 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1077) ----------------------------- +--R +-------+ +-------+ +--R (b x + a)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1293 +r0:=2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/_ + (b^(3/2)*sqrt(e))-2*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*sqrt(a+b*x)) +--R +--R +--R (1078) +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R (2B a e - 2B b d)\|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +--R (2A b - 2B a)\|b \|e \|e x + d +--R / +--R 2 +-+ +-+ +-------+ +--R (a b e - b d)\|b \|e \|b x + a +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1293 +--a0:=integrate(t0,x) +--E 1166 + +--S 1167 of 1293 +--m0:=a0-r0 +--E 1167 + +--S 1168 of 1293 +--d0:=D(m0,x) +--E 1168 + +--S 1169 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(3/2)) +--R +--R +--R B x + A +--R (1079) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b e x + (a e + b d)x + a d)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1293 +r0:=-2*(B*d-A*e)/(e*(b*d-a*e)*sqrt(a+b*x)*sqrt(d+e*x))+_ + 2*(b*B*d-2*A*b*e+a*B*e)*sqrt(d+e*x)/(e*(b*d-a*e)^2*sqrt(a+b*x)) +--R +--R +--R ((- 4A b + 2B a)e + 2B b d)x - 2A a e + (- 2A b + 4B a)d +--R (1080) -------------------------------------------------------- +--R 2 2 2 2 +-------+ +-------+ +--R (a e - 2a b d e + b d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1081) +--R 2 2 2 +--R ((- 12A a b + 6B a )d e + 6B a b d )x - 6A a d e +--R + +--R 2 2 +--R (- 6A a b + 12B a )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 2 +--R (- A a b d - 9A a b)e +--R + +--R 2 2 2 2 +--R ((- A b + 2B a b)d + (- 9A a b + 18B a b)d)e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R (- A a d - 9A a )e + ((- 2A a b + 2B a )d + (- 18A a b + 18B a )d)e +--R + +--R 2 3 2 2 2 +--R (- A b + 2B a b)d + (- 9A a b + 18B a b)d +--R * +--R x +--R + +--R 2 2 3 2 3 2 3 2 +--R (- A a d - 9A a d)e + (- A a b + 2B a )d + (- 9A a b + 18B a )d +--R / +--R 3 3 2 2 2 2 3 3 2 +--R (3a b d e - 6a b d e + 3a b d e)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 2 2 4 +--R (3a d e - 3a b d e - 3a b d e + 3a b d )x + 3a d e - 6a b d e + 3a b d +--R Type: Union(Expression(Integer),...) +--E 1171 + +--S 1172 of 1293 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R (- A a d - 9A a )e + (- A b + 2B a)d + (- 9A a b + 18B a )d +--R (1082) ------------------------------------------------------------ +--R 3 2 2 2 2 3 +--R 3a d e - 6a b d e + 3a b d +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1293 +d0:=D(m0,x) +--R +--R +--R (1083) 0 +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(5/2)) +--R +--R +--R (1084) +--R B x + A +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1293 +r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a+b*x))+_ + 2/3*(b*B*d-4*A*b*e+3*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+_ + 4/3*(b*B*d-4*A*b*e+3*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (1085) +--R 2 2 2 2 +--R ((16A b - 12B a b)e - 4B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((8A a b - 6B a )e + (24A b - 20B a b)d e - 6B b d )x - 2A a e +--R + +--R 2 2 2 +--R (12A a b - 4B a )d e + (6A b - 12B a b)d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a e - 9a b d e + 9a b d e - 3b d e)x + 3a d e - 9a b d e +--R + +--R 2 3 3 4 +--R 9a b d e - 3b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1086) +--R 2 2 2 2 2 3 2 +--R ((64A a b - 48B a b)d e - 16B a b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 +--R ((32A a b - 24B a )d e + (96A a b - 80B a b)d e - 24B a b d )x +--R + +--R 3 2 2 2 3 3 2 2 4 +--R - 8A a d e + (48A a b - 16B a )d e + (24A a b - 48B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 3 4 +--R (A a b d + 16A a b)e +--R + +--R 2 2 2 2 2 3 3 +--R ((- 6A a b + 2B a b)d + (- 96A a b + 32B a b)d)e +--R + +--R 3 2 3 3 2 2 2 2 +--R ((- 3A b + 6B a b )d + (- 48A a b + 96B a b )d )e +--R * +--R 3 +--R x +--R + +--R 3 4 4 2 3 2 3 4 3 +--R (A a d + 16A a )e + ((- 4A a b + 2B a )d + (- 64A a b + 32B a )d)e +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 15A a b + 10B a b)d + (- 240A a b + 160B a b)d )e +--R + +--R 3 2 4 3 2 2 3 +--R ((- 6A b + 12B a b )d + (- 96A a b + 192B a b )d )e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 +--R (2A a d + 32A a d)e +--R + +--R 2 3 3 3 4 2 2 +--R ((- 11A a b + 4B a )d + (- 176A a b + 64B a )d )e +--R + +--R 2 2 4 2 2 3 3 +--R ((- 12A a b + 14B a b)d + (- 192A a b + 224B a b)d )e +--R + +--R 3 2 5 3 2 2 4 +--R (- 3A b + 6B a b )d + (- 48A a b + 96B a b )d +--R * +--R x +--R + +--R 3 3 4 2 2 2 3 4 3 4 3 +--R (A a d + 16A a d )e + ((- 6A a b + 2B a )d + (- 96A a b + 32B a )d )e +--R + +--R 2 2 5 2 2 3 4 +--R (- 3A a b + 6B a b)d + (- 48A a b + 96B a b)d +--R / +--R 4 2 5 3 2 3 4 2 3 4 3 4 5 2 3 +--R (12a b d e - 36a b d e + 36a b d e - 12a b d e )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (12a d e - 12a b d e - 36a b d e + 60a b d e - 24a b d e)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (24a d e - 60a b d e + 36a b d e + 12a b d e - 12a b d )x + 12a d e +--R + +--R 4 5 2 3 2 6 2 3 7 +--R - 36a b d e + 36a b d e - 12a b d +--R Type: Union(Expression(Integer),...) +--E 1176 + +--S 1177 of 1293 +m0:=a0-r0 +--R +--R +--R (1087) +--R 2 3 2 2 2 2 3 +--R (A a d + 16A a )e + ((- 6A a b + 2B a )d + (- 96A a b + 32B a )d)e +--R + +--R 2 3 2 2 2 +--R (- 3A b + 6B a b)d + (- 48A a b + 96B a b)d +--R / +--R 4 2 3 3 3 2 2 2 4 3 5 +--R 12a d e - 36a b d e + 36a b d e - 12a b d +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1293 +d0:=D(m0,x) +--R +--R +--R (1088) 0 +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(7/2)) +--R +--R +--R (1089) +--R B x + A +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1293 +r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a+b*x))+_ + 2/5*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + 8/15*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*(d+e*x)^(3/2))+_ + 16/15*b*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (1090) +--R 3 2 3 3 2 3 +--R ((- 96A b + 80B a b )e + 16B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 48A a b + 40B a b)e + (- 240A b + 208B a b )d e + 40B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (12A a b - 10B a )e + (- 120A a b + 98B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 180A b + 170B a b )d e + 30B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (30A a b - 4B a )d e + (- 90A a b + 40B a b)d e +--R + +--R 3 2 3 +--R (- 30A b + 60B a b )d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (15a e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a d e - 120a b d e + 180a b d e - 120a b d e + 30b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1091) +--R 3 2 2 3 3 3 4 2 3 +--R ((- 96A a b + 80B a b )d e + 16B a b d e )x +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (- 48A a b + 40B a b)d e + (- 240A a b + 208B a b )d e +--R + +--R 3 5 +--R 40B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 3 3 2 2 3 4 2 +--R (12A a b - 10B a )d e + (- 120A a b + 98B a b)d e +--R + +--R 3 2 2 5 3 6 +--R (- 180A a b + 170B a b )d e + 30B a b d +--R * +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R - 6A a d e + (30A a b - 4B a )d e + (- 90A a b + 40B a b)d e +--R + +--R 3 2 2 6 +--R (- 30A a b + 60B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 4 6 +--R (3A a b d + 3A a b)e +--R + +--R 2 2 3 2 3 2 4 5 +--R ((- 15A a b + 2B a b)d + (- 15A a b + 2B a b)d)e +--R + +--R 3 2 2 3 2 3 3 2 2 4 +--R ((45A a b - 20B a b )d + (45A a b - 20B a b )d )e +--R + +--R 4 3 4 4 2 3 3 3 +--R ((15A b - 30B a b )d + (15A a b - 30B a b )d )e +--R * +--R 4 +--R x +--R + +--R 4 5 6 3 4 2 4 5 5 +--R (3A a d + 3A a )e + ((- 6A a b + 2B a )d + (- 6A a b + 2B a )d)e +--R + +--R 3 3 4 2 4 +--R (- 14B a b d - 14B a b d )e +--R + +--R 3 2 2 4 2 3 3 2 3 3 +--R ((150A a b - 90B a b )d + (150A a b - 90B a b )d )e +--R + +--R 4 3 5 4 2 3 4 2 +--R ((45A b - 90B a b )d + (45A a b - 90B a b )d )e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 +--R (9A a d + 9A a d)e +--R + +--R 3 4 3 4 5 2 4 +--R ((- 36A a b + 6B a )d + (- 36A a b + 6B a )d )e +--R + +--R 2 2 3 4 3 2 4 3 3 +--R ((90A a b - 54B a b)d + (90A a b - 54B a b)d )e +--R + +--R 3 2 2 5 2 3 3 2 4 2 +--R ((180A a b - 150B a b )d + (180A a b - 150B a b )d )e +--R + +--R 4 3 6 4 2 3 5 +--R ((45A b - 90B a b )d + (45A a b - 90B a b )d )e +--R * +--R 2 +--R x +--R + +--R 4 3 5 2 4 +--R (9A a d + 9A a d )e +--R + +--R 3 4 4 4 5 3 3 +--R ((- 42A a b + 6B a )d + (- 42A a b + 6B a )d )e +--R + +--R 2 2 3 5 3 2 4 4 2 +--R ((120A a b - 58B a b)d + (120A a b - 58B a b)d )e +--R + +--R 3 2 2 6 2 3 3 2 5 +--R ((90A a b - 110B a b )d + (90A a b - 110B a b )d )e +--R + +--R 4 3 7 4 2 3 6 +--R (15A b - 30B a b )d + (15A a b - 30B a b )d +--R * +--R x +--R + +--R 4 4 5 3 3 3 4 5 4 5 4 2 +--R (3A a d + 3A a d )e + ((- 15A a b + 2B a )d + (- 15A a b + 2B a )d )e +--R + +--R 2 2 3 6 3 2 4 5 +--R ((45A a b - 20B a b)d + (45A a b - 20B a b)d )e +--R + +--R 3 2 2 7 2 3 3 2 6 +--R (15A a b - 30B a b )d + (15A a b - 30B a b )d +--R / +--R 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 5 7 3 4 +--R (15a b d e - 60a b d e + 90a b d e - 60a b d e + 15a b d e )x +--R + +--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4 2 4 7 3 +--R 15a d e - 15a b d e - 90a b d e + 210a b d e - 165a b d e +--R + +--R 5 8 2 +--R 45a b d e +--R * +--R 3 +--R x +--R + +--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2 +--R 45a d e - 135a b d e + 90a b d e + 90a b d e - 135a b d e +--R + +--R 5 9 +--R 45a b d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 2 4 9 +--R 45a d e - 165a b d e + 210a b d e - 90a b d e - 15a b d e +--R + +--R 5 10 +--R 15a b d +--R * +--R x +--R + +--R 6 6 4 5 7 3 4 2 8 2 3 3 9 2 4 10 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R Type: Union(Expression(Integer),...) +--E 1181 + +--S 1182 of 1293 +m0:=a0-r0 +--R +--R +--R (1092) +--R 3 4 3 2 3 2 3 4 2 +--R (3A a d + 3A a )e + ((- 15A a b + 2B a )d + (- 15A a b + 2B a )d)e +--R + +--R 2 2 3 2 2 3 2 +--R ((45A a b - 20B a b)d + (45A a b - 20B a b)d )e +--R + +--R 3 2 4 3 2 2 3 +--R (15A b - 30B a b )d + (15A a b - 30B a b )d +--R / +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1293 +d0:=D(m0,x) +--R +--R +--R (1093) 0 +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(9/2)) +--R +--R +--R (1094) +--R B x + A +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1293 +r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a+b*x))+_ + 2/7*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(7/2))+_ + 12/35*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*(d+e*x)^(5/2))+_ + 16/35*b*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2))+_ + 32/35*b^2*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (1095) +--R 4 3 4 4 3 4 +--R ((256A b - 224B a b )e - 32B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((128A a b - 112B a b )e + (896A b - 800B a b )d e - 112B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 32A a b + 28B a b)e + (448A a b - 388B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (1120A b - 1036B a b )d e - 140B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (16A a b - 14B a )e + (- 112A a b + 96B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (560A a b - 476B a b )d e + (560A b - 560B a b )d e - 70B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 10A a e + (56A a b - 4B a )d e + (- 140A a b + 28B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (280A a b - 140B a b )d e + (70A b - 140B a b )d +--R / +--R 5 8 4 7 3 2 2 6 2 3 3 5 4 4 4 +--R 35a e - 175a b d e + 350a b d e - 350a b d e + 175a b d e +--R + +--R 5 5 3 +--R - 35b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 4 5 3 +--R 105a d e - 525a b d e + 1050a b d e - 1050a b d e + 525a b d e +--R + +--R 5 6 2 +--R - 105b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 4 6 2 +--R 105a d e - 525a b d e + 1050a b d e - 1050a b d e + 525a b d e +--R + +--R 5 7 +--R - 105b d e +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 4 7 5 8 +--R 35a d e - 175a b d e + 350a b d e - 350a b d e + 175a b d e - 35b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1096) +--R 4 2 3 4 4 4 5 3 4 +--R ((256A a b - 224B a b )d e - 32B a b d e )x +--R + +--R 2 3 3 2 4 4 4 2 3 5 3 +--R (128A a b - 112B a b )d e + (896A a b - 800B a b )d e +--R + +--R 4 6 2 +--R - 112B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 4 2 3 3 2 5 3 +--R (- 32A a b + 28B a b)d e + (448A a b - 388B a b )d e +--R + +--R 4 2 3 6 2 4 7 +--R (1120A a b - 1036B a b )d e - 140B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 4 4 3 2 4 5 3 +--R (16A a b - 14B a )d e + (- 112A a b + 96B a b)d e +--R + +--R 2 3 3 2 6 2 4 2 3 7 +--R (560A a b - 476B a b )d e + (560A a b - 560B a b )d e +--R + +--R 4 8 +--R - 70B a b d +--R * +--R x +--R + +--R 5 4 4 4 5 5 3 3 2 4 6 2 +--R - 10A a d e + (56A a b - 4B a )d e + (- 140A a b + 28B a b)d e +--R + +--R 2 3 3 2 7 4 2 3 8 +--R (280A a b - 140B a b )d e + (70A a b - 140B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 8 +--R (5A a b d + 5A a b)e +--R + +--R 3 2 4 2 4 2 5 7 +--R ((- 28A a b + 2B a b)d + (- 28A a b + 2B a b)d)e +--R + +--R 2 3 3 2 3 3 3 4 2 2 6 +--R ((70A a b - 14B a b )d + (70A a b - 14B a b )d )e +--R + +--R 4 2 3 4 2 4 3 3 3 5 +--R ((- 140A a b + 70B a b )d + (- 140A a b + 70B a b )d )e +--R + +--R 5 4 5 5 2 4 4 4 +--R ((- 35A b + 70B a b )d + (- 35A a b + 70B a b )d )e +--R * +--R 5 +--R x +--R + +--R 5 6 8 4 5 2 5 6 7 +--R (5A a d + 5A a )e + ((- 8A a b + 2B a )d + (- 8A a b + 2B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 6 +--R ((- 42A a b - 6B a b)d + (- 42A a b - 6B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 5 +--R ((140A a b + 14B a b )d + (140A a b + 14B a b )d )e +--R + +--R 4 2 3 5 2 4 3 3 4 4 +--R ((- 595A a b + 350B a b )d + (- 595A a b + 350B a b )d )e +--R + +--R 5 4 6 5 2 4 5 3 +--R ((- 140A b + 280B a b )d + (- 140A a b + 280B a b )d )e +--R * +--R 4 +--R x +--R + +--R 5 2 6 7 +--R (20A a d + 20A a d)e +--R + +--R 4 5 3 5 6 2 6 +--R ((- 82A a b + 8B a )d + (- 82A a b + 8B a )d )e +--R + +--R 3 2 4 4 4 2 5 3 5 +--R ((112A a b - 44B a b)d + (112A a b - 44B a b)d )e +--R + +--R 2 3 3 2 5 3 3 4 2 4 4 +--R ((- 140A a b + 196B a b )d + (- 140A a b + 196B a b )d )e +--R + +--R 4 2 3 6 2 4 3 3 5 3 +--R ((- 980A a b + 700B a b )d + (- 980A a b + 700B a b )d )e +--R + +--R 5 4 7 5 2 4 6 2 +--R ((- 210A b + 420B a b )d + (- 210A a b + 420B a b )d )e +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 6 +--R (30A a d + 30A a d )e +--R + +--R 4 5 4 5 6 3 5 +--R ((- 148A a b + 12B a )d + (- 148A a b + 12B a )d )e +--R + +--R 3 2 4 5 4 2 5 4 4 +--R ((308A a b - 76B a b)d + (308A a b - 76B a b)d )e +--R + +--R 2 3 3 2 6 3 3 4 2 5 3 +--R ((- 560A a b + 364B a b )d + (- 560A a b + 364B a b )d )e +--R + +--R 4 2 3 7 2 4 3 3 6 2 +--R ((- 770A a b + 700B a b )d + (- 770A a b + 700B a b )d )e +--R + +--R 5 4 8 5 2 4 7 +--R ((- 140A b + 280B a b )d + (- 140A a b + 280B a b )d )e +--R * +--R 2 +--R x +--R + +--R 5 4 6 3 5 +--R (20A a d + 20A a d )e +--R + +--R 4 5 5 5 6 4 4 +--R ((- 107A a b + 8B a )d + (- 107A a b + 8B a )d )e +--R + +--R 3 2 4 6 4 2 5 5 3 +--R ((252A a b - 54B a b)d + (252A a b - 54B a b)d )e +--R + +--R 2 3 3 2 7 3 3 4 2 6 2 +--R ((- 490A a b + 266B a b )d + (- 490A a b + 266B a b )d )e +--R + +--R 4 2 3 8 2 4 3 3 7 +--R ((- 280A a b + 350B a b )d + (- 280A a b + 350B a b )d )e +--R + +--R 5 4 9 5 2 4 8 +--R (- 35A b + 70B a b )d + (- 35A a b + 70B a b )d +--R * +--R x +--R + +--R 5 5 6 4 4 4 5 6 5 6 5 3 +--R (5A a d + 5A a d )e + ((- 28A a b + 2B a )d + (- 28A a b + 2B a )d )e +--R + +--R 3 2 4 7 4 2 5 6 2 +--R ((70A a b - 14B a b)d + (70A a b - 14B a b)d )e +--R + +--R 2 3 3 2 8 3 3 4 2 7 +--R ((- 140A a b + 70B a b )d + (- 140A a b + 70B a b )d )e +--R + +--R 4 2 3 9 2 4 3 3 8 +--R (- 35A a b + 70B a b )d + (- 35A a b + 70B a b )d +--R / +--R 6 4 9 5 2 5 8 4 3 6 7 3 4 7 6 2 5 8 5 +--R 35a b d e - 175a b d e + 350a b d e - 350a b d e + 175a b d e +--R + +--R 6 9 4 +--R - 35a b d e +--R * +--R 5 +--R x +--R + +--R 7 4 9 6 5 8 5 2 6 7 4 3 7 6 3 4 8 5 +--R 35a d e - 35a b d e - 350a b d e + 1050a b d e - 1225a b d e +--R + +--R 2 5 9 4 6 10 3 +--R 665a b d e - 140a b d e +--R * +--R 4 +--R x +--R + +--R 7 5 8 6 6 7 5 2 7 6 4 3 8 5 3 4 9 4 +--R 140a d e - 490a b d e + 350a b d e + 700a b d e - 1400a b d e +--R + +--R 2 5 10 3 6 11 2 +--R 910a b d e - 210a b d e +--R * +--R 3 +--R x +--R + +--R 7 6 7 6 7 6 5 2 8 5 4 3 9 4 3 4 10 3 +--R 210a d e - 910a b d e + 1400a b d e - 700a b d e - 350a b d e +--R + +--R 2 5 11 2 6 12 +--R 490a b d e - 140a b d e +--R * +--R 2 +--R x +--R + +--R 7 7 6 6 8 5 5 2 9 4 4 3 10 3 3 4 11 2 +--R 140a d e - 665a b d e + 1225a b d e - 1050a b d e + 350a b d e +--R + +--R 2 5 12 6 13 +--R 35a b d e - 35a b d +--R * +--R x +--R + +--R 7 8 5 6 9 4 5 2 10 3 4 3 11 2 3 4 12 +--R 35a d e - 175a b d e + 350a b d e - 350a b d e + 175a b d e +--R + +--R 2 5 13 +--R - 35a b d +--R Type: Union(Expression(Integer),...) +--E 1186 + +--S 1187 of 1293 +m0:=a0-r0 +--R +--R +--R (1097) +--R 4 5 4 3 4 2 4 5 3 +--R (5A a d + 5A a )e + ((- 28A a b + 2B a )d + (- 28A a b + 2B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 2 +--R ((70A a b - 14B a b)d + (70A a b - 14B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R ((- 140A a b + 70B a b )d + (- 140A a b + 70B a b )d )e +--R + +--R 4 3 5 4 2 3 4 +--R (- 35A b + 70B a b )d + (- 35A a b + 70B a b )d +--R / +--R 6 4 5 5 5 4 4 2 6 3 3 3 7 2 2 4 8 5 9 +--R 35a d e - 175a b d e + 350a b d e - 350a b d e + 175a b d e - 35a b d +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1293 +d0:=D(m0,x) +--R +--R +--R (1098) 0 +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1293 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^(5/2) +--R +--R +--R (1099) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1293 +r0:=-2/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ + 35/8*(b*d-a*e)^2*(b*B*d+2*A*b*e-3*a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(11/2)-_ + 2*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+_ + 35/12*e*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/b^4+_ + 7/3*e*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(5/2)*sqrt(a+b*x)/_ + (b^3*(b*d-a*e))+35/8*e*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/b^5 +--R +--R +--R (1100) +--R 2 2 3 3 3 2 2 2 +--R (210A a b - 315B a b)e + (- 420A a b + 735B a b )d e +--R + +--R 4 3 2 4 3 +--R (210A b - 525B a b )d e + 105B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 315B a )e + (- 420A a b + 735B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (210A a b - 525B a b )d e + 105B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|e \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 8B b e x + ((12A b - 18B a b )e + 38B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 42A a b + 63B a b )e + (78A b - 138B a b )d e + 87B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 280A a b + 420B a b)e + (476A a b - 854B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 160A b + 478B a b )d e - 48B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 315B a )e + (350A a b - 630B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 112A a b + 343B a b )d e + (- 16A b - 32B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 5 +-+ +-------+ +--R (24b x + 24a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1293 +--a0:=integrate(t0,x) +--E 1191 + +--S 1192 of 1293 +--m0:=a0-r0 +--E 1192 + +--S 1193 of 1293 +--d0:=D(m0,x) +--E 1193 + +--S 1194 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1101) ---------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1293 +r0:=-2/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ + 5/4*(b*d-a*e)*(3*b*B*d+4*A*b*e-7*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(9/2)-2/3*(3*b*B*d+4*A*b*e-7*a*B*e)*_ + (d+e*x)^(5/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+5/6*e*_ + (3*b*B*d+4*A*b*e-7*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/(b^3*(b*d-a*e))+_ + 5/4*e*(3*b*B*d+4*A*b*e-7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/b^4 +--R +--R +--R (1102) +--R 2 2 2 3 2 3 2 +--R ((- 60A a b + 105B a b)e + (60A b - 150B a b )d e + 45B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 60A a b + 105B a )e + (60A a b - 150B a b)d e + 45B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|e \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((12A b - 21B a b )e + 27B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((80A a b - 140B a b)e + (- 56A b + 158B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (60A a b - 105B a )e + (- 40A a b + 115B a b)d e +--R + +--R 3 2 2 +--R (- 8A b - 16B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 4 +-+ +-------+ +--R (12b x + 12a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1293 +--a0:=integrate(t0,x) +--E 1196 + +--S 1197 of 1293 +--m0:=a0-r0 +--E 1197 + +--S 1198 of 1293 +--d0:=D(m0,x) +--E 1198 + +--S 1199 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1103) --------------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1293 +r0:=-2/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ + (3*b*B*d+2*A*b*e-5*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(d+e*x)))*sqrt(e)/b^(7/2)-2/3*(3*b*B*d+2*A*b*e-5*a*B*e)*_ + (d+e*x)^(3/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+e*(3*b*B*d+2*A*b*e-5*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e)) +--R +--R +--R (1104) +--R 2 2 2 +-+ +--R (((6A b - 15B a b)e + 9B b d)x + (6A a b - 15B a )e + 9B a b d)\|e +--R * +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 +--R 3B b e x + ((- 8A b + 20B a b)e - 6B b d)x + (- 6A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 4B a b)d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1293 +--a0:=integrate(t0,x) +--E 1201 + +--S 1202 of 1293 +--m0:=a0-r0 +--E 1202 + +--S 1203 of 1293 +--d0:=D(m0,x) +--E 1203 + +--S 1204 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1105) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1293 +r0:=-2/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ + 2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(5/2)-_ + 2*B*sqrt(d+e*x)/(b^2*sqrt(a+b*x)) +--R +--R +--R (1106) +--R 2 2 +-+ +-------+ +--R ((6B a b e - 6B b d)x + 6B a e - 6B a b d)\|e \|b x + a +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 +-+ +-------+ +--R (((2A b - 8B a b)e + 6B b d)x - 6B a e + (2A b + 4B a b)d)\|b \|e x + d +--R / +--R 3 4 2 2 3 +-+ +-------+ +--R ((3a b e - 3b d)x + 3a b e - 3a b d)\|b \|b x + a +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1293 +--a0:=integrate(t0,x) +--E 1206 + +--S 1207 of 1293 +--m0:=a0-r0 +--E 1207 + +--S 1208 of 1293 +--d0:=D(m0,x) +--E 1208 + +--S 1209 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1107) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (b x + 2a b x + a )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1293 +r0:=-2/3*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^(3/2))-_ + 2/3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a+b*x)) +--R +--R +--R (1108) +--R +-------+ +--R (((4A b + 2B a)e - 6B b d)x + 6A a e + (- 2A b - 4B a)d)\|e x + d +--R ---------------------------------------------------------------------- +--R 2 2 2 3 2 3 2 2 2 2 +-------+ +--R ((3a b e - 6a b d e + 3b d )x + 3a e - 6a b d e + 3a b d )\|b x + a +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1109) +--R 2 3 2 3 2 3 +--R (((12A a b + 6B a )e - 18B a b d)x + 18A a e + (- 6A a b - 12B a )d) +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 2 2 3 2 2 +--R (3A a b d + 27A a b )e + (- A b - 2B a b )d +--R + +--R 3 2 2 +--R (- 9A a b - 18B a b )d +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 +--R (6A a b d + 54A a b)e + (- 2A a b - 4B a b)d +--R + +--R 2 2 3 +--R (- 18A a b - 36B a b)d +--R * +--R x +--R + +--R 3 4 2 3 2 3 4 +--R (3A a d + 27A a )e + (- A a b - 2B a )d + (- 9A a b - 18B a )d +--R / +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (9a b e - 18a b d e + 9a b d )x + (18a b e - 36a b d e + 18a b d )x +--R + +--R 6 2 5 4 2 2 +--R 9a e - 18a b d e + 9a b d +--R Type: Union(Expression(Integer),...) +--E 1211 + +--S 1212 of 1293 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R (3A a d + 27A a )e + (- A b - 2B a)d + (- 9A a b - 18B a )d +--R (1110) ------------------------------------------------------------ +--R 4 2 3 2 2 2 +--R 9a e - 18a b d e + 9a b d +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1293 +d0:=D(m0,x) +--R +--R +--R (1111) 0 +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(3/2)) +--R +--R +--R (1112) +--R B x + A +--R ----------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1293 +r0:=-2*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*sqrt(d+e*x))+_ + 2/3*(3*b*B*d-4*A*b*e+a*B*e)*sqrt(d+e*x)/(e*(b*d-a*e)^2*(a+b*x)^(3/2))-_ + 4/3*(3*b*B*d-4*A*b*e+a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a+b*x)) +--R +--R +--R (1113) +--R 2 2 2 2 +--R ((- 16A b + 4B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 24A a b + 6B a )e + (- 8A b + 20B a b)d e + 6B b d )x - 6A a e +--R + +--R 2 2 2 +--R (- 12A a b + 12B a )d e + (2A b + 4B a b)d +--R / +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d )x + 3a e - 9a b d e +--R + +--R 2 2 2 3 3 +--R 9a b d e - 3a b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1114) +--R 2 2 3 2 2 2 2 2 +--R ((- 16A a b + 4B a b)d e + 12B a b d e)x +--R + +--R 3 4 2 2 2 3 2 2 2 3 +--R ((- 24A a b + 6B a )d e + (- 8A a b + 20B a b)d e + 6B a b d )x +--R + +--R 4 2 3 4 2 2 2 3 3 +--R - 6A a d e + (- 12A a b + 12B a )d e + (2A a b + 4B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 2 3 2 3 +--R (3A a b d + 3A a b )e +--R + +--R 3 2 2 2 2 3 3 2 2 +--R ((6A a b - 6B a b )d + (6A a b - 6B a b )d)e +--R + +--R 4 3 3 4 2 3 2 +--R ((- A b - 2B a b )d + (- A a b - 2B a b )d )e +--R * +--R 3 +--R x +--R + +--R 3 4 3 +--R (6A a b d + 6A a b)e +--R + +--R 2 2 3 2 3 2 4 2 +--R ((15A a b - 12B a b)d + (15A a b - 12B a b)d)e +--R + +--R 3 2 2 3 2 3 3 2 2 +--R ((4A a b - 10B a b )d + (4A a b - 10B a b )d )e +--R + +--R 4 3 4 4 2 3 3 +--R (- A b - 2B a b )d + (- A a b - 2B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 4 2 4 5 2 +--R (3A a d + 3A a )e + ((12A a b - 6B a )d + (12A a b - 6B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 +--R ((11A a b - 14B a b)d + (11A a b - 14B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R (- 2A a b - 4B a b )d + (- 2A a b - 4B a b )d +--R * +--R x +--R + +--R 4 2 5 2 3 4 3 4 5 2 +--R (3A a d + 3A a d)e + ((6A a b - 6B a )d + (6A a b - 6B a )d )e +--R + +--R 2 2 3 4 3 2 4 3 +--R (- A a b - 2B a b)d + (- A a b - 2B a b)d +--R / +--R 5 2 4 4 3 2 3 3 4 3 2 2 5 4 3 +--R (3a b d e - 9a b d e + 9a b d e - 3a b d e)x +--R + +--R 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 2 +--R (6a b d e - 15a b d e + 9a b d e + 3a b d e - 3a b d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 7 2 3 +--R (3a d e - 3a b d e - 9a b d e + 15a b d e - 6a b d )x + 3a d e +--R + +--R 6 3 2 5 2 4 4 3 5 +--R - 9a b d e + 9a b d e - 3a b d +--R Type: Union(Expression(Integer),...) +--E 1216 + +--S 1217 of 1293 +m0:=a0-r0 +--R +--R +--R (1115) +--R 2 3 2 2 2 2 3 +--R (3A a d + 3A a )e + ((6A a b - 6B a )d + (6A a b - 6B a )d)e +--R + +--R 2 3 2 2 2 +--R (- A b - 2B a b)d + (- A a b - 2B a b)d +--R / +--R 5 3 4 2 2 3 2 3 2 3 4 +--R 3a d e - 9a b d e + 9a b d e - 3a b d +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 1293 +d0:=D(m0,x) +--R +--R +--R (1116) 0 +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(5/2)) +--R +--R +--R (1117) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1293 +r0:=-2/3*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2))+_ + 2/3*(b*B*d-2*A*b*e+a*B*e)/(e*(b*d-a*e)^2*(a+b*x)^(3/2)*sqrt(d+e*x))-_ + 8/3*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*sqrt(a+b*x)*sqrt(d+e*x))-_ + 16/3*e*(b*B*d-2*A*b*e+a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (1118) +--R 3 2 3 3 2 3 +--R ((32A b - 16B a b )e - 16B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((48A a b - 24B a b)e + (48A b - 48B a b )d e - 24B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (12A a b - 6B a )e + (72A a b - 42B a b)d e +--R + +--R 3 2 2 3 3 +--R (12A b - 42B a b )d e - 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (18A a b - 4B a )d e + (18A a b - 24B a b)d e +--R + +--R 3 2 3 +--R (- 2A b - 4B a b )d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b e - 12a b d e + 18a b d e - 12a b d e + 3b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a e - 9a b d e + 6a b d e + 6a b d e - 9a b d e + 3b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a d e - 12a b d e + 18a b d e - 12a b d e + 3a b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1119) +--R 2 3 3 2 2 3 2 3 3 2 3 +--R ((160A a b - 80B a b )d e - 80B a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (240A a b - 120B a b)d e + (240A a b - 240B a b )d e +--R + +--R 2 3 4 +--R - 120B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 2 3 3 2 4 3 2 +--R (60A a b - 30B a )d e + (360A a b - 210B a b)d e +--R + +--R 2 3 3 2 4 2 3 5 +--R (60A a b - 210B a b )d e - 30B a b d +--R * +--R x +--R + +--R 5 2 3 4 5 3 2 3 2 4 4 +--R - 10A a d e + (90A a b - 20B a )d e + (90A a b - 120B a b)d e +--R + +--R 2 3 3 2 5 +--R (- 10A a b - 20B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 2 4 2 5 +--R (- A a b d - 25A a b )e +--R + +--R 2 3 3 2 2 3 3 4 2 4 +--R ((9A a b - 2B a b )d + (225A a b - 50B a b )d)e +--R + +--R 4 2 3 3 2 4 3 3 2 3 +--R ((9A a b - 12B a b )d + (225A a b - 300B a b )d )e +--R + +--R 5 4 4 5 2 4 3 2 +--R ((- A b - 2B a b )d + (- 25A a b - 50B a b )d )e +--R * +--R 4 +--R x +--R + +--R 4 5 5 +--R (- 2A a b d - 50A a b)e +--R + +--R 3 2 4 2 4 2 5 4 +--R ((16A a b - 4B a b)d + (400A a b - 100B a b)d)e +--R + +--R 2 3 3 2 3 3 3 4 2 2 3 +--R ((36A a b - 28B a b )d + (900A a b - 700B a b )d )e +--R + +--R 4 2 3 4 2 4 3 3 3 2 +--R ((16A a b - 28B a b )d + (400A a b - 700B a b )d )e +--R + +--R 5 4 5 5 2 4 4 +--R ((- 2A b - 4B a b )d + (- 50A a b - 100B a b )d )e +--R * +--R 3 +--R x +--R + +--R 5 6 5 4 5 2 5 6 4 +--R (- A a d - 25A a )e + ((5A a b - 2B a )d + (125A a b - 50B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 3 +--R ((44A a b - 20B a b)d + (1100A a b - 500B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 2 +--R ((44A a b - 52B a b )d + (1100A a b - 1300B a b )d )e +--R + +--R 4 2 3 5 2 4 3 3 4 +--R ((5A a b - 20B a b )d + (125A a b - 500B a b )d )e +--R + +--R 5 4 6 5 2 4 5 +--R (- A b - 2B a b )d + (- 25A a b - 50B a b )d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 +--R (- 2A a d - 50A a d)e +--R + +--R 4 5 3 5 6 2 3 +--R ((16A a b - 4B a )d + (400A a b - 100B a )d )e +--R + +--R 3 2 4 4 4 2 5 3 2 +--R ((36A a b - 28B a b)d + (900A a b - 700B a b)d )e +--R + +--R 2 3 3 2 5 3 3 4 2 4 +--R ((16A a b - 28B a b )d + (400A a b - 700B a b )d )e +--R + +--R 4 2 3 6 2 4 3 3 5 +--R (- 2A a b - 4B a b )d + (- 50A a b - 100B a b )d +--R * +--R x +--R + +--R 5 3 6 2 3 4 5 4 5 6 3 2 +--R (- A a d - 25A a d )e + ((9A a b - 2B a )d + (225A a b - 50B a )d )e +--R + +--R 3 2 4 5 4 2 5 4 +--R ((9A a b - 12B a b)d + (225A a b - 300B a b)d )e +--R + +--R 2 3 3 2 6 3 3 4 2 5 +--R (- A a b - 2B a b )d + (- 25A a b - 50B a b )d +--R / +--R 6 2 2 6 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2 4 +--R (15a b d e - 60a b d e + 90a b d e - 60a b d e + 15a b d e )x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 +--R 30a b d e - 90a b d e + 60a b d e + 60a b d e - 90a b d e +--R + +--R 2 6 7 +--R 30a b d e +--R * +--R 3 +--R x +--R + +--R 8 2 6 6 2 4 4 5 3 5 3 4 4 6 2 2 6 8 2 +--R (15a d e - 135a b d e + 240a b d e - 135a b d e + 15a b d )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R (30a d e - 90a b d e + 60a b d e + 60a b d e - 90a b d e + 30a b d )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R Type: Union(Expression(Integer),...) +--E 1221 + +--S 1222 of 1293 +m0:=a0-r0 +--R +--R +--R (1120) +--R 3 4 3 2 3 2 3 4 2 +--R (- A a d - 25A a )e + ((9A a b - 2B a )d + (225A a b - 50B a )d)e +--R + +--R 2 2 3 2 2 3 2 +--R ((9A a b - 12B a b)d + (225A a b - 300B a b)d )e +--R + +--R 3 2 4 3 2 2 3 +--R (- A b - 2B a b )d + (- 25A a b - 50B a b )d +--R / +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1293 +d0:=D(m0,x) +--R +--R +--R (1121) 0 +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(7/2)) +--R +--R +--R (1122) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1293 +r0:=-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(5/2))-_ + 2/3*(3*b*B*d-8*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*_ + (d+e*x)^(5/2)*sqrt(a+b*x))-4/5*e*(3*b*B*d-8*A*b*e+5*a*B*e)*_ + sqrt(a+b*x)/(b*(b*d-a*e)^3*(d+e*x)^(5/2))-16/15*e*_ + (3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2))-_ + 32/15*b*e*(3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (1123) +--R 4 3 4 4 3 4 +--R ((- 256A b + 160B a b )e + 96B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 384A a b + 240B a b )e + (- 640A b + 544B a b )d e +--R + +--R 4 2 2 +--R 240B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 96A a b + 60B a b)e + (- 960A a b + 636B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 480A b + 660B a b )d e + 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (16A a b - 10B a )e + (- 240A a b + 144B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 720A a b + 540B a b )d e + (- 80A b + 320B a b )d e + 30B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (40A a b - 4B a )d e + (- 180A a b + 60B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 120A a b + 180B a b )d e + (10A b + 20B a b )d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 15a b e - 75a b d e + 150a b d e - 150a b d e + 75a b d e +--R + +--R 6 5 2 +--R - 15b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 +--R 15a e - 45a b d e + 150a b d e - 225a b d e + 135a b d e +--R + +--R 6 6 +--R - 30b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 +--R 30a d e - 135a b d e + 225a b d e - 150a b d e + 45a b d e +--R + +--R 6 7 +--R - 15b d +--R * +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R 15a d e - 75a b d e + 150a b d e - 150a b d e + 75a b d e - 15a b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1124) +--R 2 4 3 3 3 4 2 4 4 3 4 +--R ((- 1024A a b + 640B a b )d e + 384B a b d e )x +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 1536A a b + 960B a b )d e + (- 2560A a b + 2176B a b )d e +--R + +--R 2 4 5 2 +--R 960B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 384A a b + 240B a b)d e + (- 3840A a b + 2544B a b )d e +--R + +--R 2 4 3 3 5 2 2 4 6 +--R (- 1920A a b + 2640B a b )d e + 720B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 3 4 4 2 5 4 3 +--R (64A a b - 40B a )d e + (- 960A a b + 576B a b)d e +--R + +--R 3 3 4 2 5 2 2 4 3 3 6 +--R (- 2880A a b + 2160B a b )d e + (- 320A a b + 1280B a b )d e +--R + +--R 2 4 7 +--R 120B a b d +--R * +--R x +--R + +--R 6 3 4 5 6 4 3 4 2 5 5 2 +--R - 24A a d e + (160A a b - 16B a )d e + (- 720A a b + 240B a b)d e +--R + +--R 3 3 4 2 6 2 4 3 3 7 +--R (- 480A a b + 720B a b )d e + (40A a b + 80B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 2 5 2 7 +--R (- 3A a b d - 48A a b )e +--R + +--R 3 3 4 2 2 4 3 5 2 6 +--R ((20A a b - 2B a b )d + (320A a b - 32B a b )d)e +--R + +--R 2 4 3 3 3 3 4 4 3 2 5 +--R ((- 90A a b + 30B a b )d + (- 1440A a b + 480B a b )d )e +--R + +--R 5 2 4 4 2 5 3 4 3 4 +--R ((- 60A a b + 90B a b )d + (- 960A a b + 1440B a b )d )e +--R + +--R 6 5 5 6 2 5 4 3 +--R ((5A b + 10B a b )d + (80A a b + 160B a b )d )e +--R * +--R 5 +--R x +--R + +--R 5 6 7 +--R (- 6A a b d - 96A a b)e +--R + +--R 4 2 5 2 5 2 6 6 +--R ((31A a b - 4B a b)d + (496A a b - 64B a b)d)e +--R + +--R 3 3 4 2 3 4 3 5 2 2 5 +--R ((- 120A a b + 54B a b )d + (- 1920A a b + 864B a b )d )e +--R + +--R 2 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6 4 7 3 4 +--R (- 3A a d - 48A a d )e +--R + +--R 5 6 5 6 7 4 3 +--R ((20A a b - 2B a )d + (320A a b - 32B a )d )e +--R + +--R 4 2 5 6 5 2 6 5 2 +--R ((- 90A a b + 30B a b)d + (- 1440A a b + 480B a b)d )e +--R + +--R 3 3 4 2 7 4 3 5 2 6 +--R ((- 60A a b + 90B a b )d + (- 960A a b + 1440B a b )d )e +--R + +--R 2 4 3 3 8 3 4 4 3 7 +--R (5A a b + 10B a b )d + (80A a b + 160B a b )d +--R / +--R 7 2 3 8 6 3 4 7 5 4 5 6 4 5 6 5 3 6 7 4 +--R 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 7 8 3 +--R - 60a b d e +--R * +--R 5 +--R x +--R + +--R 8 3 8 7 2 4 7 6 3 5 6 5 4 6 5 4 5 7 4 +--R 120a b d e - 420a b d e + 300a b d e + 600a b d e - 1200a b d e +--R + +--R 3 6 8 3 2 7 9 2 +--R 780a b d e - 180a b d e +--R * +--R 4 +--R x +--R + +--R 9 3 8 8 4 7 7 2 5 6 6 3 6 5 5 4 7 4 +--R 60a d e + 60a b d e - 1020a b d e + 2100a b d e - 1500a b d e +--R + +--R 4 5 8 3 3 6 9 2 2 7 10 +--R - 60a b d e + 540a b d e - 180a b d e +--R * +--R 3 +--R x +--R + +--R 9 4 7 8 5 6 7 2 6 5 6 3 7 4 5 4 8 3 +--R 180a d e - 540a b d e + 60a b d e + 1500a b d e - 2100a b d e +--R + +--R 4 5 9 2 3 6 10 2 7 11 +--R 1020a b d e - 60a b d e - 60a b d +--R * +--R 2 +--R x +--R + +--R 9 5 6 8 6 5 7 2 7 4 6 3 8 3 5 4 9 2 +--R 180a d e - 780a b d e + 1200a b d e - 600a b d e - 300a b d e +--R + +--R 4 5 10 3 6 11 +--R 420a b d e - 120a b d +--R * +--R x +--R + +--R 9 6 5 8 7 4 7 2 8 3 6 3 9 2 5 4 10 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 4 5 11 +--R - 60a b d +--R Type: Union(Expression(Integer),...) +--E 1226 + +--S 1227 of 1293 +m0:=a0-r0 +--R +--R +--R (1125) +--R 4 5 4 3 4 2 4 5 3 +--R (- 3A a d - 48A a )e + ((20A a b - 2B a )d + (320A a b - 32B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 2 +--R ((- 90A a b + 30B a b)d + (- 1440A a b + 480B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R ((- 60A a b + 90B a b )d + (- 960A a b + 1440B a b )d )e +--R + +--R 4 3 5 4 2 3 4 +--R (5A b + 10B a b )d + (80A a b + 160B a b )d +--R / +--R 7 3 5 6 4 4 5 2 5 3 4 3 6 2 3 4 7 2 5 8 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e - 60a b d +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1293 +d0:=D(m0,x) +--R +--R +--R (1126) 0 +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(9/2)) +--R +--R +--R (1127) +--R B x + A +--R / +--R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 +--R b e x + (2a b e + 4b d e )x + (a e + 8a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 3 2 2 2 3 2 4 2 +--R (4a d e + 12a b d e + 4b d e)x + (6a d e + 8a b d e + b d )x +--R + +--R 2 3 4 2 4 +--R (4a d e + 2a b d )x + a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1293 +r0:=-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(7/2))-_ + 2/3*(3*b*B*d-10*A*b*e+7*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(7/2)*_ + sqrt(a+b*x))-16/21*e*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/_ + (b*(b*d-a*e)^3*(d+e*x)^(7/2))-32/35*e*(3*b*B*d-10*A*b*e+7*a*B*e)*_ + sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(5/2))-128/105*b*e*_ + (3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*(d+e*x)^(3/2))-_ + 256/105*b^2*e*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/_ + ((b*d-a*e)^6*sqrt(d+e*x)) +--R +--R +--R (1128) +--R 5 4 5 5 4 5 +--R ((2560A b - 1792B a b )e - 768B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (3840A a b - 2688B a b )e + (8960A b - 7424B a b )d e +--R + +--R 5 2 3 +--R - 2688B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (960A a b - 672B a b )e + (13440A a b - 9696B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (11200A b - 11872B a b )d e - 3360B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 160A a b + 112B a b)e + (3360A a b - 2304B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (16800A a b - 12768B a b )d e + (5600A b - 8960B a b )d e +--R + +--R 5 4 +--R - 1680B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (60A a b - 42B a )e + (- 560A a b + 374B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (4200A a b - 2772B a b )d e + (8400A a b - 7140B a b )d e +--R + +--R 5 4 4 5 5 +--R (700A b - 3010B a b )d e - 210B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 30A a e + (210A a b - 12B a )d e + (- 700A a b + 112B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (2100A a b - 840B a b )d e + (1050A a b - 1680B a b )d e +--R + +--R 5 4 5 +--R (- 70A b - 140B a b )d +--R / +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 +--R 105a b e - 630a b d e + 1575a b d e - 2100a b d e +--R + +--R 2 5 4 5 6 5 4 7 6 3 +--R 1575a b d e - 630a b d e + 105b d e +--R * +--R 4 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 3 4 4 5 +--R 105a e - 315a b d e - 315a b d e + 2625a b d e - 4725a b d e +--R + +--R 2 5 5 4 6 6 3 7 7 2 +--R 4095a b d e - 1785a b d e + 315b d e +--R * +--R 3 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 315a d e - 1575a b d e + 2835a b d e - 1575a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R - 1575a b d e + 2835a b d e - 1575a b d e + 315b d e +--R * +--R 2 +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 315a d e - 1785a b d e + 4095a b d e - 4725a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R 2625a b d e - 315a b d e - 315a b d e + 105b d +--R * +--R x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 +--R 105a d e - 630a b d e + 1575a b d e - 2100a b d e + 1575a b d e +--R + +--R 2 5 8 6 9 +--R - 630a b d e + 105a b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1129) +--R 2 5 3 4 4 5 2 5 5 4 5 +--R ((10240A a b - 7168B a b )d e - 3072B a b d e )x +--R + +--R 3 4 4 3 4 5 2 5 3 4 5 4 +--R (15360A a b - 10752B a b )d e + (35840A a b - 29696B a b )d e +--R + +--R 2 5 6 3 +--R - 10752B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 4 5 3 4 4 3 5 4 +--R (3840A a b - 2688B a b )d e + (53760A a b - 38784B a b )d e +--R + +--R 2 5 3 4 6 3 2 5 7 2 +--R (44800A a b - 47488B a b )d e - 13440B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 5 4 3 5 2 5 4 +--R (- 640A a b + 448B a b)d e + (13440A a b - 9216B a b )d e +--R + +--R 3 4 4 3 6 3 2 5 3 4 7 2 +--R (67200A a b - 51072B a b )d e + (22400A a b - 35840B a b )d e +--R + +--R 2 5 8 +--R - 6720B a b d e +--R * +--R 2 +--R x +--R + +--R 6 7 4 5 5 2 6 5 4 +--R (240A a b - 168B a )d e + (- 2240A a b + 1496B a b)d e +--R + +--R 4 3 5 2 6 3 3 4 4 3 7 2 +--R (16800A a b - 11088B a b )d e + (33600A a b - 28560B a b )d e +--R + +--R 2 5 3 4 8 2 5 9 +--R (2800A a b - 12040B a b )d e - 840B a b d +--R * +--R x +--R + +--R 7 4 5 6 7 5 4 +--R - 120A a d e + (840A a b - 48B a )d e +--R + +--R 5 2 6 6 3 4 3 5 2 7 2 +--R (- 2800A a b + 448B a b)d e + (8400A a b - 3360B a b )d e +--R + +--R 3 4 4 3 8 2 5 3 4 9 +--R (4200A a b - 6720B a b )d e + (- 280A a b - 560B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 5 2 6 2 9 +--R (- 15A a b d - 240A a b )e +--R + +--R 4 3 5 2 2 5 3 6 2 8 +--R ((105A a b - 6B a b )d + (1680A a b - 96B a b )d)e +--R + +--R 3 4 4 3 3 4 4 5 3 2 7 +--R ((- 350A a b + 56B a b )d + (- 5600A a b + 896B a b )d )e +--R + +--R 2 5 3 4 4 3 5 4 4 3 6 +--R ((1050A a b - 420B a b )d + (16800A a b - 6720B a b )d )e +--R + +--R 6 2 5 5 2 6 3 5 4 5 +--R ((525A a b - 840B a b )d + (8400A a b - 13440B a b )d )e +--R + +--R 7 6 6 7 2 6 5 4 +--R ((- 35A b - 70B a b )d + (- 560A a b - 1120B a b )d )e +--R * +--R 6 +--R x +--R + +--R 6 7 9 +--R (- 30A a b d - 480A a b)e +--R + +--R 5 2 6 2 6 2 7 8 +--R ((150A a b - 12B a b)d + (2400A a b - 192B a b)d)e +--R + +--R 4 3 5 2 3 5 3 6 2 2 7 +--R ((- 280A a b + 88B a b )d + (- 4480A a b + 1408B a b )d )e +--R + +--R 3 4 4 3 4 4 4 5 3 3 6 +--R ((700A a b - 616B a b )d + (11200A a b - 9856B a b )d )e +--R + +--R 2 5 3 4 5 3 5 4 4 4 5 +--R ((5250A a b - 3360B a b )d + (84000A a b - 53760B a b )d )e +--R + +--R 6 2 5 6 2 6 3 5 5 4 +--R ((2030A a b - 3500B a b )d + (32480A a b - 56000B a b )d )e +--R + +--R 7 6 7 7 2 6 6 3 +--R ((- 140A b - 280B a b )d + (- 2240A a b - 4480B a b )d )e +--R * +--R 5 +--R x +--R + +--R 7 8 9 +--R (- 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16512B a b )d )e +--R + +--R 3 4 4 3 6 4 4 5 3 5 4 +--R ((13300A a b - 8176B a b )d + (212800A a b - 130816B a b )d )e +--R + +--R 2 5 3 4 7 3 5 4 4 6 3 +--R ((10360A a b - 12040B a b )d + (165760A a b - 192640B a b )d )e +--R + +--R 6 2 5 8 2 6 3 5 7 2 +--R ((1680A a b - 4200B a b )d + (26880A a b - 67200B a b )d )e +--R + +--R 7 6 9 7 2 6 8 +--R ((- 140A b - 280B a b )d + (- 2240A a b - 4480B a b )d )e +--R * +--R 3 +--R x +--R + +--R 7 3 8 2 7 +--R (- 90A a d - 1440A a d )e +--R + +--R 6 7 4 7 8 3 6 +--R ((510A a b - 36B a )d + (8160A a b - 576B a )d )e +--R + +--R 5 2 6 5 6 2 7 4 5 +--R ((- 1275A a b + 288B a b)d + (- 20400A a b + 4608B a b)d )e +--R + +--R 4 3 5 2 6 5 3 6 2 5 4 +--R ((3605A a b - 2078B a b )d + (57680A a b - 33248B a b )d )e +--R + +--R 3 4 4 3 7 4 4 5 3 6 3 +--R ((11200A a b - 8344B a b )d + (179200A a b - 133504B a b )d )e +--R + +--R 2 5 3 4 8 3 5 4 4 7 2 +--R ((5040A a b - 7560B a b )d + (80640A a b - 120960B a b )d )e +--R + +--R 6 2 5 9 2 6 3 5 8 +--R ((245A a b - 1400B a b )d + (3920A a b - 22400B a b )d )e +--R + +--R 7 6 10 7 2 6 9 +--R (- 35A b - 70B a b )d + (- 560A a b - 1120B a b )d +--R * +--R 2 +--R x +--R + +--R 7 4 8 3 6 +--R (- 60A a d - 960A a d )e +--R + +--R 6 7 5 7 8 4 5 +--R ((390A a b - 24B a )d + (6240A a b - 384B a )d )e +--R + +--R 5 2 6 6 6 2 7 5 4 +--R ((- 1190A a b + 212B a b)d + (- 19040A a b + 3392B a b)d )e +--R + +--R 4 3 5 2 7 5 3 6 2 6 3 +--R ((3500A a b - 1568B a b )d + (56000A a b - 25088B a b )d )e +--R + +--R 3 4 4 3 8 4 4 5 3 7 2 +--R ((4200A a b - 4200B a b )d + (67200A a b - 67200B a b )d )e +--R + +--R 2 5 3 4 9 3 5 4 4 8 +--R ((910A a b - 1960B a b )d + (14560A a b - 31360B a b )d )e +--R + +--R 6 2 5 10 2 6 3 5 9 +--R (- 70A a b - 140B a b )d + (- 1120A a b - 2240B a b )d +--R * +--R x +--R + +--R 7 5 8 4 5 +--R (- 15A a d - 240A a d )e +--R + +--R 6 7 6 7 8 5 4 +--R ((105A a b - 6B a )d + (1680A a b - 96B a )d )e +--R + +--R 5 2 6 7 6 2 7 6 3 +--R ((- 350A a b + 56B a b)d + (- 5600A a b + 896B a b)d )e +--R + +--R 4 3 5 2 8 5 3 6 2 7 2 +--R ((1050A a b - 420B a b )d + (16800A a b - 6720B a b )d )e +--R + +--R 3 4 4 3 9 4 4 5 3 8 +--R ((525A a b - 840B a b )d + (8400A a b - 13440B a b )d )e +--R + +--R 2 5 3 4 10 3 5 4 4 9 +--R (- 35A a b - 70B a b )d + (- 560A a b - 1120B a b )d +--R / +--R 8 2 4 10 7 3 5 9 6 4 6 8 5 5 7 7 +--R 420a b d e - 2520a b d e + 6300a b d e - 8400a b d e +--R + +--R 4 6 8 6 3 7 9 5 2 8 10 4 +--R 6300a b d e - 2520a b d e + 420a b d e +--R * +--R 6 +--R x +--R + +--R 9 4 10 8 2 5 9 7 3 6 8 6 4 7 7 +--R 840a b d e - 3360a b d e + 2520a b d e + 8400a b d e +--R + +--R 5 5 8 6 4 6 9 5 3 7 10 4 2 8 11 3 +--R - 21000a b d e + 20160a b d e - 9240a b d e + 1680a b d e +--R * +--R 5 +--R x +--R + +--R 10 4 10 9 5 9 8 2 6 8 7 3 7 7 +--R 420a d e + 840a b d e - 11340a b d e + 26880a b d e +--R + +--R 6 4 8 6 5 5 9 5 4 6 10 4 3 7 11 3 +--R - 23100a b d e - 2520a b d e + 18060a b d e - 11760a b d e +--R + +--R 2 8 12 2 +--R 2520a b d e +--R * +--R 4 +--R x +--R + +--R 10 5 9 9 6 8 8 2 7 7 7 3 8 6 +--R 1680a d e - 5040a b d e - 3360a b d e + 31920a b d e +--R + +--R 6 4 9 5 5 5 10 4 4 6 11 3 3 7 12 2 +--R - 50400a b d e + 31920a b d e - 3360a b d e - 5040a b d e +--R + +--R 2 8 13 +--R 1680a b d e +--R * +--R 3 +--R x +--R + +--R 10 6 8 9 7 7 8 2 8 6 7 3 9 5 +--R 2520a d e - 11760a b d e + 18060a b d e - 2520a b d e +--R + +--R 6 4 10 4 5 5 11 3 4 6 12 2 3 7 13 +--R - 23100a b d e + 26880a b d e - 11340a b d e + 840a b d e +--R + +--R 2 8 14 +--R 420a b d +--R * +--R 2 +--R x +--R + +--R 10 7 7 9 8 6 8 2 9 5 7 3 10 4 +--R 1680a d e - 9240a b d e + 20160a b d e - 21000a b d e +--R + +--R 6 4 11 3 5 5 12 2 4 6 13 3 7 14 +--R 8400a b d e + 2520a b d e - 3360a b d e + 840a b d +--R * +--R x +--R + +--R 10 8 6 9 9 5 8 2 10 4 7 3 11 3 6 4 12 2 +--R 420a d e - 2520a b d e + 6300a b d e - 8400a b d e + 6300a b d e +--R + +--R 5 5 13 4 6 14 +--R - 2520a b d e + 420a b d +--R Type: Union(Expression(Integer),...) +--E 1231 + +--S 1232 of 1293 +m0:=a0-r0 +--R +--R +--R (1130) +--R 5 6 5 +--R (- 15A a d - 240A a )e +--R + +--R 4 5 2 5 6 4 +--R ((105A a b - 6B a )d + (1680A a b - 96B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 3 +--R ((- 350A a b + 56B a b)d + (- 5600A a b + 896B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 2 +--R ((1050A a b - 420B a b )d + (16800A a b - 6720B a b )d )e +--R + +--R 4 2 3 5 2 4 3 3 4 +--R ((525A a b - 840B a b )d + (8400A a b - 13440B a b )d )e +--R + +--R 5 4 6 5 2 4 5 +--R (- 35A b - 70B a b )d + (- 560A a b - 1120B a b )d +--R / +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 420a d e - 2520a b d e + 6300a b d e - 8400a b d e + 6300a b d e +--R + +--R 3 5 9 2 6 10 +--R - 2520a b d e + 420a b d +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1293 +d0:=D(m0,x) +--R +--R +--R (1131) 0 +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1293 +t0:=(a+b*x)*(c+d*x)^n/(e+f*x)^n +--R +--R +--R n +--R (b x + a)(d x + c) +--R (1132) ------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1293 +--r0:=1/2*b*(c+d*x)^(1+n)*(e+f*x)^(1-n)/(d*f)+1/2*(2*a*d*f-b*(c*f*(1-n)+_ +--d*e*(1+n)))*(c+d*x)^n*(e+f*x)^(1-n)*_ +--hypergeometric(1-n,-n,2-n,d*(e+f*x)/(d*e-c*f))/_ +--(d*f^2*(1-n)*(-f*(c+d*x)/(d*e-c*f))^n) +--E 1235 + +--S 1236 of 1293 +--a0:=integrate(t0,x) +--E 1236 + +--S 1237 of 1293 +--m0:=a0-r0 +--E 1237 + +--S 1238 of 1293 +--d0:=D(m0,x) +--E 1238 + +--S 1239 of 1293 +t0:=(a+b*x)*(c+d*x)^(-1+n)/(e+f*x)^n +--R +--R +--R n - 1 +--R (b x + a)(d x + c) +--R (1133) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1293 +--r0:=-(b*c-a*d)*(c+d*x)^n*(e+f*x)^(1-n)/(d*(d*e-c*f)*n)-(a*d*f-b*(c*f*(1-n)+_ +--d*e*n))*(c+d*x)^n*(e+f*x)^(1-n)*_ +--hypergeometric(1-n,-n,2-n,d*(e+f*x)/(d*e-c*f))/(d*f*(d*e-c*f)*(1-n)*n*_ +--(-f*(c+d*x)/(d*e-c*f))^n) +--E 1240 + +--S 1241 of 1293 +--a0:=integrate(t0,x) +--E 1241 + +--S 1242 of 1293 +--m0:=a0-r0 +--E 1242 + +--S 1243 of 1293 +--d0:=D(m0,x) +--E 1243 + +--S 1244 of 1293 +t0:=(a+b*x)*(c+d*x)^(-2+n)/(e+f*x)^n +--R +--R +--R n - 2 +--R (b x + a)(d x + c) +--R (1134) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1293 +--r0:=(b*c-a*d)*(c+d*x)^(-1+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(1-n))+_ +--b*(c+d*x)^n*(e+f*x)^(1-n)/(d*(d*e-c*f)*n)-b*(c+d*x)^n*(e+f*x)^(1-n)*_ +--hypergeometric(1-n,-n,2-n,d*(e+f*x)/(d*e-c*f))/(d*(d*e-c*f)*(1-n)*n*_ +--(-f*(c+d*x)/(d*e-c*f))^n) +--E 1245 + +--S 1246 of 1293 +--a0:=integrate(t0,x) +--E 1246 + +--S 1247 of 1293 +--m0:=a0-r0 +--E 1247 + +--S 1248 of 1293 +--d0:=D(m0,x) +--E 1248 + +--S 1249 of 1293 +t0:=(a+b*x)*(c+d*x)^(-3+n)/(e+f*x)^n +--R +--R +--R n - 3 +--R (b x + a)(d x + c) +--R (1135) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1293 +r0:=(b*c-a*d)*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(2-n))+_ + (a*d*f+b*(c*f*(1-n)-d*e*(2-n)))*(c+d*x)^(-1+n)*_ + (e+f*x)^(1-n)/(d*(d*e-c*f)^2*(1-n)*(2-n)) +--R +--R +--R (1136) +--R n - 1 +--R ((- b c f + b d e)n + (a d + b c)f - 2b d e)(d x + c) +--R + +--R 2 2 2 +--R ((- a c d + b c )f + (a d - b c d)e)n + (a c d - b c )f +--R + +--R 2 +--R (- a d + b c d)e +--R * +--R n - 2 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R / +--R 2 2 2 3 2 2 2 2 2 3 2 2 2 +--R (c d f - 2c d e f + d e )n + (- 3c d f + 6c d e f - 3d e )n + 2c d f +--R + +--R 2 3 2 +--R - 4c d e f + 2d e +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1137) +--R 2 2 2 2 2 3 +--R ((- b c d f + b d e f)n + (a d + b c d)f - 2b d e f)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- a c d - b c )f + a d e f + b d e )n + (3a c d + b c )f +--R + +--R 2 2 +--R - 2b c d e f - 2b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 2 2 +--R (- a c f - b c e f + (a d + b c d)e )n + 2a c f + 2a c d e f +--R + +--R 2 2 +--R (- a d - 3b c d)e +--R * +--R x +--R + +--R 2 2 2 2 2 +--R (- a c e f + a c d e )n + 2a c e f + (- a c d - b c )e +--R * +--R (n - 3)log(d x + c) +--R %e +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (c f - 2c d e f + d e )n + (- 3c f + 6c d e f - 3d e )n + 2c f +--R + +--R 2 2 +--R - 4c d e f + 2d e +--R * +--R n log(f x + e) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1251 + +--S 1252 of 1293 +m0:=a0-r0 +--R +--R +--R (1138) +--R n - 1 +--R ((b c f - b d e)n + (- a d - b c)f + 2b d e)(d x + c) +--R + +--R 2 2 2 +--R ((a c d - b c )f + (- a d + b c d)e)n + (- a c d + b c )f +--R + +--R 2 +--R (a d - b c d)e +--R * +--R n - 2 +--R (d x + c) +--R * +--R - n + 1 n log(f x + e) +--R (f x + e) %e +--R + +--R 2 2 3 3 2 2 3 3 +--R ((- b c d f + b d e f)n + (a d + b c d )f - 2b d e f)x +--R + +--R 2 2 2 3 3 2 2 2 2 +--R ((- a c d - b c d)f + a d e f + b d e )n + (3a c d + b c d)f +--R + +--R 2 3 2 +--R - 2b c d e f - 2b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 3 2 2 2 2 +--R (- a c d f - b c d e f + (a d + b c d )e )n + 2a c d f +--R + +--R 2 3 2 2 +--R 2a c d e f + (- a d - 3b c d )e +--R * +--R x +--R + +--R 2 2 2 2 2 2 2 +--R (- a c d e f + a c d e )n + 2a c d e f + (- a c d - b c d)e +--R * +--R (n - 3)log(d x + c) +--R %e +--R / +--R 2 2 2 3 2 2 2 2 2 3 2 +--R (c d f - 2c d e f + d e )n + (- 3c d f + 6c d e f - 3d e )n +--R + +--R 2 2 2 3 2 +--R 2c d f - 4c d e f + 2d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 1293 +d0:=D(m0,x) +--R +--R +--R (1139) +--R 2 2 2 n - 2 +--R ((b c d f - b d e)n + (- a d - b c d)f + 2b d e)(d x + c) +--R + +--R 2 2 3 2 +--R ((a c d - b c d)f + (- a d + b c d )e)n +--R + +--R 2 2 3 2 +--R (- 2a c d + 2b c d)f + (2a d - 2b c d )e +--R * +--R n - 3 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R + +--R 2 2 n - 1 +--R ((- b c f + b d e f)n + (a d + b c)f - 2b d e f)(d x + c) +--R + +--R 2 2 2 2 2 +--R ((- a c d + b c )f + (a d - b c d)e f)n + (a c d - b c )f +--R + +--R 2 +--R (- a d + b c d)e f +--R * +--R n - 2 +--R (d x + c) +--R * +--R - n +--R (f x + e) +--R * +--R n log(f x + e) +--R %e +--R + +--R 2 2 2 3 2 2 2 2 +--R (b c d f - 2b c d e f + b d e )n - 2b c d f + 4b c d e f +--R + +--R 3 2 +--R - 2b d e +--R * +--R x +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (a c d f - 2a c d e f + a d e )n - 2a c d f + 4a c d e f - 2a d e +--R * +--R (n - 3)log(d x + c) +--R %e +--R / +--R 2 2 2 3 2 2 2 2 3 2 n log(f x + e) +--R ((c d f - 2c d e f + d e )n - 2c d f + 4c d e f - 2d e )%e +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1293 +t0:=(a+b*x)*(c+d*x)^(-4+n)/(e+f*x)^n +--R +--R +--R n - 4 +--R (b x + a)(d x + c) +--R (1140) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 1293 +r0:=(b*c-a*d)*(c+d*x)^(-3+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(3-n))+_ + (2*a*d*f+b*(c*f*(1-n)-d*e*(3-n)))*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/_ + (d*(d*e-c*f)^2*(2-n)*(3-n))-f*(2*a*d*f+b*(c*f*(1-n)-d*e*(3-n)))*_ + (c+d*x)^(-1+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^3*(1-n)*(2-n)*(3-n)) +--R +--R +--R (1141) +--R 2 2 n - 1 +--R ((b c f - b d e f)n + (- 2a d - b c)f + 3b d e f)(d x + c) +--R + +--R 2 2 2 2 2 +--R (- b c f + 2b c d e f - b d e )n +--R + +--R 2 2 2 2 2 +--R ((2a c d + 2b c )f + (- 2a d - 6b c d)e f + 4b d e )n +--R + +--R 2 2 2 2 2 +--R (- 2a c d - b c )f + (2a d + 4b c d)e f - 3b d e +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 3 2 2 2 +--R (- a c d + b c )f + (2a c d - 2b c d)e f +--R + +--R 3 2 2 +--R (- a d + b c d )e +--R * +--R 2 +--R n +--R + +--R 2 3 2 2 2 +--R (3a c d - 3b c )f + (- 6a c d + 6b c d)e f +--R + +--R 3 2 2 +--R (3a d - 3b c d )e +--R * +--R n +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 2a c d + 2b c )f + (4a c d - 4b c d)e f + (- 2a d + 2b c d )e +--R * +--R n - 3 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R / +--R 3 3 2 2 2 3 2 4 3 3 +--R (c d f - 3c d e f + 3c d e f - d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (- 6c d f + 18c d e f - 18c d e f + 6d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 2 2 2 +--R (11c d f - 33c d e f + 33c d e f - 11d e )n - 6c d f + 18c d e f +--R + +--R 3 2 4 3 +--R - 18c d e f + 6d e +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1142) +--R 2 3 3 2 3 2 3 3 2 4 +--R ((b c d f - b d e f )n + (- 2a d - b c d )f + 3b d e f )x +--R + +--R 2 3 2 2 3 2 2 +--R (- b c d f + 2b c d e f - b d e f)n +--R + +--R 2 2 3 3 2 2 3 2 +--R ((2a c d + 5b c d)f + (- 2a d - 8b c d )e f + 3b d e f)n +--R + +--R 2 2 3 2 2 +--R (- 8a c d - 4b c d)f + 12b c d e f +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- a c d - b c )f + (2a c d + b c d)e f +--R + +--R 3 2 2 3 3 +--R (- a d + b c d )e f - b d e +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 2 2 +--R (7a c d + 4b c )f + (- 8a c d - 4b c d)e f +--R + +--R 3 2 2 3 3 +--R (a d - 4b c d )e f + 4b d e +--R * +--R n +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (- 12a c d - 3b c )f + 9b c d e f + 9b c d e f - 3b d e +--R * +--R 2 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - a c f + (a c d - b c )e f + (a c d + 2b c d)e f +--R + +--R 3 2 3 +--R (- a d - b c d )e +--R * +--R 2 +--R n +--R + +--R 3 3 2 3 2 2 2 2 +--R 5a c f + (- a c d + 3b c )e f + (- 7a c d - 8b c d)e f +--R + +--R 3 2 3 +--R (3a d + 5b c d )e +--R * +--R n +--R + +--R 3 3 2 2 2 2 2 +--R - 6a c f - 6a c d e f + (6a c d + 12b c d)e f +--R + +--R 3 2 3 +--R (- 2a d - 4b c d )e +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 +--R (- a c e f + 2a c d e f - a c d e )n +--R + +--R 3 2 2 3 2 2 2 3 3 2 +--R (5a c e f + (- 8a c d - b c )e f + (3a c d + b c d)e )n - 6a c e f +--R + +--R 2 3 2 2 2 3 +--R (6a c d + 3b c )e f + (- 2a c d - b c d)e +--R * +--R (n - 4)log(d x + c) +--R %e +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (c f - 3c d e f + 3c d e f - d e )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6c f + 18c d e f - 18c d e f + 6d e )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11c f - 33c d e f + 33c d e f - 11d e )n - 6c f + 18c d e f +--R + +--R 2 2 3 3 +--R - 18c d e f + 6d e +--R * +--R n log(f x + e) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1256 + +--S 1257 of 1293 +m0:=a0-r0 +--R +--R +--R (1143) +--R 2 2 n - 1 +--R ((- b c f + b d e f)n + (2a d + b c)f - 3b d e f)(d x + c) +--R + +--R 2 2 2 2 2 +--R (b c f - 2b c d e f + b d e )n +--R + +--R 2 2 2 2 2 +--R ((- 2a c d - 2b c )f + (2a d + 6b c d)e f - 4b d e )n +--R + +--R 2 2 2 2 2 +--R (2a c d + b c )f + (- 2a d - 4b c d)e f + 3b d e +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 3 2 2 2 +--R (a c d - b c )f + (- 2a c d + 2b c d)e f +--R + +--R 3 2 2 +--R (a d - b c d )e +--R * +--R 2 +--R n +--R + +--R 2 3 2 2 2 +--R (- 3a c d + 3b c )f + (6a c d - 6b c d)e f +--R + +--R 3 2 2 +--R (- 3a d + 3b c d )e +--R * +--R n +--R + +--R 2 3 2 2 2 3 2 2 +--R (2a c d - 2b c )f + (- 4a c d + 4b c d)e f + (2a d - 2b c d )e +--R * +--R n - 3 +--R (d x + c) +--R * +--R - n + 1 n log(f x + e) +--R (f x + e) %e +--R + +--R 3 3 4 2 4 3 3 4 2 4 +--R ((b c d f - b d e f )n + (- 2a d - b c d )f + 3b d e f )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- b c d f + 2b c d e f - b d e f)n +--R + +--R 3 2 2 3 4 3 2 4 2 +--R ((2a c d + 5b c d )f + (- 2a d - 8b c d )e f + 3b d e f)n +--R + +--R 3 2 2 3 3 2 +--R (- 8a c d - 4b c d )f + 12b c d e f +--R * +--R 3 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- a c d - b c d)f + (2a c d + b c d )e f +--R + +--R 4 3 2 4 3 +--R (- a d + b c d )e f - b d e +--R * +--R 2 +--R n +--R + +--R 2 2 3 3 3 2 2 2 +--R (7a c d + 4b c d)f + (- 8a c d - 4b c d )e f +--R + +--R 4 3 2 4 3 +--R (a d - 4b c d )e f + 4b d e +--R * +--R n +--R + +--R 2 2 3 3 2 2 2 3 2 4 3 +--R (- 12a c d - 3b c d)f + 9b c d e f + 9b c d e f - 3b d e +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 3 2 3 2 2 2 +--R - a c d f + (a c d - b c d)e f + (a c d + 2b c d )e f +--R + +--R 4 3 3 +--R (- a d - b c d )e +--R * +--R 2 +--R n +--R + +--R 3 3 2 2 3 2 +--R 5a c d f + (- a c d + 3b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 7a c d - 8b c d )e f + (3a d + 5b c d )e +--R * +--R n +--R + +--R 3 3 2 2 2 3 2 2 2 +--R - 6a c d f - 6a c d e f + (6a c d + 12b c d )e f +--R + +--R 4 3 3 +--R (- 2a d - 4b c d )e +--R * +--R x +--R + +--R 3 2 2 2 2 3 3 2 +--R (- a c d e f + 2a c d e f - a c d e )n +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R (5a c d e f + (- 8a c d - b c d)e f + (3a c d + b c d )e )n +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R - 6a c d e f + (6a c d + 3b c d)e f + (- 2a c d - b c d )e +--R * +--R (n - 4)log(d x + c) +--R %e +--R / +--R 3 3 2 2 2 3 2 4 3 3 +--R (c d f - 3c d e f + 3c d e f - d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (- 6c d f + 18c d e f - 18c d e f + 6d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 2 2 2 +--R (11c d f - 33c d e f + 33c d e f - 11d e )n - 6c d f + 18c d e f +--R + +--R 3 2 4 3 +--R - 18c d e f + 6d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 1293 +d0:=D(m0,x) +--R +--R +--R (1144) +--R 2 2 2 2 2 +--R ((- b c d f + b d e f)n + (2a d + b c d)f - 3b d e f) +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 2 2 3 2 2 +--R (b c d f - 2b c d e f + b d e )n +--R + +--R 2 2 2 3 2 3 2 +--R ((- 2a c d - 3b c d)f + (2a d + 8b c d )e f - 5b d e )n +--R + +--R 2 2 2 3 2 3 2 +--R (4a c d + 2b c d)f + (- 4a d - 8b c d )e f + 6b d e +--R * +--R n - 3 +--R (d x + c) +--R + +--R 2 2 3 2 3 2 2 +--R (a c d - b c d)f + (- 2a c d + 2b c d )e f +--R + +--R 4 3 2 +--R (a d - b c d )e +--R * +--R 2 +--R n +--R + +--R 2 2 3 2 3 2 2 +--R (- 5a c d + 5b c d)f + (10a c d - 10b c d )e f +--R + +--R 4 3 2 +--R (- 5a d + 5b c d )e +--R * +--R n +--R + +--R 2 2 3 2 3 2 2 +--R (6a c d - 6b c d)f + (- 12a c d + 12b c d )e f +--R + +--R 4 3 2 +--R (6a d - 6b c d )e +--R * +--R n - 4 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R + +--R 3 2 3 2 +--R ((b c f - b d e f )n + (- 2a d - b c)f + 3b d e f ) +--R * +--R n - 1 +--R (d x + c) +--R + +--R 2 3 2 2 2 2 +--R (- b c f + 2b c d e f - b d e f)n +--R + +--R 2 3 2 2 2 2 +--R ((2a c d + 2b c )f + (- 2a d - 6b c d)e f + 4b d e f)n +--R + +--R 2 3 2 2 2 2 +--R (- 2a c d - b c )f + (2a d + 4b c d)e f - 3b d e f +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 3 3 2 2 2 +--R (- a c d + b c )f + (2a c d - 2b c d)e f +--R + +--R 3 2 2 +--R (- a d + b c d )e f +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 2 2 +--R (3a c d - 3b c )f + (- 6a c d + 6b c d)e f +--R + +--R 3 2 2 +--R (3a d - 3b c d )e f +--R * +--R n +--R + +--R 2 3 3 2 2 2 +--R (- 2a c d + 2b c )f + (4a c d - 4b c d)e f +--R + +--R 3 2 2 +--R (- 2a d + 2b c d )e f +--R * +--R n - 3 +--R (d x + c) +--R * +--R - n +--R (f x + e) +--R * +--R n log(f x + e) +--R %e +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (b c d f - 3b c d e f + 3b c d e f - b d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 +--R (- 5b c d f + 15b c d e f - 15b c d e f + 5b d e )n + 6b c d f +--R + +--R 2 2 2 3 2 4 3 +--R - 18b c d e f + 18b c d e f - 6b d e +--R * +--R x +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (a c d f - 3a c d e f + 3a c d e f - a d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 +--R (- 5a c d f + 15a c d e f - 15a c d e f + 5a d e )n + 6a c d f +--R + +--R 2 2 2 3 2 4 3 +--R - 18a c d e f + 18a c d e f - 6a d e +--R * +--R (n - 4)log(d x + c) +--R %e +--R / +--R 3 3 2 2 2 3 2 4 3 2 +--R (c d f - 3c d e f + 3c d e f - d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 2 2 2 +--R (- 5c d f + 15c d e f - 15c d e f + 5d e )n + 6c d f - 18c d e f +--R + +--R 3 2 4 3 +--R 18c d e f - 6d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1293 +t0:=(a+b*x)*(c+d*x)^(-5+n)/(e+f*x)^n +--R +--R +--R n - 5 +--R (b x + a)(d x + c) +--R (1145) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1293 +r0:=(b*c-a*d)*(c+d*x)^(-4+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(4-n))+_ + (3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*(c+d*x)^(-3+n)*(e+f*x)^(1-n)/_ + (d*(d*e-c*f)^2*(3-n)*(4-n))-2*f*(3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*_ + (c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^3*(2-n)*(3-n)*(4-n))+_ + 2*f^2*(3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*(c+d*x)^(-1+n)*_ + (e+f*x)^(1-n)/(d*(d*e-c*f)^4*(1-n)*(2-n)*(3-n)*(4-n)) +--R +--R +--R (1146) +--R 3 2 3 2 n - 1 +--R ((- 2b c f + 2b d e f )n + (6a d + 2b c)f - 8b d e f )(d x + c) +--R + +--R 2 3 2 2 2 2 +--R (2b c f - 4b c d e f + 2b d e f)n +--R + +--R 2 3 2 2 2 2 +--R ((- 6a c d - 4b c )f + (6a d + 14b c d)e f - 10b d e f)n +--R + +--R 2 3 2 2 2 2 +--R (6a c d + 2b c )f + (- 6a d - 10b c d)e f + 8b d e f +--R * +--R n - 2 +--R (d x + c) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- b c f + 3b c d e f - 3b c d e f + b d e )n +--R + +--R 2 3 3 2 2 2 +--R (3a c d + 4b c )f + (- 6a c d - 15b c d)e f +--R + +--R 3 2 2 3 3 +--R (3a d + 18b c d )e f - 7b d e +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 2 2 +--R (- 9a c d - 5b c )f + (18a c d + 24b c d)e f +--R + +--R 3 2 2 3 3 +--R (- 9a d - 33b c d )e f + 14b d e +--R * +--R n +--R + +--R 2 3 3 2 2 2 +--R (6a c d + 2b c )f + (- 12a c d - 12b c d)e f +--R + +--R 3 2 2 3 3 +--R (6a d + 18b c d )e f - 8b d e +--R * +--R n - 3 +--R (d x + c) +--R + +--R 3 4 3 2 2 3 2 +--R (- a c d + b c )f + (3a c d - 3b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 3a c d + 3b c d )e f + (a d - b c d )e +--R * +--R 3 +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (6a c d - 6b c )f + (- 18a c d + 18b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (18a c d - 18b c d )e f + (- 6a d + 6b c d )e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (- 11a c d + 11b c )f + (33a c d - 33b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 33a c d + 33b c d )e f + (11a d - 11b c d )e +--R * +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (6a c d - 6b c )f + (- 18a c d + 18b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (18a c d - 18b c d )e f + (- 6a d + 6b c d )e +--R * +--R n - 4 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R / +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (c d f - 4c d e f + 6c d e f - 4c d e f + d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 10c d f + 40c d e f - 60c d e f + 40c d e f - 10d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (35c d f - 140c d e f + 210c d e f - 140c d e f + 35d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 50c d f + 200c d e f - 300c d e f + 200c d e f - 50d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R 24c d f - 96c d e f + 144c d e f - 96c d e f + 24d e +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1147) +--R 3 4 4 3 4 3 4 4 3 5 +--R ((- 2b c d f + 2b d e f )n + (6a d + 2b c d )f - 8b d e f )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (2b c d f - 4b c d e f + 2b d e f )n +--R + +--R 3 2 2 4 4 3 3 4 2 2 +--R ((- 6a c d - 12b c d )f + (6a d + 20b c d )e f - 8b d e f )n +--R + +--R 3 2 2 4 3 3 +--R (30a c d + 10b c d )f - 40b c d e f +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (- b c d f + 3b c d e f - 3b c d e f + b d e f)n +--R + +--R 2 2 3 4 3 2 2 3 +--R (3a c d + 10b c d)f + (- 6a c d - 25b c d )e f +--R + +--R 4 3 2 2 4 3 +--R (3a d + 20b c d )e f - 5b d e f +--R * +--R 2 +--R n +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 27a c d - 29b c d)f + (30a c d + 66b c d )e f +--R + +--R 4 3 2 2 4 3 +--R (- 3a d - 41b c d )e f + 4b d e f +--R * +--R n +--R + +--R 2 2 3 4 2 2 3 +--R (60a c d + 20b c d)f - 80b c d e f +--R * +--R 3 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (- a c d - b c )f + (3a c d + 2b c d)e f - 3a c d e f +--R + +--R 4 3 3 4 4 +--R (a d - 2b c d )e f + b d e +--R * +--R 3 +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (12a c d + 8b c )f + (- 27a c d - 14b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (18a c d - 3b c d )e f + (- 3a d + 16b c d )e f - 7b d e +--R * +--R 2 +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (- 47a c d - 19b c )f + (60a c d + 36b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 15a c d + 15b c d )e f + (2a d - 46b c d )e f + 14b d e +--R * +--R n +--R + +--R 3 4 4 3 3 2 2 2 2 3 3 +--R (60a c d + 12b c )f - 48b c d e f - 48b c d e f + 32b c d e f +--R + +--R 4 4 +--R - 8b d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 3 3 2 2 +--R - a c f + (2a c d - b c )e f + 3b c d e f +--R + +--R 3 2 2 3 4 3 4 +--R (- 2a c d - 3b c d )e f + (a d + b c d )e +--R * +--R 3 +--R n +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 9a c f + (- 12a c d + 7b c )e f + (- 9a c d - 22b c d)e f +--R + +--R 3 2 2 3 4 3 4 +--R (18a c d + 23b c d )e f + (- 6a d - 8b c d )e +--R * +--R 2 +--R n +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 26a c f + (10a c d - 12b c )e f + (45a c d + 55b c d)e f +--R + +--R 3 2 2 3 4 3 4 +--R (- 40a c d - 60b c d )e f + (11a d + 17b c d )e +--R * +--R n +--R + +--R 4 4 3 3 2 2 3 2 2 +--R 24a c f + 24a c d e f + (- 36a c d - 60b c d)e f +--R + +--R 3 2 2 3 4 3 4 +--R (24a c d + 40b c d )e f + (- 6a d - 10b c d )e +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- a c e f + 3a c d e f - 3a c d e f + a c d e )n +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 9a c e f + (- 24a c d - b c )e f + (21a c d + 2b c d)e f +--R + +--R 3 2 2 4 +--R (- 6a c d - b c d )e +--R * +--R 2 +--R n +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R - 26a c e f + (57a c d + 7b c )e f + (- 42a c d - 10b c d)e f +--R + +--R 3 2 2 4 +--R (11a c d + 3b c d )e +--R * +--R n +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 24a c e f + (- 36a c d - 12b c )e f + (24a c d + 8b c d)e f +--R + +--R 3 2 2 4 +--R (- 6a c d - 2b c d )e +--R * +--R (n - 5)log(d x + c) +--R %e +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (c f - 4c d e f + 6c d e f - 4c d e f + d e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (- 10c f + 40c d e f - 60c d e f + 40c d e f - 10d e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35c f - 140c d e f + 210c d e f - 140c d e f + 35d e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (- 50c f + 200c d e f - 300c d e f + 200c d e f - 50d e )n + 24c f +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96c d e f + 144c d e f - 96c d e f + 24d e +--R * +--R n log(f x + e) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1261 + +--S 1262 of 1293 +m0:=a0-r0 +--R +--R +--R (1148) +--R 3 2 3 2 +--R ((2b c f - 2b d e f )n + (- 6a d - 2b c)f + 8b d e f ) +--R * +--R n - 1 +--R (d x + c) +--R + +--R 2 3 2 2 2 2 +--R (- 2b c f + 4b c d e f - 2b d e f)n +--R + +--R 2 3 2 2 2 2 +--R ((6a c d + 4b c )f + (- 6a d - 14b c d)e f + 10b d e f)n +--R + +--R 2 3 2 2 2 2 +--R (- 6a c d - 2b c )f + (6a d + 10b c d)e f - 8b d e f +--R * +--R n - 2 +--R (d x + c) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (b c f - 3b c d e f + 3b c d e f - b d e )n +--R + +--R 2 3 3 2 2 2 +--R (- 3a c d - 4b c )f + (6a c d + 15b c d)e f +--R + +--R 3 2 2 3 3 +--R (- 3a d - 18b c d )e f + 7b d e +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 2 2 +--R (9a c d + 5b c )f + (- 18a c d - 24b c d)e f +--R + +--R 3 2 2 3 3 +--R (9a d + 33b c d )e f - 14b d e +--R * +--R n +--R + +--R 2 3 3 2 2 2 +--R (- 6a c d - 2b c )f + (12a c d + 12b c d)e f +--R + +--R 3 2 2 3 3 +--R (- 6a d - 18b c d )e f + 8b d e +--R * +--R n - 3 +--R (d x + c) +--R + +--R 3 4 3 2 2 3 2 +--R (a c d - b c )f + (- 3a c d + 3b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (3a c d - 3b c d )e f + (- a d + b c d )e +--R * +--R 3 +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (- 6a c d + 6b c )f + (18a c d - 18b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 18a c d + 18b c d )e f + (6a d - 6b c d )e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (11a c d - 11b c )f + (- 33a c d + 33b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (33a c d - 33b c d )e f + (- 11a d + 11b c d )e +--R * +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (- 6a c d + 6b c )f + (18a c d - 18b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 18a c d + 18b c d )e f + (6a d - 6b c d )e +--R * +--R n - 4 +--R (d x + c) +--R * +--R - n + 1 n log(f x + e) +--R (f x + e) %e +--R + +--R 4 4 5 3 5 4 4 5 3 5 +--R ((- 2b c d f + 2b d e f )n + (6a d + 2b c d )f - 8b d e f )x +--R + +--R 2 3 4 4 3 5 2 2 2 +--R (2b c d f - 4b c d e f + 2b d e f )n +--R + +--R 4 2 3 4 5 4 3 5 2 2 +--R ((- 6a c d - 12b c d )f + (6a d + 20b c d )e f - 8b d e f )n +--R + +--R 4 2 3 4 4 3 +--R (30a c d + 10b c d )f - 40b c d e f +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 3 +--R (- b c d f + 3b c d e f - 3b c d e f + b d e f)n +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (3a c d + 10b c d )f + (- 6a c d - 25b c d )e f +--R + +--R 5 4 2 2 5 3 +--R (3a d + 20b c d )e f - 5b d e f +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 27a c d - 29b c d )f + (30a c d + 66b c d )e f +--R + +--R 5 4 2 2 5 3 +--R (- 3a d - 41b c d )e f + 4b d e f +--R * +--R n +--R + +--R 2 3 3 2 4 2 3 3 +--R (60a c d + 20b c d )f - 80b c d e f +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 4 2 2 +--R (- a c d - b c d)f + (3a c d + 2b c d )e f - 3a c d e f +--R + +--R 5 4 3 5 4 +--R (a d - 2b c d )e f + b d e +--R * +--R 3 +--R n +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12a c d + 8b c d)f + (- 27a c d - 14b c d )e f +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (18a c d - 3b c d )e f + (- 3a d + 16b c d )e f - 7b d e +--R * +--R 2 +--R n +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 47a c d - 19b c d)f + (60a c d + 36b c d )e f +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 15a c d + 15b c d )e f + (2a d - 46b c d )e f + 14b d e +--R * +--R n +--R + +--R 3 2 4 4 3 2 3 2 3 2 2 +--R (60a c d + 12b c d)f - 48b c d e f - 48b c d e f +--R + +--R 4 3 5 4 +--R 32b c d e f - 8b d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 2 4 3 3 2 2 2 +--R - a c d f + (2a c d - b c d)e f + 3b c d e f +--R + +--R 4 2 3 3 5 4 4 +--R (- 2a c d - 3b c d )e f + (a d + b c d )e +--R * +--R 3 +--R n +--R + +--R 4 4 3 2 4 3 +--R 9a c d f + (- 12a c d + 7b c d)e f +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 9a c d - 22b c d )e f + (18a c d + 23b c d )e f +--R + +--R 5 4 4 +--R (- 6a d - 8b c d )e +--R * +--R 2 +--R n +--R + +--R 4 4 3 2 4 3 +--R - 26a c d f + (10a c d - 12b c d)e f +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (45a c d + 55b c d )e f + (- 40a c d - 60b c d )e f +--R + +--R 5 4 4 +--R (11a d + 17b c d )e +--R * +--R n +--R + +--R 4 4 3 2 3 2 3 3 2 2 2 +--R 24a c d f + 24a c d e f + (- 36a c d - 60b c d )e f +--R + +--R 4 2 3 3 5 4 4 +--R (24a c d + 40b c d )e f + (- 6a d - 10b c d )e +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 3 +--R (- a c d e f + 3a c d e f - 3a c d e f + a c d e )n +--R + +--R 4 3 3 2 4 2 2 2 3 3 2 3 +--R 9a c d e f + (- 24a c d - b c d)e f + (21a c d + 2b c d )e f +--R + +--R 4 2 3 4 +--R (- 6a c d - b c d )e +--R * +--R 2 +--R n +--R + +--R 4 3 3 2 4 2 2 +--R - 26a c d e f + (57a c d + 7b c d)e f +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (- 42a c d - 10b c d )e f + (11a c d + 3b c d )e +--R * +--R n +--R + +--R 4 3 3 2 4 2 2 2 3 3 2 3 +--R 24a c d e f + (- 36a c d - 12b c d)e f + (24a c d + 8b c d )e f +--R + +--R 4 2 3 4 +--R (- 6a c d - 2b c d )e +--R * +--R (n - 5)log(d x + c) +--R %e +--R / +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (c d f - 4c d e f + 6c d e f - 4c d e f + d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 10c d f + 40c d e f - 60c d e f + 40c d e f - 10d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (35c d f - 140c d e f + 210c d e f - 140c d e f + 35d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 50c d f + 200c d e f - 300c d e f + 200c d e f - 50d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R 24c d f - 96c d e f + 144c d e f - 96c d e f + 24d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1293 +d0:=D(m0,x) +--R +--R +--R (1149) +--R 3 2 2 2 3 2 2 +--R ((2b c d f - 2b d e f )n + (- 6a d - 2b c d)f + 8b d e f ) +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 3 2 2 3 2 2 +--R (- 2b c d f + 4b c d e f - 2b d e f)n +--R + +--R 2 2 3 3 2 2 +--R (6a c d + 6b c d)f + (- 6a d - 18b c d )e f +--R + +--R 3 2 +--R 12b d e f +--R * +--R n +--R + +--R 2 2 3 3 2 2 3 2 +--R (- 12a c d - 4b c d)f + (12a d + 20b c d )e f - 16b d e f +--R * +--R n - 3 +--R (d x + c) +--R + +--R 3 3 2 2 2 3 2 4 3 3 +--R (b c d f - 3b c d e f + 3b c d e f - b d e )n +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 3a c d - 6b c d)f + (6a c d + 21b c d )e f +--R + +--R 4 3 2 4 3 +--R (- 3a d - 24b c d )e f + 9b d e +--R * +--R 2 +--R n +--R + +--R 2 2 3 3 3 2 2 2 +--R (15a c d + 11b c d)f + (- 30a c d - 48b c d )e f +--R + +--R 4 3 2 4 3 +--R (15a d + 63b c d )e f - 26b d e +--R * +--R n +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 18a c d - 6b c d)f + (36a c d + 36b c d )e f +--R + +--R 4 3 2 4 3 +--R (- 18a d - 54b c d )e f + 24b d e +--R * +--R n - 4 +--R (d x + c) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (a c d - b c d)f + (- 3a c d + 3b c d )e f +--R + +--R 4 2 3 2 5 4 3 +--R (3a c d - 3b c d )e f + (- a d + b c d )e +--R * +--R 3 +--R n +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 9a c d + 9b c d)f + (27a c d - 27b c d )e f +--R + +--R 4 2 3 2 5 4 3 +--R (- 27a c d + 27b c d )e f + (9a d - 9b c d )e +--R * +--R 2 +--R n +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (26a c d - 26b c d)f + (- 78a c d + 78b c d )e f +--R + +--R 4 2 3 2 5 4 3 +--R (78a c d - 78b c d )e f + (- 26a d + 26b c d )e +--R * +--R n +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 24a c d + 24b c d)f + (72a c d - 72b c d )e f +--R + +--R 4 2 3 2 5 4 3 +--R (- 72a c d + 72b c d )e f + (24a d - 24b c d )e +--R * +--R n - 5 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R + +--R 4 3 4 3 +--R ((- 2b c f + 2b d e f )n + (6a d + 2b c)f - 8b d e f ) +--R * +--R n - 1 +--R (d x + c) +--R + +--R 2 4 3 2 2 2 2 +--R (2b c f - 4b c d e f + 2b d e f )n +--R + +--R 2 4 2 3 2 2 2 +--R ((- 6a c d - 4b c )f + (6a d + 14b c d)e f - 10b d e f )n +--R + +--R 2 4 2 3 2 2 2 +--R (6a c d + 2b c )f + (- 6a d - 10b c d)e f + 8b d e f +--R * +--R n - 2 +--R (d x + c) +--R + +--R 3 4 2 3 2 2 2 3 3 3 +--R (- b c f + 3b c d e f - 3b c d e f + b d e f)n +--R + +--R 2 3 4 2 2 3 +--R (3a c d + 4b c )f + (- 6a c d - 15b c d)e f +--R + +--R 3 2 2 2 3 3 +--R (3a d + 18b c d )e f - 7b d e f +--R * +--R 2 +--R n +--R + +--R 2 3 4 2 2 3 +--R (- 9a c d - 5b c )f + (18a c d + 24b c d)e f +--R + +--R 3 2 2 2 3 3 +--R (- 9a d - 33b c d )e f + 14b d e f +--R * +--R n +--R + +--R 2 3 4 2 2 3 +--R (6a c d + 2b c )f + (- 12a c d - 12b c d)e f +--R + +--R 3 2 2 2 3 3 +--R (6a d + 18b c d )e f - 8b d e f +--R * +--R n - 3 +--R (d x + c) +--R + +--R 3 4 4 2 2 3 3 +--R (- a c d + b c )f + (3a c d - 3b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 3a c d + 3b c d )e f + (a d - b c d )e f +--R * +--R 3 +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (6a c d - 6b c )f + (- 18a c d + 18b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 +--R (18a c d - 18b c d )e f + (- 6a d + 6b c d )e f +--R * +--R 2 +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (- 11a c d + 11b c )f + (33a c d - 33b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 33a c d + 33b c d )e f + (11a d - 11b c d )e f +--R * +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (6a c d - 6b c )f + (- 18a c d + 18b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 +--R (18a c d - 18b c d )e f + (- 6a d + 6b c d )e f +--R * +--R n - 4 +--R (d x + c) +--R * +--R - n +--R (f x + e) +--R * +--R n log(f x + e) +--R %e +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (b c d f - 4b c d e f + 6b c d e f - 4b c d e f + b d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R - 9b c d f + 36b c d e f - 54b c d e f + 36b c d e f +--R + +--R 5 4 +--R - 9b d e +--R * +--R 2 +--R n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 26b c d f - 104b c d e f + 156b c d e f - 104b c d e f +--R + +--R 5 4 +--R 26b d e +--R * +--R n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R - 24b c d f + 96b c d e f - 144b c d e f + 96b c d e f +--R + +--R 5 4 +--R - 24b d e +--R * +--R x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (a c d f - 4a c d e f + 6a c d e f - 4a c d e f + a d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (- 9a c d f + 36a c d e f - 54a c d e f + 36a c d e f - 9a d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 26a c d f - 104a c d e f + 156a c d e f - 104a c d e f +--R + +--R 5 4 +--R 26a d e +--R * +--R n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R - 24a c d f + 96a c d e f - 144a c d e f + 96a c d e f - 24a d e +--R * +--R (n - 5)log(d x + c) +--R %e +--R / +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (c d f - 4c d e f + 6c d e f - 4c d e f + d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (- 9c d f + 36c d e f - 54c d e f + 36c d e f - 9d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (26c d f - 104c d e f + 156c d e f - 104c d e f + 26d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R - 24c d f + 96c d e f - 144c d e f + 96c d e f - 24d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1293 +t0:=(c+d*x)*(e+f*x)^n/(a+b*x)^n +--R +--R +--R n +--R (d x + c)(f x + e) +--R (1150) ------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 1293 +--r0:=1/2*d*(a+b*x)^(1-n)*(e+f*x)^(1+n)/(b*f)+1/2*(b*(2*c*f-d*e*(1-n))-_ +--a*d*f*(1+n))*(-f*(a+b*x)/(b*e-a*f))^n*(e+f*x)^(1+n)*_ +--hypergeometric(n,1+n,2+n,b*(e+f*x)/(b*e-a*f))/(b*f^2*(1+n)*(a+b*x)^n) +--E 1265 + +--S 1266 of 1293 +--a0:=integrate(t0,x) +--E 1266 + +--S 1267 of 1293 +--m0:=a0-r0 +--E 1267 + +--S 1268 of 1293 +--d0:=D(m0,x) +--E 1268 + +--S 1269 of 1293 +t0:=(c+d*x)*(e+f*x)^(-1+n)/(a+b*x)^n +--R +--R +--R n - 1 +--R (d x + c)(f x + e) +--R (1151) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1293 +--r0:=(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^n/(f*(b*e-a*f)*n)+(b*(c*f-d*e*(1-n))-_ +--a*d*f*n)*(-f*(a+b*x)/(b*e-a*f))^n*(e+f*x)^(1+n)*_ +--hypergeometric(n,1+n,2+n,b*(e+f*x)/(b*e-a*f))/(f^2*(b*e-a*f)*n*_ +--(1+n)*(a+b*x)^n) +--E 1270 + +--S 1271 of 1293 +--a0:=integrate(t0,x) +--E 1271 + +--S 1272 of 1293 +--m0:=a0-r0 +--E 1272 + +--S 1273 of 1293 +--d0:=D(m0,x) +--E 1273 + +--S 1274 of 1293 +t0:=(c+d*x)*(e+f*x)^(-2+n)/(a+b*x)^n +--R +--R +--R n - 2 +--R (d x + c)(f x + e) +--R (1152) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1293 +--r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/(f*(b*e-a*f)*(1-n))-_ +--d*(a+b*x)^(1-n)*(e+f*x)^n/(f*(b*e-a*f)*n)+b*d*(-f*(a+b*x)/(b*e-a*f))^n*_ +--(e+f*x)^(1+n)*hypergeometric(n,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +--(f^2*(b*e-a*f)*n*(1+n)*(a+b*x)^n) +--E 1275 + +--S 1276 of 1293 +--a0:=integrate(t0,x) +--E 1276 + +--S 1277 of 1293 +--m0:=a0-r0 +--E 1277 + +--S 1278 of 1293 +--d0:=D(m0,x) +--E 1278 + +--S 1279 of 1293 +t0:=(c+d*x)*(e+f*x)^(-3+n)/(a+b*x)^n +--R +--R +--R n - 3 +--R (d x + c)(f x + e) +--R (1153) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1293 +r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)*(2-n))-_ + (a*d*f*(2-n)-b*(c*f+d*(e-e*n)))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/_ + (f*(b*e-a*f)^2*(1-n)*(2-n)) +--R +--R +--R (1154) +--R - n + 1 +--R ((a d f - b d e)n + (- 2a d + b c)f + b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 +--R (a c f + (- a d - b c)e f + b d e )n - a c f + (a d + b c)e f +--R + +--R 2 +--R - b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R / +--R 2 3 2 2 2 2 2 3 2 2 2 2 3 +--R (a f - 2a b e f + b e f)n + (- 3a f + 6a b e f - 3b e f)n + 2a f +--R + +--R 2 2 2 +--R - 4a b e f + 2b e f +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1155) +--R 2 2 2 2 2 3 +--R ((a b d f - b d e f)n + (- 2a b d + b c)f + b d e f)x +--R + +--R 2 2 2 2 2 2 2 +--R ((a d + a b c)f - b c e f - b d e )n - 2a d f +--R + +--R 2 2 2 +--R (- 2a b d + 3b c)e f + b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 2 2 +--R (a c f + a d e f + (- a b d - b c)e )n - a c f +--R + +--R 2 2 2 +--R (- 3a d + 2a b c)e f + 2b c e +--R * +--R x +--R + +--R 2 2 2 2 2 +--R (a c e f - a b c e )n - a c e f + (- a d + 2a b c)e +--R * +--R (n - 3)log(f x + e) +--R %e +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a f - 2a b e f + b e )n + (- 3a f + 6a b e f - 3b e )n + 2a f +--R + +--R 2 2 +--R - 4a b e f + 2b e +--R * +--R n log(b x + a) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1281 + +--S 1282 of 1293 +m0:=a0-r0 +--R +--R +--R (1156) +--R 3 2 2 2 3 2 2 3 +--R ((a b d f - b d e f )n + (- 2a b d + b c)f + b d e f )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((a d + a b c)f - b c e f - b d e f)n - 2a d f +--R + +--R 2 2 2 2 +--R (- 2a b d + 3b c)e f + b d e f +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 2 3 +--R (a c f + a d e f + (- a b d - b c)e f)n - a c f +--R + +--R 2 2 2 2 +--R (- 3a d + 2a b c)e f + 2b c e f +--R * +--R x +--R + +--R 2 2 2 2 2 2 2 +--R (a c e f - a b c e f)n - a c e f + (- a d + 2a b c)e f +--R * +--R (n - 3)log(f x + e) +--R %e +--R + +--R - n + 1 +--R ((- a d f + b d e)n + (2a d - b c)f - b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 +--R (- a c f + (a d + b c)e f - b d e )n + a c f + (- a d - b c)e f +--R + +--R 2 +--R b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 2 3 2 2 2 2 2 3 2 2 2 2 3 +--R (a f - 2a b e f + b e f)n + (- 3a f + 6a b e f - 3b e f)n + 2a f +--R + +--R 2 2 2 +--R - 4a b e f + 2b e f +--R * +--R n log(b x + a) +--R %e +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1293 +d0:=D(m0,x) +--R +--R +--R (1157) +--R 2 3 2 2 2 2 3 2 +--R (a d f - 2a b d e f + b d e f)n - 2a d f + 4a b d e f +--R + +--R 2 2 +--R - 2b d e f +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (a c f - 2a b c e f + b c e f)n - 2a c f + 4a b c e f - 2b c e f +--R * +--R (n - 3)log(f x + e) +--R %e +--R + +--R 2 2 2 - n +--R ((a b d f - b d e)n + (- 2a b d + b c)f + b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 +--R ((- a d f + b d e f)n + (2a d - b c)f - b d e f) +--R * +--R - n + 1 +--R (b x + a) +--R + +--R 2 2 2 2 2 +--R (a b c f + (- a b d - b c)e f + b d e )n - a b c f +--R + +--R 2 2 2 +--R (a b d + b c)e f - b d e +--R * +--R - n +--R (b x + a) +--R * +--R n - 2 +--R (f x + e) +--R + +--R 3 2 2 3 +--R (- a c f + (a d + b c)e f - b d e f)n + 2a c f +--R + +--R 2 2 +--R (- 2a d - 2b c)e f + 2b d e f +--R * +--R - n + 1 n - 3 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 2 3 2 2 2 2 3 2 2 2 n log(b x + a) +--R ((a f - 2a b e f + b e f)n - 2a f + 4a b e f - 2b e f)%e +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1293 +t0:=(c+d*x)*(e+f*x)^(-4+n)/(a+b*x)^n +--R +--R +--R n - 4 +--R (d x + c)(f x + e) +--R (1158) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1293 +r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-3+n)/(f*(b*e-a*f)*(3-n))+_ + (b*(2*c*f+d*e*(1-n))-a*d*f*(3-n))*(a+b*x)^(1-n)*_ + (e+f*x)^(-2+n)/(f*(b*e-a*f)^2*(2-n)*(3-n))+b*(b*(2*c*f+d*e*(1-n))-_ + a*d*f*(3-n))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/(f*(b*e-a*f)^3*(1-n)*_ + (2-n)*(3-n)) +--R +--R +--R (1159) +--R 2 2 2 - n + 1 +--R ((a b d f - b d e)n + (- 3a b d + 2b c)f + b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 2 2 +--R (a d f - 2a b d e f + b d e )n +--R + +--R 2 2 2 2 2 +--R ((- 4a d + 2a b c)f + (6a b d - 2b c)e f - 2b d e )n +--R + +--R 2 2 2 2 2 +--R (3a d - 2a b c)f + (- 4a b d + 2b c)e f + b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (a c f + (- a d - 2a b c)e f + (2a b d + b c)e f - b d e )n +--R + +--R 2 3 2 2 2 2 2 3 +--R (- 3a c f + (3a d + 6a b c)e f + (- 6a b d - 3b c)e f + 3b d e )n +--R + +--R 2 3 2 2 2 2 2 3 +--R 2a c f + (- 2a d - 4a b c)e f + (4a b d + 2b c)e f - 2b d e +--R * +--R - n + 1 n - 3 +--R (b x + a) (f x + e) +--R / +--R 3 4 2 3 2 2 2 3 3 3 +--R (a f - 3a b e f + 3a b e f - b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (- 6a f + 18a b e f - 18a b e f + 6b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 2 3 +--R (11a f - 33a b e f + 33a b e f - 11b e f)n - 6a f + 18a b e f +--R + +--R 2 2 2 3 3 +--R - 18a b e f + 6b e f +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1160) +--R 2 3 3 2 2 3 3 3 2 4 +--R ((a b d f - b d e f )n + (- 3a b d + 2b c)f + b d e f )x +--R + +--R 2 3 2 2 3 2 2 +--R (a b d f - 2a b d e f + b d e f)n +--R + +--R 2 2 3 2 3 2 3 2 +--R ((- 3a b d + 2a b c)f + (8a b d - 2b c)e f - 5b d e f)n +--R + +--R 2 3 2 3 2 +--R (- 12a b d + 8b c)e f + 4b d e f +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 2 2 2 3 2 +--R (a d + a b c)f + (- a b d - 2a b c)e f + (- a b d + b c)e f +--R + +--R 3 3 +--R b d e +--R * +--R 2 +--R n +--R + +--R 3 2 3 2 2 2 2 3 2 +--R (- 4a d - a b c)f + (4a b d + 8a b c)e f + (4a b d - 7b c)e f +--R + +--R 3 3 +--R - 4b d e +--R * +--R n +--R + +--R 3 3 2 2 2 3 2 3 3 +--R 3a d f - 9a b d e f + (- 9a b d + 12b c)e f + 3b d e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 2 2 +--R a c f + (a d - a b c)e f + (- 2a b d - a b c)e f +--R + +--R 2 3 3 +--R (a b d + b c)e +--R * +--R 2 +--R n +--R + +--R 3 3 3 2 2 2 2 2 +--R - 3a c f + (- 5a d + 7a b c)e f + (8a b d + a b c)e f +--R + +--R 2 3 3 +--R (- 3a b d - 5b c)e +--R * +--R n +--R + +--R 3 3 3 2 2 2 2 2 3 3 +--R 2a c f + (4a d - 6a b c)e f + (- 12a b d + 6a b c)e f + 6b c e +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 +--R (a c e f - 2a b c e f + a b c e )n +--R + +--R 3 2 3 2 2 2 2 3 3 2 +--R (- 3a c e f + (- a d + 8a b c)e f + (a b d - 5a b c)e )n + 2a c e f +--R + +--R 3 2 2 2 2 3 +--R (a d - 6a b c)e f + (- 3a b d + 6a b c)e +--R * +--R (n - 4)log(f x + e) +--R %e +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a f - 3a b e f + 3a b e f - b e )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6a f + 18a b e f - 18a b e f + 6b e )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a f - 33a b e f + 33a b e f - 11b e )n - 6a f + 18a b e f +--R + +--R 2 2 3 3 +--R - 18a b e f + 6b e +--R * +--R n log(b x + a) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1286 + +--S 1287 of 1293 +m0:=a0-r0 +--R +--R +--R (1161) +--R 2 4 3 3 2 3 4 3 3 4 +--R ((a b d f - b d e f )n + (- 3a b d + 2b c)f + b d e f )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (a b d f - 2a b d e f + b d e f )n +--R + +--R 2 2 4 2 3 3 3 2 2 +--R ((- 3a b d + 2a b c)f + (8a b d - 2b c)e f - 5b d e f )n +--R + +--R 2 3 3 3 2 2 +--R (- 12a b d + 8b c)e f + 4b d e f +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 2 3 +--R (a d + a b c)f + (- a b d - 2a b c)e f +--R + +--R 2 3 2 2 3 3 +--R (- a b d + b c)e f + b d e f +--R * +--R 2 +--R n +--R + +--R 3 2 4 2 2 3 +--R (- 4a d - a b c)f + (4a b d + 8a b c)e f +--R + +--R 2 3 2 2 3 3 +--R (4a b d - 7b c)e f - 4b d e f +--R * +--R n +--R + +--R 3 4 2 3 2 3 2 2 3 3 +--R 3a d f - 9a b d e f + (- 9a b d + 12b c)e f + 3b d e f +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 3 2 2 2 2 +--R a c f + (a d - a b c)e f + (- 2a b d - a b c)e f +--R + +--R 2 3 3 +--R (a b d + b c)e f +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R - 3a c f + (- 5a d + 7a b c)e f + (8a b d + a b c)e f +--R + +--R 2 3 3 +--R (- 3a b d - 5b c)e f +--R * +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 3 3 +--R 2a c f + (4a d - 6a b c)e f + (- 12a b d + 6a b c)e f + 6b c e f +--R * +--R x +--R + +--R 3 3 2 2 2 2 3 2 +--R (a c e f - 2a b c e f + a b c e f)n +--R + +--R 3 3 3 2 2 2 2 2 3 +--R (- 3a c e f + (- a d + 8a b c)e f + (a b d - 5a b c)e f)n +--R + +--R 3 3 3 2 2 2 2 2 3 +--R 2a c e f + (a d - 6a b c)e f + (- 3a b d + 6a b c)e f +--R * +--R (n - 4)log(f x + e) +--R %e +--R + +--R 2 2 2 - n + 1 +--R ((- a b d f + b d e)n + (3a b d - 2b c)f - b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 2 2 +--R (- a d f + 2a b d e f - b d e )n +--R + +--R 2 2 2 2 2 +--R ((4a d - 2a b c)f + (- 6a b d + 2b c)e f + 2b d e )n +--R + +--R 2 2 2 2 2 +--R (- 3a d + 2a b c)f + (4a b d - 2b c)e f - b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (- a c f + (a d + 2a b c)e f + (- 2a b d - b c)e f + b d e )n +--R + +--R 2 3 2 2 2 2 2 3 +--R (3a c f + (- 3a d - 6a b c)e f + (6a b d + 3b c)e f - 3b d e )n +--R + +--R 2 3 2 2 2 2 2 3 +--R - 2a c f + (2a d + 4a b c)e f + (- 4a b d - 2b c)e f + 2b d e +--R * +--R - n + 1 n - 3 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 3 4 2 3 2 2 2 3 3 3 +--R (a f - 3a b e f + 3a b e f - b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (- 6a f + 18a b e f - 18a b e f + 6b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 2 3 +--R (11a f - 33a b e f + 33a b e f - 11b e f)n - 6a f + 18a b e f +--R + +--R 2 2 2 3 3 +--R - 18a b e f + 6b e f +--R * +--R n log(b x + a) +--R %e +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1293 +d0:=D(m0,x) +--R +--R +--R (1162) +--R 3 4 2 3 2 2 2 3 3 2 +--R (a d f - 3a b d e f + 3a b d e f - b d e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (- 5a d f + 15a b d e f - 15a b d e f + 5b d e f)n + 6a d f +--R + +--R 2 3 2 2 2 3 3 +--R - 18a b d e f + 18a b d e f - 6b d e f +--R * +--R x +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (a c f - 3a b c e f + 3a b c e f - b c e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (- 5a c f + 15a b c e f - 15a b c e f + 5b c e f)n + 6a c f +--R + +--R 2 3 2 2 2 3 3 +--R - 18a b c e f + 18a b c e f - 6b c e f +--R * +--R (n - 4)log(f x + e) +--R %e +--R + +--R 2 3 2 3 3 - n +--R ((a b d f - b d e)n + (- 3a b d + 2b c)f + b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 2 2 +--R ((- a b d f + b d e f)n + (3a b d - 2b c)f - b d e f) +--R * +--R - n + 1 +--R (b x + a) +--R + +--R 2 2 2 3 2 2 +--R (a b d f - 2a b d e f + b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R ((- 4a b d + 2a b c)f + (6a b d - 2b c)e f - 2b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R (3a b d - 2a b c)f + (- 4a b d + 2b c)e f + b d e +--R * +--R - n +--R (b x + a) +--R * +--R n - 2 +--R (f x + e) +--R + +--R 2 3 2 2 2 2 +--R (- a d f + 2a b d e f - b d e f)n +--R + +--R 2 3 2 2 2 2 +--R ((5a d - 2a b c)f + (- 8a b d + 2b c)e f + 3b d e f)n +--R + +--R 2 3 2 2 2 2 +--R (- 6a d + 4a b c)f + (8a b d - 4b c)e f - 2b d e f +--R * +--R - n + 1 +--R (b x + a) +--R + +--R 2 3 2 2 2 2 3 2 +--R a b c f + (- a b d - 2a b c)e f + (2a b d + b c)e f +--R + +--R 3 3 +--R - b d e +--R * +--R 2 +--R n +--R + +--R 2 3 2 2 2 +--R - 3a b c f + (3a b d + 6a b c)e f +--R + +--R 2 3 2 3 3 +--R (- 6a b d - 3b c)e f + 3b d e +--R * +--R n +--R + +--R 2 3 2 2 2 2 3 2 +--R 2a b c f + (- 2a b d - 4a b c)e f + (4a b d + 2b c)e f +--R + +--R 3 3 +--R - 2b d e +--R * +--R - n +--R (b x + a) +--R * +--R n - 3 +--R (f x + e) +--R + +--R 2 4 2 3 2 2 2 +--R - a c f + (a d + 2a b c)e f + (- 2a b d - b c)e f +--R + +--R 2 3 +--R b d e f +--R * +--R 2 +--R n +--R + +--R 2 4 2 3 2 2 2 +--R 5a c f + (- 5a d - 10a b c)e f + (10a b d + 5b c)e f +--R + +--R 2 3 +--R - 5b d e f +--R * +--R n +--R + +--R 2 4 2 3 2 2 2 +--R - 6a c f + (6a d + 12a b c)e f + (- 12a b d - 6b c)e f +--R + +--R 2 3 +--R 6b d e f +--R * +--R - n + 1 n - 4 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 3 4 2 3 2 2 2 3 3 2 +--R (a f - 3a b e f + 3a b e f - b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 2 3 +--R (- 5a f + 15a b e f - 15a b e f + 5b e f)n + 6a f - 18a b e f +--R + +--R 2 2 2 3 3 +--R 18a b e f - 6b e f +--R * +--R n log(b x + a) +--R %e +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1293 +t0:=(c+d*x)*(e+f*x)^(-5+n)/(a+b*x)^n +--R +--R +--R n - 5 +--R (d x + c)(f x + e) +--R (1163) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1293 +r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-4+n)/(f*(b*e-a*f)*(4-n))+_ + (b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*(a+b*x)^(1-n)*(e+f*x)^(-3+n)/_ + (f*(b*e-a*f)^2*(3-n)*(4-n))+2*b*(b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*_ + (a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)^3*(2-n)*(3-n)*(4-n))+_ + 2*b^2*(b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/_ + (f*(b*e-a*f)^4*(1-n)*(2-n)*(3-n)*(4-n)) +--R +--R +--R (1164) +--R 2 3 2 3 3 - n + 1 +--R ((2a b d f - 2b d e)n + (- 8a b d + 6b c)f + 2b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 3 2 2 +--R (2a b d f - 4a b d e f + 2b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R ((- 10a b d + 6a b c)f + (14a 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(18a b d + 6b c)e f - 6b d e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R 11a c f + (- 11a d - 33a b c)e f + (33a b d + 33a b c)e f +--R + +--R 2 3 3 3 4 +--R (- 33a b d - 11b c)e f + 11b d e +--R * +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R - 6a c f + (6a d + 18a b c)e f + (- 18a b d - 18a b c)e f +--R + +--R 2 3 3 3 4 +--R (18a b d + 6b c)e f - 6b d e +--R * +--R - n + 1 n - 4 +--R (b x + a) (f x + e) +--R / +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 +--R (a f - 4a b e f + 6a b e f - 4a b e f + b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (- 10a f + 40a b e f - 60a b e f + 40a b e f - 10b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (35a f - 140a b e f + 210a b e f - 140a b e f + 35b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 5 +--R (- 50a f + 200a b e f - 300a b e f + 200a b e f - 50b e f)n + 24a f +--R + +--R 3 4 2 2 2 3 3 3 2 4 4 +--R - 96a b e f + 144a b e f - 96a b e f + 24b e f +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (1165) +--R 3 4 4 3 3 4 4 4 3 5 +--R ((2a b d f - 2b d e f )n + (- 8a b d + 6b c)f + 2b d e f )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (2a b d f - 4a b d e f + 2b d e f )n +--R + +--R 2 2 3 4 3 4 3 4 2 2 +--R ((- 8a b d + 6a b c)f + (20a b d - 6b c)e f - 12b d e f )n +--R + +--R 3 4 3 4 2 2 +--R (- 40a b d + 30b c)e f + 10b d e f +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (a b d f - 3a b d e f + 3a b d e f - b d e f)n +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 5a b d + 3a b c)f + (20a b d - 6a b c)e f +--R + +--R 3 4 2 2 4 3 +--R (- 25a b d + 3b c)e f + 10b d e f +--R * +--R 2 +--R n +--R + +--R 3 2 2 4 2 2 3 3 +--R (4a b d - 3a b c)f + (- 41a b d + 30a b c)e f +--R + +--R 3 4 2 2 4 3 +--R (66a b d - 27b c)e f - 29b d e f +--R * +--R n +--R + +--R 3 4 2 2 4 3 +--R (- 80a b d + 60b c)e f + 20b d e f +--R * +--R 3 +--R x +--R + +--R 4 3 4 3 2 2 3 3 2 2 +--R (a d + a b c)f + (- 2a b d - 3a b c)e f + 3a b c e f +--R + +--R 3 4 3 4 4 +--R (2a b d - b c)e f - b d e +--R * +--R 3 +--R n +--R + +--R 4 3 4 3 2 2 3 +--R (- 7a d - 3a b c)f + (16a b d + 18a b c)e f +--R + +--R 2 2 3 2 2 3 4 3 4 4 +--R (- 3a b d - 27a b c)e f + (- 14a b d + 12b c)e f + 8b d e +--R * +--R 2 +--R n +--R + +--R 4 3 4 3 2 2 3 +--R (14a d + 2a b c)f + (- 46a b d - 15a b c)e f +--R + +--R 2 2 3 2 2 3 4 3 4 4 +--R (15a b d + 60a b c)e f + (36a b d - 47b c)e f - 19b d e +--R * +--R n +--R + +--R 4 4 3 3 2 2 2 2 3 4 3 +--R - 8a d f + 32a b d e f - 48a b d e f + (- 48a b d + 60b c)e f +--R + +--R 4 4 +--R 12b d e +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 3 2 2 +--R a c f + (a d - 2a b c)e f - 3a b d e f +--R + +--R 2 2 3 3 3 4 4 +--R (3a b d + 2a b c)e f + (- a b d - b c)e +--R * +--R 3 +--R n +--R + +--R 4 4 4 3 3 3 2 2 2 2 +--R - 6a c f + (- 8a d + 18a b c)e f + (23a b d - 9a b c)e f +--R + +--R 2 2 3 3 3 4 4 +--R (- 22a b d - 12a b c)e f + (7a b d + 9b c)e +--R * +--R 2 +--R n +--R + +--R 4 4 4 3 3 3 2 2 2 2 +--R 11a c f + (17a d - 40a b c)e f + (- 60a b d + 45a b c)e f +--R + +--R 2 2 3 3 3 4 4 +--R (55a b d + 10a b c)e f + (- 12a b d - 26b c)e +--R * +--R n +--R + +--R 4 4 4 3 3 3 2 2 2 2 +--R - 6a c f + (- 10a d + 24a b c)e f + (40a b d - 36a b c)e f +--R + +--R 2 2 3 3 4 4 +--R (- 60a b d + 24a b c)e f + 24b c e +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (a c e f - 3a b c e f + 3a b c e f - a b c e )n +--R + +--R 4 3 4 3 2 2 3 2 2 3 +--R - 6a c e f + (- a d + 21a b c)e f + (2a b d - 24a b c)e f +--R + +--R 2 2 3 4 +--R (- a b d + 9a b c)e +--R * +--R 2 +--R n +--R + +--R 4 3 4 3 2 2 3 2 2 3 +--R 11a c e f + (3a d - 42a b c)e f + (- 10a b d + 57a b c)e f +--R + +--R 2 2 3 4 +--R (7a b d - 26a b c)e +--R * +--R n +--R + +--R 4 3 4 3 2 2 3 2 2 3 +--R - 6a c e f + (- 2a d + 24a b c)e f + (8a b d - 36a b c)e f +--R + +--R 2 2 3 4 +--R (- 12a b d + 24a b c)e +--R * +--R (n - 5)log(f x + e) +--R %e +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a f - 4a b e f + 6a b e f - 4a b e f + b e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (- 10a f + 40a b e f - 60a b e f + 40a b e f - 10b e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35a f - 140a b e f + 210a b e f - 140a b e f + 35b e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (- 50a f + 200a b e f - 300a b e f + 200a b e f - 50b e )n + 24a f +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b e f + 144a b e f - 96a b e f + 24b e +--R * +--R n log(b x + a) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1291 + +--S 1292 of 1293 +m0:=a0-r0 +--R +--R +--R (1166) +--R 3 5 4 4 3 4 5 4 4 5 +--R ((2a b d f - 2b d e f )n + (- 8a b d + 6b c)f + 2b d e f )x +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (2a b d f - 4a b d e f + 2b d e f )n +--R + +--R 2 2 3 5 3 4 4 4 2 3 +--R ((- 8a b d + 6a b c)f + (20a b d - 6b c)e f - 12b d e f )n +--R + +--R 3 4 4 4 2 3 +--R (- 40a b d + 30b c)e f + 10b d e f +--R * +--R 4 +--R x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (a b d f - 3a b d e f + 3a b d e f - b d e f )n +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 5a b d + 3a b c)f + (20a b d - 6a b c)e f +--R + +--R 3 4 2 3 4 3 2 +--R (- 25a b d + 3b c)e f + 10b d e f +--R * +--R 2 +--R n +--R + +--R 3 2 2 5 2 2 3 4 +--R (4a b d - 3a b c)f + (- 41a b d + 30a b c)e f +--R + +--R 3 4 2 3 4 3 2 +--R (66a b d - 27b c)e f - 29b d e f +--R * +--R n +--R + +--R 3 4 2 3 4 3 2 +--R (- 80a b d + 60b c)e f + 20b d e f +--R * +--R 3 +--R x +--R + +--R 4 3 5 3 2 2 4 3 2 3 +--R (a d + a b c)f + (- 2a b d - 3a b c)e f + 3a b c e f +--R + +--R 3 4 3 2 4 4 +--R (2a b d - b c)e f - b d e f +--R * +--R 3 +--R n +--R + +--R 4 3 5 3 2 2 4 +--R (- 7a d - 3a b c)f + (16a b d + 18a b c)e f +--R + +--R 2 2 3 2 3 3 4 3 2 4 4 +--R (- 3a b d - 27a b c)e f + (- 14a b d + 12b c)e f + 8b d e f +--R * +--R 2 +--R n +--R + +--R 4 3 5 3 2 2 4 +--R (14a d + 2a b c)f + (- 46a b d - 15a b c)e f +--R + +--R 2 2 3 2 3 3 4 3 2 4 4 +--R (15a b d + 60a b c)e f + (36a b d - 47b c)e f - 19b d e f +--R * +--R n +--R + +--R 4 5 3 4 2 2 2 3 3 4 3 2 +--R - 8a d f + 32a b d e f - 48a b d e f + (- 48a b d + 60b c)e f +--R + +--R 4 4 +--R 12b d e f +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 4 3 2 3 +--R a c f + (a d - 2a b c)e f - 3a b d e f +--R + +--R 2 2 3 3 2 3 4 4 +--R (3a b d + 2a b c)e f + (- a b d - b c)e f +--R * +--R 3 +--R n +--R + +--R 4 5 4 3 4 3 2 2 2 3 +--R - 6a c f + (- 8a d + 18a b c)e f + (23a b d - 9a b c)e f +--R + +--R 2 2 3 3 2 3 4 4 +--R (- 22a b d - 12a b c)e f + (7a b d + 9b c)e f +--R * +--R 2 +--R n +--R + +--R 4 5 4 3 4 3 2 2 2 3 +--R 11a c f + (17a d - 40a b c)e f + (- 60a b d + 45a b c)e f +--R + +--R 2 2 3 3 2 3 4 4 +--R (55a b d + 10a b c)e f + (- 12a b d - 26b c)e f +--R * +--R n +--R + +--R 4 5 4 3 4 3 2 2 2 3 +--R - 6a c f + (- 10a d + 24a b c)e f + (40a b d - 36a b c)e f +--R + +--R 2 2 3 3 2 4 4 +--R (- 60a b d + 24a b c)e f + 24b c e f +--R * +--R x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 3 +--R (a c e f - 3a b c e f + 3a b c e f - a b c e f)n +--R + +--R 4 4 4 3 2 3 3 2 2 3 2 +--R - 6a c e f + (- a d + 21a b c)e f + (2a b d - 24a b c)e f +--R + +--R 2 2 3 4 +--R (- a b d + 9a b c)e f +--R * +--R 2 +--R n +--R + +--R 4 4 4 3 2 3 3 2 2 3 2 +--R 11a c e f + (3a d - 42a b c)e f + (- 10a b d + 57a b c)e f +--R + +--R 2 2 3 4 +--R (7a b d - 26a b c)e f +--R * +--R n +--R + +--R 4 4 4 3 2 3 3 2 2 3 2 +--R - 6a c e f + (- 2a d + 24a b c)e f + (8a b d - 36a b c)e f +--R + +--R 2 2 3 4 +--R (- 12a b d + 24a b c)e f +--R * +--R (n - 5)log(f x + e) +--R %e +--R + +--R 2 3 2 3 3 +--R ((- 2a b d f + 2b d e)n + (8a b d - 6b c)f - 2b d e) +--R * +--R - n + 1 n - 1 +--R (b x + a) (f x + e) +--R + +--R 2 2 2 3 2 2 +--R (- 2a b d f + 4a b d e f - 2b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R ((10a b d - 6a b c)f + (- 14a b d + 6b c)e f + 4b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R (- 8a b d + 6a b c)f + (10a b d - 6b c)e f - 2b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a d f + 3a b d e f - 3a b d e f + b d e )n +--R + +--R 3 2 3 2 2 2 +--R (7a d - 3a b c)f + (- 18a b d + 6a b c)e f +--R + +--R 2 3 2 3 3 +--R (15a b d - 3b c)e f - 4b d e +--R * +--R 2 +--R n +--R + +--R 3 2 3 2 2 2 +--R (- 14a d + 9a b c)f + (33a b d - 18a b c)e f +--R + +--R 2 3 2 3 3 +--R (- 24a b d + 9b c)e f + 5b d e +--R * +--R n +--R + +--R 3 2 3 2 2 2 +--R (8a d - 6a b c)f + (- 18a b d + 12a b c)e f +--R + +--R 2 3 2 3 3 +--R (12a b d - 6b c)e f - 2b d e +--R * +--R - n + 1 n - 3 +--R (b x + a) (f x + e) +--R + +--R 3 4 3 2 3 2 2 2 2 +--R - a c f + (a d + 3a b c)e f + (- 3a b d - 3a b c)e f +--R + +--R 2 3 3 3 4 +--R (3a b d + b c)e f - b d e +--R * +--R 3 +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R 6a c f + (- 6a d - 18a b c)e f + (18a b d + 18a b c)e f +--R + +--R 2 3 3 3 4 +--R (- 18a b d - 6b c)e f + 6b d e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 3 +--R - 11a c f + (11a d + 33a b c)e f +--R + +--R 2 2 2 2 2 3 3 3 4 +--R (- 33a b d - 33a b c)e f + (33a b d + 11b c)e f - 11b d e +--R * +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R 6a c f + (- 6a d - 18a b c)e f + (18a b d + 18a b c)e f +--R + +--R 2 3 3 3 4 +--R (- 18a b d - 6b c)e f + 6b d e +--R * +--R - n + 1 n - 4 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 +--R (a f - 4a b e f + 6a b e f - 4a b e f + b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (- 10a f + 40a b e f - 60a b e f + 40a b e f - 10b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (35a f - 140a b e f + 210a b e f - 140a b e f + 35b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (- 50a f + 200a b e f - 300a b e f + 200a b e f - 50b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R 24a f - 96a b e f + 144a b e f - 96a b e f + 24b e f +--R * +--R n log(b x + a) +--R %e +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1293 +d0:=D(m0,x) +--R +--R +--R (1167) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (a d f - 4a b d e f + 6a b d e f - 4a b d e f + b d e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 +--R - 9a d f + 36a b d e f - 54a b d e f + 36a b d e f +--R + +--R 4 4 +--R - 9b d e f +--R * +--R 2 +--R n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 +--R 26a d f - 104a b d e f + 156a b d e f - 104a b d e f +--R + +--R 4 4 +--R 26b d e f +--R * +--R n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 +--R - 24a d f + 96a b d e f - 144a b d e f + 96a b d e f +--R + +--R 4 4 +--R - 24b d e f +--R * +--R x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (a c f - 4a b c e f + 6a b c e f - 4a b c e f + b c e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 9a c f + 36a b c e f - 54a b c e f + 36a b c e f - 9b c e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 +--R 26a c f - 104a b c e f + 156a b c e f - 104a b c e f +--R + +--R 4 4 +--R 26b c e f +--R * +--R n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R - 24a c f + 96a b c e f - 144a b c e f + 96a b c e f - 24b c e f +--R * +--R (n - 5)log(f x + e) +--R %e +--R + +--R 3 4 3 4 4 - n +--R ((2a b d f - 2b d e)n + (- 8a b d + 6b c)f + 2b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 3 2 3 2 3 +--R ((- 2a b d f + 2b d e f)n + (8a b d - 6b c)f - 2b d e f) +--R * +--R - n + 1 +--R (b x + a) +--R + +--R 2 2 2 3 4 2 2 +--R (2a b d f - 4a b d e f + 2b d e )n +--R + +--R 2 2 3 2 3 4 4 2 +--R ((- 10a b d + 6a b c)f + (14a b d - 6b c)e f - 4b d e )n +--R + +--R 2 2 3 2 3 4 4 2 +--R (8a b d - 6a b c)f + (- 10a b d + 6b c)e f + 2b d e +--R * +--R - n +--R (b x + a) +--R * +--R n - 2 +--R (f x + e) +--R + +--R 2 3 2 2 3 2 2 +--R (- 2a b d f + 4a b d e f - 2b d e f)n +--R + +--R 2 2 3 2 3 2 3 2 +--R ((12a b d - 6a b c)f + (- 18a b d + 6b c)e f + 6b d e f)n +--R + +--R 2 2 3 2 3 2 3 2 +--R (- 16a b d + 12a b c)f + (20a b d - 12b c)e f - 4b d e f +--R * +--R - n + 1 +--R (b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 3 +--R (a b d f - 3a b d e f + 3a b d e f - b d e )n +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 7a b d + 3a b c)f + (18a b d - 6a b c)e f +--R + +--R 3 4 2 4 3 +--R (- 15a b d + 3b c)e f + 4b d e +--R * +--R 2 +--R n +--R + +--R 3 2 2 3 2 2 3 2 +--R (14a b d - 9a b c)f + (- 33a b d + 18a b c)e f +--R + +--R 3 4 2 4 3 +--R (24a b d - 9b c)e f - 5b d e +--R * +--R n +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 8a b d + 6a b c)f + (18a b d - 12a b c)e f +--R + +--R 3 4 2 4 3 +--R (- 12a b d + 6b c)e f + 2b d e +--R * +--R - n +--R (b x + a) +--R * +--R n - 3 +--R (f x + e) +--R + +--R 3 4 2 3 2 2 2 3 3 3 +--R (- a d f + 3a b d e f - 3a b d e f + b d e f)n +--R + +--R 3 2 4 2 2 3 +--R (9a d - 3a b c)f + (- 24a b d + 6a b c)e f +--R + +--R 2 3 2 2 3 3 +--R (21a b d - 3b c)e f - 6b d e f +--R * +--R 2 +--R n +--R + +--R 3 2 4 2 2 3 +--R (- 26a d + 15a b c)f + (63a b d - 30a b c)e f +--R + +--R 2 3 2 2 3 3 +--R (- 48a b d + 15b c)e f + 11b d e f +--R * +--R n +--R + +--R 3 2 4 2 2 3 +--R (24a d - 18a b c)f + (- 54a b d + 36a b c)e f +--R + +--R 2 3 2 2 3 3 +--R (36a b d - 18b c)e f - 6b d e f +--R * +--R - n + 1 +--R (b x + a) +--R + +--R 3 4 3 2 2 3 2 2 3 2 2 +--R a b c f + (- a b d - 3a b c)e f + (3a b d + 3a b c)e f +--R + +--R 3 4 3 4 4 +--R (- 3a b d - b c)e f + b d e +--R * +--R 3 +--R n +--R + +--R 3 4 3 2 2 3 +--R - 6a b c f + (6a b d + 18a b c)e f +--R + +--R 2 2 3 2 2 3 4 3 4 4 +--R (- 18a b d - 18a b c)e f + (18a b d + 6b c)e f - 6b d e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 2 3 +--R 11a b c f + (- 11a b d - 33a b c)e f +--R + +--R 2 2 3 2 2 3 4 3 4 4 +--R (33a b d + 33a b c)e f + (- 33a b d - 11b c)e f + 11b d e +--R * +--R n +--R + +--R 3 4 3 2 2 3 +--R - 6a b c f + (6a b d + 18a b c)e f +--R + +--R 2 2 3 2 2 3 4 3 4 4 +--R (- 18a b d - 18a b c)e f + (18a b d + 6b c)e f - 6b d e +--R * +--R - n +--R (b x + a) +--R * +--R n - 4 +--R (f x + e) +--R + +--R 3 5 3 2 4 2 2 2 3 +--R - a c f + (a d + 3a b c)e f + (- 3a b d - 3a b c)e f +--R + +--R 2 3 3 2 3 4 +--R (3a b d + b c)e f - b d e f +--R * +--R 3 +--R n +--R + +--R 3 5 3 2 4 2 2 2 3 +--R 9a c f + (- 9a d - 27a b c)e f + (27a b d + 27a b c)e f +--R + +--R 2 3 3 2 3 4 +--R (- 27a b d - 9b c)e f + 9b d e f +--R * +--R 2 +--R n +--R + +--R 3 5 3 2 4 +--R - 26a c f + (26a d + 78a b c)e f +--R + +--R 2 2 2 3 2 3 3 2 3 4 +--R (- 78a b d - 78a b c)e f + (78a b d + 26b c)e f - 26b d e f +--R * +--R n +--R + +--R 3 5 3 2 4 2 2 2 3 +--R 24a c f + (- 24a d - 72a b c)e f + (72a b d + 72a b c)e f +--R + +--R 2 3 3 2 3 4 +--R (- 72a b d - 24b c)e f + 24b d e f +--R * +--R - n + 1 n - 5 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (a f - 4a b e f + 6a b e f - 4a b e f + b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 9a f + 36a b e f - 54a b e f + 36a b e f - 9b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 5 +--R (26a f - 104a b e f + 156a b e f - 104a b e f + 26b e f)n - 24a f +--R + +--R 3 4 2 2 2 3 3 3 2 4 4 +--R 96a b e f - 144a b e f + 96a b e f - 24b e f +--R * +--R n log(b x + a) +--R %e +--R Type: Expression(Integer) +--E 1293 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document}